sfde: shuffled frog-leaping differential evolution and its...

Research ArticleSFDE Shuffled Frog-Leaping Differential Evolution andIts Application on Cognitive Radio Throughput

Hongbo Wang 12 Xiaoxiao Zhen1 and Xuyan Tu1

1School of Computer and Communication Engineering University of Science and Technology Beijing Beijing 100083 China2Beijing Key Lab of Knowledge Engineering for Materials Science No 30 Xueyuan Road Haidian Zone Beijing 100083 China

Correspondence should be addressed to Hongbo Wang foreverwhb126com

Received 2 July 2018 Revised 11 January 2019 Accepted 10 February 2019 Published 4 March 2019

Guest Editor Charles Yaacoub

Copyright copy 2019 Hongbo Wang et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Differential Evolution (abbreviation for DE) is showing many advantages in solving optimization problems such as fastconvergence strong robustness and so on However when DE faces a complex target space the diversity of its population willdegenerate in a small scope even sometimes it is premature to fall into the local minimum All things contend in beauty in theworld a Shuffled Frog Leaping Algorithm (abbreviation for SFLA) has a strong global ability unfortunately its convergence speedis also slow In order to overcome the shortcoming this article suggests a Shuffled Frog-leapingDifferential Evolution (abbreviationfor SFDE) algorithm in a cognitive radio network which combines Differential Evolution with Shuffled Frog Leaping AlgorithmThis proposed method hikes its local searching for a certain number of subgroups and their individuals join together and sharetheir mutual information among different subgroups which improves the population diversity and achieves the purpose of fastglobal search during the whole Differential Evolution The SFDE is examined by 20 well-known numerical benchmark functionsand those obtained results are compared with four other related algorithms The experimental simulation in solving the problemof effective throughput optimization for cognitive users shows that the proposed SFDE is effective

1 Introduction

The convergence of the basic Differential Evolution (abbrevi-ation forDE) is closely related to its control parametersManyresearchers have worked on improving its performance invariousways and developedmany variants In [1] amethod ofSelf-adaptive Differential Evolution algorithm with discretemutation control parameters (DMPSADE) is proposed InDMPSADE each vector has its own mutation cross param-eters and control strategies Those original unified controlparameters and mutation strategies are divided into eachindividual so that the evolutionary granularity becomessmaller and the performance improves In [2] a fuzzy systemis introduced to dynamically adaptive control parameters toimprove DE An improved DE named ADE is proposed in[3] where the author suggests DE with two-level parameteradaptation The first level of control parameters FP and CRP isused to control the global optimization ability and the secondlevel of control parameters Fi and CRi corresponds with eachindividual to improve the local search of the algorithm The

main characteristic of DE is its mutation strategy Price andStorn proposed more than ten different differential strategiesto implement mutation operation such as DErand1binDErand2bin DEbest1bin DErand-to-bestbin and soon Among them DErand1bin and DEbest2bin are themost widely used and most successful differential strategiesThe former can maintain the diversity of the population andthe latter pays more attention to the speed of its convergence

Reference [4] introduces a fitness Euclidean-distanceratio for multimodal optimization In [5] a novel mutationstrategy named eliterand1 which divides a whole popu-lation into two subpopulations on the basis of the fitnessand then extracts the maximum information from an eliteindividual MDE in [6] includes three new steps Opposition-Based Learning (OBL) tournament method for mutationand a single population structure A parameter adaptiveselection can dynamically evaluate their performance duringevolution and guide the direction of its development in thenext iteration process [7] Based on the abstract convextheory a dynamic adaptive differential evolution algorithm

HindawiWireless Communications and Mobile ComputingVolume 2019 Article ID 2965061 18 pageshttpsdoiorg10115520192965061

2 Wireless Communications and Mobile Computing

(DADE) is proposed in [8] Shuffled Frog Leaping Algorithm(SFLA) is proposed in [9] which is inspired by the individualslearning from each other during the foraging behaviour offrogs In [10] a multiphase hybrid algorithm implements alocal depth search using SFLA for every cluster and readjustsits global solutions An improved hybrid bifurcation algo-rithmbased on cloudmodel is proposed in [11] which focuseson the transformation between qualitative and quantitativecomputing Reference [12] proposed crossing and variationfrog leaping algorithm (KSFLA) where the individuals of thesubpopulations vary from the ranking list before producingnew individuals instead of the poor ones Reference [13] pro-posed a Self-adaptive Differential Evolution algorithm withImproved Mutation Mode (IMMSADE) which improves themutation model of DE and introduces some new controlparameters

Based on the above discussion SFLA has slow the con-vergence low efficiency and precision in the high dimensioncontinuous optimization problems in that its core strategy isto continuously update the location of the worst individualBut DE does not do anything with the worst individualA hybrid algorithm based on frog leaping algorithm andDifferential Evolution is suggested in this article whichcombines the advantages of SFLA and DE in order to obtaina significant performance on convergence speed and theaccuracy

The rest of this paper is organized as follows In order toensure the readability the related mathematics description ofDifferential Evolution and Shuffled Frog Leaping Algorithmis summarized in Section 2 Section 3 formally definesmodelsof an improvement in a Shuffled Frog-leaping Differen-tial Evolutionary algorithm (SFDE) Section 4 designs thecomparative experiments of well-known public benchmarkfunctions and analyses the related T-test and F-test resultsfor proof of the effective SFDE The analysis of convergencein SFDE is described in detail in Section 4 Simulation exper-iments on the problem of effective throughput optimizationfor cognitive users are given in Section 5 Section 6 concludesthis article with a summary and future direction

2 The Related Work

21 About Differential Evolution DE is a random searchbased on population and also a heuristic swarm intelligencealgorithm It mainly uses mutation crossover and selectionoperations to perform an intelligent evolutionary search DEhas five operations which are described as follows

(1) Initialization Operation Initializing a population ran-domly in the search space the j-th parameter of the i-thindividual in the 0-th generation is initialized by formula (1)

119909119895119894 (0) = 119909119871119900119908119895119894 + 119903119886119899119889 (0 1) sdot (119909119880119901119895119894 minus 119909119871119900119908119895119894 ) (1)

In formula (1) xUp and xLow are the upper and lower boundaryof the j-th parameter of the i-th individual respectively119903119886119899119889(0 1) denotes a random number which is limitedbetween 0 to 1

(2) Mutation Operation In DE the most common in muta-tion operations isDErand1 which selects two individuals atrandom in a population Then the vectors are combined withthe target vector for mutating into an intermediate vectorV119894(119892) The process can be expressed as follows in formula (2)

V119894 (119892) = 1199091199031 (119892) + 119865 sdot (1199091199032 (119892) minus 1199091199033 (119892)) (2)

Obviously the smaller the difference between 1199091199032(119892) and1199091199033(119892) is the smaller the difference between 1199091199031(119892) and V119894(119892)is This means that in the initial stage the disturbancesare large because of the far distance between individualsand the search range of the algorithm is large But in thelater period of the iteration the detective range will be ashrink Several commonmutation strategies are shown in thefollowing formulas (3) (4) and (5)

A DErand2

V119894 (119892) = 1199091199031 (119892) + 119865 (1199091199032 (119892) minus 1199091199033 (119892))+ 119865 (1199091199034 (119892) minus 1199091199035 (119892)) (3)

B DEcurrent-to-best1

V119894 (119892) = 119909119894 (119892) + 119865 (119909119887119890119904119905 (119892) minus 119909119894 (119892))+ 119865 (1199091199031 (119892) minus 1199091199032 (119892)) (4)

C DEbest1

V119894 (119892) = 119909119887119890119904119905 (119892) + 119865 (1199091199032 (119892) minus 1199091199033 (119892)) (5)

Among them the subscript variables 1199031 1199032 1199033 1199034 and 1199035represent different individuals and 119909119887119890119904119905(119892) represents theoptimal vector in the 119892-th generation(3) Correcting Operation After the mutation operation thealgorithm must ensure that each component (gene) of theintermediate vector satisfies the predefined boundary con-straints If a component (gene) of an intermediate vectorexceeds the scope the vector individual must be correctedThe following formula (6) is a simple but most frequentlyused correction strategy

V119894 (119892)=

min 119909119880119901119895119894 2119909119871119900119908119895119894 minus V119894 (119892) 119894119891 V119894 (119892) lt 119909119871119900119908119895119894max 119909119871119900119908119895119894 2119909119880119901119895119894 minus V119894 (119892) 119894119891 V119894 (119892) gt 119909119880119901119895119894

(6)

(4) Crossover Crossover is tomixture the 119909119895119894(119892) and V119895119894(119892) inthe 119892-th generation producing test vectors The process canbe expressed as follows in formula (7)

119906119895119894 (119892)=

V119895119894 (119892) 119894119891 119903119886119899119889 (0 1) le 119862119877 119900119903 119895 = 119895119903119886119899119889119909119895119894 (119892) 119900119905ℎ119890119903119908119894119904119890(7)

Wireless Communications and Mobile Computing 3

In formula (7) CR is the cross probability and 119895119903119886119899119889 is arandom integer of [1 2 D](5) Selecting Operation By comparing the function values ofthe target vectors in the test function 119891(119909119894(119892)) with the testfunction values of the corresponding test vectors 119891(119906119894(119892))which is determined whether the test vectors can be putinto the next generation or not the standard DifferentialEvolution algorithm employs a greedy algorithm for theselection operation The process can be expressed as followsin formula (8)

119909119894 (119892 + 1) = 119906119894 (119892) 119894119891 119891 (119906119894 (119892)) le 119891 (119909119894 (119892))119909119894 (119892) 119900119905ℎ119890119903119908119894119904119890 (8)

22 Shuffled Frog Leaping Algorithm Suppose that there are119873 frogs in the n-dimensional space catching their foodThe basic Shuffled Frog Leaping Algorithm sorts all theindividuals in descending order according to the fitness ofthe objective function and then puts the first frog individualinto the first group the second frog individual into thesecond group and so forth The first 119898 frogs entry owngroup in order respectively thus each group contains a frogBeginningwith the119898+1119904119905 frog the remaining frogs join theirown group according to the rule of Round Robin (namelyMod m)

In each group 119883119894 = (1199091198941 1199091198942 119909119894119899) represents thecurrent position of the 119894 minus 119905ℎ frog 119901119887119890119904119905119894 = min(11990111988711989011990411990511989411199011198871198901199041199051198942 119901119887119890119904119905119894119900) is the optimal location in the 119894 minus119905ℎ group called the local optimal position 119901119908119900119903119904119905119894 =max(1199011199081199001199031199041199051198941 1199011199081199001199031199041199051198942 119901119908119900119903119904119905119894119872) is the worst in the119894 minus 119905ℎ group called the local worst position

Let 119891(119883) be a minimal objective function and useformula (9) to calculate the local optimal frog location for the119894 minus 119905ℎ group119901119887119890119904119905119894 (t + 1)=

119901119887119890119904119905119894 (119905) 119894119891 119891 (119883119894 (119905 + 1)) ge 119891 (119901119887119890119904119905119894 (119905))119883119894 (119905 + 1) 119894119891 119891 (119883119894 (119905 + 1)) lt 119891 (119901119887119890119904119905119894 (119905))(9)

Assume that the number of the frogs is 119873 and it is dividedinto 119898 groups according to the grouping operator Theoptimal position 119892119887119890119904119905(119905) for each group is the global optimallocation as shown in formula (10)

119892119887119890119904119905 (119905) = min 119891 (1199011198871198901199041199051 (119905)) 119891 (1199011198871198901199041199052 (119905)) 119891 (119901119887119890119904119905119898 (119905)) (10)

According to the local location update operator adjustingthe position of the worst frog in each group the concreteadjustment method is as follows

The frog moving distance is as shown in formula (11)

119901119898119900V119890119894 = 119903119886119899119889 lowast (119901119887119890119904119905119894 minus 119901119908119900119903119904119905119894) (11)

Update the worst frog individuals as follows

119901119908119900119903119904119905119894= 119901119908119900119903119904119905119894+ 119901119898119900V119890119894 (minus119901119898119900V119890119898119886119909 ≪ 119901119898119900V119890119894 ≪ 119901119898119900V119890119898119886119909)

(12)

In formula (11) 119903119886119899119889 is a random number between 0 and 1119901119898119900V119890119898119886119909 in formula (12) represents the maximum distancethat the frog can move during its foraging for food If thepositions obtained from formulas (11) and (12) are closer tothe food source than the position of the worst frog in thegroup the worst frog leaps to this new position The positionof the worst frog 119901119908119900119903119904119905119894 is further closer to the food sourceOtherwise 119901119887119890119904119905119894 is replaced by 119892119887119890119904119905119894 and the worst frogcontinues to search for a new leaping position as follows

119901119898119900V119890119894 = rand lowast (119892119887119890119904119905119894 minus 119901119908119900119903119904119905119894) (13)

119901119908119900119903119904119905119894 = 119901119908119900119903119904119905119894 + 119901119898119900V119890119894(minus119901119898119900V119890119898119886119909 ≪ 119901119898119900V119890119894 ≪ 119901119898119900V119890119898119886119909) (14)

If the position obtained from formulas (13) and (14) is stillnot closer to the food source than the worst frog in the groupor the worst frog individual needs to skip more than themaximum step size the worst frog leaps to a new position atrandom Otherwise the worst frog leaps to the new positiongenerated from formula (14) SFLA performs an iterativeevolution of the frogs within each group via adjusting andupdating of the worst frog

In the evolutionary process of SFLA each iterationinvolves the local optimal solution 119901119887119890119904119905119894 and the globaloptimal 119892119887119890119904119905 In the whole population there exist119898 groupsand therefore there are 119898 local optimal solutions and thereis only one global optimal SFLA uses a grouping operatorand a mechanism of individual integration into groups fortransmitting messages and sharing information The group-ing operator divides all the frogs in the population into 119898groups and then the worst frog in each group updates itselflocal search strategy When all groups finish searching ashuffle share information and interact with each other Thismechanismmakes SFLA have better global search ability Theprocedure of basic SFLA is shown as follows

Step 1 Initialize the positions of all the frogs in the populationat random to make the frogs randomly distributed in thesearch space and initialize the population size119873 the numberof frogs in a group 119876 the number of evolution of the119894119899119899119890119903 119894119905119890119903119886119905119894119900119899 the maximum step size of the frogs allowedto move 119901119898119900V119890119898119886119909 and maximum number of iterations ofpopulation 119898119886119909 119894119905119890119903119886119905119894119900119899Step 2 Calculate the fitness of all frogs in the population andsorting them in descending order 119892119887119890119904119905 is initialized withthe best frog position and the frogs are sorted into119898 groupsaccording to a grouping operator

Step 3 Adjust the worst frog in the group according toformulas (11) and (12)


Step 4 If the position of the frog in Step 3 is improved replacethe worst frog position in the group with the new positionthen skip to Step 6 or readjust the worst frog position of thegroup according to formulas (13) and (14)

Step 5 If a position of the frog from Step 4 is improvedreplace the worst frog position in the group with the newposition then skip to Step 6 or generate a new randomposition instead of the worst frog position in the currentgroup

Step 6 Calculate the fitness of all frogs in the group andsort them in descending order to determine if the internaliteration is over If not skip to Step 3

Step 7 Share shuffle information among all the frogs in thesame group

Step 8 Judge whether the end condition meets or not If itdoes output the optimal solution directly If not skip to Step 2and it continues

The end condition of SFLA can achieve the maximumnumber of iterations or meet an error criterion which maybe a combination of the above two In the case where theoptimal value of the objective function and the allowableerror are determined in advance the end condition can be setto satisfy a certain error range When the difference betweenthe objective value and the optimum is less than the settingerror output the optimal value otherwise it continues

3 The Shuffled Frog-Leaping DifferentialEvolutionary (SFDE)

Although combining a new algorithm with simple assemblycan improve the accuracy or convergence of the algorithm toa certain degree it is still far from the theoretical value of thetest function so how to integrate the two algorithms is themost important problem

31 Integration Strategy between SFLA and DE There arethree main steps in the integration strategy between SFLAand DE Step (1) initialize populations Step (2) dividethe whole population into several groups and integratewithin a group Step (3) shuffle the whole population afteriterations in each groupWe use the idea of dividing thewholepopulation into several subpopulations and considering eachsubpopulation as a group So before dividing the wholepopulation into groups individuals are sorted by the fitnessvalue of the test function then a new group with the strategyis shown as in Figure 1

As shown in Figure 1 SFLA helps to adjust the worstindividuals in the groups If the fitness value of the individualsgenerated from formulas (11) and (12) is improved the worstone in the original group will be replaced Otherwise itsposition of the group should be readjusted according toformulas (13) and (14) If it is worse than original one thendiscard it and randomly generate a new one to replace itThen

pworst

pbestUpdated pworst

pmove

Figure 1 The worst individual position adjustment process in theSFDE

we use DE to deal with the new population The operationsinclude mutation crossover and selection

The evolutionary process of the individual population isshown in Figure 2 where the sequence (1 2 3 4) is the stagenumber of each group evolution (1) The worst individualposition is adjusted for each subpopulation according toFigure 1 then the operation of the Differential Evolution forall the individuals in the subpopulation that is the variationof the evolution and the selection operation (2)The wholepopulation run mutation and cross operation of DifferentialEvolution stage thus resulting in the middle of the vectorof individuals (represented in Figure 2 with a red circle ofindividuals) for the latter part of the selection operation(3) Select the operation for the generation of intermediateindividuals and original target individuals

In Figure 2 the next generation has the intermediatevector individuals (individual with red virtual coil) and theoriginal target individuals In SFDE the mutation strategyuses DEbest1bin

32 The Basic Process of Shuffled Frog-Leaping DifferentialEvolutionary (SFDE) The basic SFDE can be described inAlgorithm 1

In Algorithm 1 T is the number of subpopulation119892119887119890119904119905119894 denotes the best individual in population 119901119908119900119903119904119905119894is the worst individual in subpopulation pbesti is the bestindividual in subpopulation V119894119895 denotes the current mutatedvectors

4 Experimentation

This section compares the proposed SFDEwith twenty classicwell-known test functions

41 Experimental Setting and Parameterization Twenty testfunctions with 30 high dimensions check the performance ofSFDE The detailed definitions of them are shown in Table 1

Experimental environment configuration operation sys-tem is Windows 7 Minimum memory is 4G processor typeis Intel (R) Core (TM) i5-2370M 240GHz developmenttools and version are Matlab-R2012a

To be fair the initial conditions of each algorithm areconsistent (1) Population size of all Differential Evolution


fw

fb

Group_1

fb

fw

Group_2

fb

fwGroup_3

gb

1 group computing

2 mutation and crossover

3 selection

SFLA DE

Figure 2The integration strategy between SFLA and DE

algorithms is set to be 200 (2)Thenumber of subpopulationsof SFDE is set to 10 (3) The number of iterations is setaccording to the complexity of the problem but the numberof iterations of all Differential Evolution algorithms is equalevery time

42 Computational Results and Discussion We record theoptimal value obtained at the end of every computing in30 runs Then the average optimal value and the standarddeviation of the optimal value are calculated by using the30 dependently runs And the standard deviation of the bestaverage value and the optimal value is inputted into the tableto facilitate the analysis of the experimental results In orderto highlight the experimental data close to the theoreticalvalue of the function we test each test function in the tableclosest to the theoretical value of the experimental databold The output images reflect the variation curve of theaverage optimal value for each test function in 30 separateexperiments

The convergence curves plots of five algorithms for 9benchmark functions with 30 dimensions are drawn inFigure 3 (AckleMichalwicz Function and Schwefelrsquos Problem12) Figure 4 (Perm Function Rastrigin Sphere Function)and Figure 5 (Rotated Hyper-Ellipsoid Shifted and ZakharovFunction Dixon-Price Function) respectively The 9 resultsconfirm the good performance of SFDEThe optimal value ofthe function curve is shown in Figure 3 and the full optimalvalue of the function is shown in Table 2

Schwefelrsquos Problem 12 functionrsquos algorithm is difficult toobtain the theoretical value on 30 dimensions (iterations2000 times) From the experimental results it can be seenthat the convergence rate of SFDE is faster than that of otheralgorithms and the final accuracy is also better than otheralgorithms and even 34 units of magnitude are higher thanthe accuracy of EPSDE algorithm

Rotated Hyper-Ellipsoid is a continuous convex single-peak which is an extension of the axis-parallel super-ellipsoidfunction and also becomes a square sum function From the

experimental results SFDE is better than other algorithmsand with the iteration of the algorithm the accuracy of thealgorithm is getting better

The Perm Function is characterized by a large numberof local optimal value of the single-peak function and itis a well test function which can test the function of thealgorithm It can be seen from the experimental results thatSFDE has the highest precision and the fastest convergencerate for Zakharov Function with 30 dimensions (iterations2000 times)

The convergence curves of five algorithms for 9 bench-mark functions with 30 dimensions are drawn in Figure 3respectively For each benchmark function there are twocurves the left one is plotted with iterations and averagefunction values are plotted with NFEs at right Figures3(a)ndash3(c) and 4(a) present multimodal benchmark functionsand Figures 4(b)-4(c) 5(a)ndash5(c) present unimodal bench-mark functions Figure 3(a) is the curves of average optimalof F1 In Figure 3(b) SFDE and CODE almost have thesame best value on F2 The convergence curves of comparedalgorithms for F3 function and F13 function are given inFigures 3(c) and 4(a) Figure 4(b) present convergence curvesof test results for F10 function In Figure 4(c) 5(a)-5(b) plotsof SFDE are much better than other variants for F4 F6 andF8 functions In Figure 5(c) SFDE demonstrates best averageand convergence speed for 30 dimensions on F9 function andMDE is the second best on F9

43 Results Analysis Table 2 shows the comparison betweenSFDE and classic DE It can be seen from the aboveexperimental results that SFDE does better in most of thebase functions compared with other differential evolutionaryalgorithms and the convergence speed is also accelerated

In Table 2 the eight test functions 1198914(119909) 1198916(119909) 1198918(119909)1198919(119909) 11989114(119909) and 11989119(119909) are unimodal functions and thesolving accuracy of SFDE is better than that of other algo-rithms In the results of the multimodal test function theindividual test function is poor performance such as 1198912(119909)


SFDE Shuffled Frog-leaping Differential Evolutionary AlgorithmInput An initial population 119909119894119895 | 119909119894119895 isin [119871119900119908119861119900119906119899119889119890119903119910119880119901119861119900119906119899119889119890119903119910] 119894 = 1 119873119875 119895 = 1 2 119863

Benchmark 119891(119909) or object function 119892(119909)Terminal conditions Maximum iterationsalefsym or Acceptable error 1205760

Output optimal 119892119887119890119904119905Begin(1) Initialization(2) Dividing 119909119894119895 into 119879 subpopulations at random(3)While ((t lt alefsym) 119900119903 (120576 gt 1205760))(4) 119901119887119890119904119905119894(t + 1) =

119901119887119890119904119905119894(119905) 119894119891 119891(119883119894(119905 + 1)) ge 119891(119901119887119890119904119905119894(119905))119883119894(119905 + 1) 119894119891 119891(119883119894(119905 + 1)) lt 119891(119901119887119890119904119905119894(119905)) lowast computing pbesti according to Eq (9) lowast

(5) 119892119887119890119904119905(119905) = min119891(1199011198871198901199041199051(119905)) 119891(1199011198871198901199041199052(119905)) 119891(119901119887119890119904119905119898(119905)) lowast finding the 119892119887119890119904119905119894 according to Eq (10) lowastlowast updating the position of the119901119908119900119903119904119905119894 in each subpopulation according to Formulas (11) and (12) lowast

(6) 119901119898119900V119890119894 = rand lowast (119901119887119890119904119905119894 minus 119901119908119900119903119904119905119894)(7) 119901119908119900119903119904119905119894 = 119901119908119900119903119904119905119894 + 119901119898119900V119890119894(8) While 119901119908119900119903119904119905119894 is not increased

lowast updating the position of the119901119908119900119903119904119905119894 in each subpopulation according to Formulas (13) and (14) lowast(9) 119901119898119900V119890119894 = 119903119886119899119889 lowast (119892119887119890119904119905119894 minus 119901119908119900119903119904119905119894)(10) 119901119908119900119903119904119905119894 = 119901119908119900119903119904119905119894 + 119901119898119900V119890119894(11) EndWhile(12) For i=1 to NP(13) V119894119895 = 1199091199031119895 + 119865 lowast (1199091199032119895 minus 1199091199033119895) V119894119895 = 119909119887119890119904119905119895 + 119865 lowast (1199091199031119895 minus 1199091199032119895) lowastMutation operation lowast(14) Correction() lowast Correction operationlowast(15) Crossover() lowast Crossover operationlowast(16) Selection() lowast Selection operation lowast(17) End For(18) 120576 = |(119891(119909) minus 119891(119909lowast)|(19) 119905 = 119905 + 1(20) EndWhile(21) Return 119905 120576 and 119892119887119890119904119905(22) End

Algorithm 1 Pseudocode of Shuffled Frog-leaping Differential Evolutionary (SFDE)

and 1198917(119909) However the solving accuracy of SFDE is muchhigher than that of other algorithms and SFDE is more stableMore importantly SFDE algorithm itself is very simple andfast and has an absolute advantage

In order to determine whether SFDE is more effectivethan other methods statistical methods need to detect theresults of CPU running time this paper selected the pairedT-test and the paired F-testThe T-test is an important test ofthe mean difference between the two samples with the aimof checking the system error The F-test is a significant testof the variance of the two samples with the aim of testingthe accident error Usually we compare the value of 005 Ifthe test result is less than 005 the cell will mark the resultwith lsquo+rsquo instead the cell will mark the result with lsquo-rsquo Thepercentage of lsquo+rsquo in all results is the likelihood that SFDEwill handle the reliability and advantage of the test problemSpecific test results as shown in Table 3 each column istest function efficiency detection methods and a variety ofintelligent optimization

To compare SFDE with other algorithms we selectadvanced variants of DE namely JADE DMPSADE andIMMSADE which is introduced in [12] The comparisonresults are as shown as follows in Table 4

Table 4 shows a clear comparison of SFDE-SaDE SFDE-JADE SFDE-DMPSADE and SFDE-IMMASDE FromTable 4 it is clear to see that the convergence speed of SFDEis faster among the considered algorithms for most of testfunctions

5 Simulation of SpectrumThroughput Optimization

There are three ways of spectrum sensing energy detectionmatched filter detection and cyclone-stationary propertydetection the most commonly used of which is energydetection In this way if the length of each frame is fixedits sensing time synchronizes with its energy accumulationAt the same time if authorized users have good protectionthe false alarm probability will be smaller and the detectionrate will be larger but the data transmission time will beshortened [14] That is to say the idle time of the cognitiveuserrsquos usage spectrum becomes shorter resulting in lowerthroughput of the cognitive user Therefore how to arrangean effective schedule tomaximize the throughput of cognitiveusers (ie authorized users have a right of first class service)is a hot research topic


Table1Detaileddefin

ition

softhe

testfunctio

nF

Nam

eDescriptio

nDim

Ra

nge

Opt

119891 1(119909)

Ackle

119891 1(119909)=minus

20exp(minus0

2radic1 119873119873 sum 119894=11199092 119894

)minusexp1 119873119873 sum 119894=1co

s (2120587119909 119894)+

20+119890

30[minus60

0600]

0

119891 2(119909)

Michalewicz

119891 2(119909)=minus

119873 sum 119894=1sin(119909 119894)

sin2119898(1198941199092 119894 120587

)119898=10

30[0120587

]-966

119891 3(119909)

Schw

efelrsquos

prob

lem

12119891 3(119909

)=119873 sum 119894=1

(119894 sum 119895119909 119894)2

30[minus50

0500]

0

119891 4(119909)

Sphere

119891 4(119909)=

N sum i=1

1199092 11989430

[minus50050

0]0

119891 5(119909)

Rosenb

rock

119891 5(119909)=Nminus1 sum i=1

(100(1199092 119894minus

119909 119894+1)2+(119909119894minus1)2

)30

[minus10010

0]0

119891 6(119909)

Rotated

Hyper-Ellipsoid

119891 6(119909)=119899 sum 119894=1119894 sum 119895=11199092 119895

30[minus65

536553]

0

119891 7(119909)

Shifted

and

Rotated

Schw

efelrsquos

Functio

n

119891 7(119909)=5

00+4189

829times119899minus119899 sum 119894=1119892(119910 119894)

119910 119894=119911 119894+

42096873

6119890+002

119892(119910 119894)=

119910 119894sin(1003816 1003816 1003816 1003816119910 1198941003816 1003816 1003816 100381612)

1198941198911003816 1003816 1003816 10038161199101198941003816 1003816 1003816 1003816le5

00((50

0minusmod(119910 1198945

00))sin(radic1003816 1003816 1003816 10038165

00minusmod(119910 1198945

00)1003816 1003816 1003816 1003816))minus

(119910 119894minus500)2

10000119899

119894119891119910 119894gt50

0((m

od(1003816 1003816 1003816 1003816119910 1198941003816 1003816 1003816 1003816

500)minus5

00)sin(radic1003816 1003816 1003816 10038165

00minusmod(1003816 1003816 1003816 1003816119910 1198941003816 1003816 1003816 1003816

500)1003816 1003816 1003816 1003816))

minus(119910119894+50

0)21000

0119899119894119891119910 119894

ltminus500

119911=1198725(10

00(119909minus119900 5) 100

)119900 3=

[119900 31119900 32

119900 3n]

30[minus10

0100]

500


Table1Con

tinued

FNam

eDescriptio

nDim

Ra

nge

Opt

119891 8(119909)

Zakh

arov

119891 8=119873 sum 119894=1119909 1198942+ (119873 sum 119894=105119894times

119909 1198942 )2

+ (119873 sum 119894=105119894times

119909 1198942 )4

30[minus10

10]0

119891 9(119909)

Dixon

-Pric

e119891 9=

119873 sum 119894=2119894(2119909 1198942

minus119909 119894minus1)2 +

(119909 119894minus1)2

30[minus10

10]0

119891 10(119909)

Perm

119891 10=119889 sum 119894=1(119889 sum 119895=1(119895119894+120573 )

((119909119895 119895)119894minus1 )

)230

[0120587]

-966

119891 11(119909)

Grie

wank

119891 11=1 4000119873 sum 119894=11199092

minus119873 prod 119894=1cos(119909119894 radic 119894)+1

30[minus60

0600]

0

119891 12(119909)

Schw

efel

119891 12=119873 sum 119894=1[minus

119909 119894sin(radic1003816 1003816 1003816 1003816119909

1198941003816 1003816 1003816 1003816)]30

[minus50050

0]-418982d

119891 13(119909)

Rastr

igin

119891 13=119873 sum 119894=1(1199091198942minus10

cos(2120587

119909 119894)+10)

30[minus51

2512]

0

119891 14(119909)

Sum

ofdifferent

powe

rs119891 14=

(119873 sum 119894=11003816 1003816 1003816 1003816119909 1198941003816 1003816 1003816 1003816119894+1)

30[minus1

1]0

119891 15(119909)

Shub

ert

119891 15=(5 sum 119894=1119894

cos( (119894

+1 )119909 1+

119894))+(5 sum 119894=1119894

cos( (119894

+1 )119909 2+

119894))2

[minus1010]

-1867309

119891 16(119909)

Powe

ll119891 16=

1198894 sum 119894=1[(119909 4119894minus3

+10119909 4119894minus2

)2 +5(119909 4119894minus1minus119909 4119894

)2 +(119909 4119894minus2minus21199094119894minus1)4 +

10(1199094119894minus3minus21199094119894)4 ]

30[minus4

5]0

119891 17(119909)

Drop-Wave

119891 17=1+c

os(12radic

119909 12 +119909 22 )

05(119909 12 +

119909 22 )+2

2[minus51

2512]

-1

119891 18(119909)

Levy

119891 18=sin2(120587120596 1

)+119889minus1 sum 119894=1(1205961minus1)2

[1+10sin2(120587120596 1

+1)]+(120596119889minus1)2

[1+10sin

2(2120587120596119889)]

30[minus10

10]0

119891 19(119909)

SumSquares

119891 19=119889 sum 119894=11198941199091198942

30[minus10

10]0

119891 20(119909)

Weierstr

ass

119891 20=119873 sum 119894=1(119896max sum 119896=0[119886119896 co

s(2120587119887119896 (119909119894+05

))]minus119899119896max sum 119896=0[

119886119896 cos(2120587

119887119896 times05)]

)30

[minus0505]

0


SFDEEPSDEMDE

CODEMDESELF

0 05 1 15 2 25 3 35 4Number of Function Evaluations (NFE)

SFDEEPSDEMDE

CODEMDESELF

times105

10minus120

10minus100

10minus80

10minus60

10minus40

10minus20

100

1020Fu

nctio

n V

alue

200 400 600 800 1000 1200 1400 1600 1800 20000Iteration times

10minus15

10minus10

10minus5

100

105

1010

Func

tion

Val

ue

(a) Ackle Function

SFDEEPSDEMDE

CODEMDESELF

SFDEEPSDEMDE

CODEMDESELF

times105

minus102

minus101

minus100

Func

tion

Val

ue

200 400 600 800 1000 1200 1400 1600 1800 20000Iteration times

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue

05 1 15 2 25 3 35 40Number of Function Evaluations (NFE)

(b) Michalwicz Function

SFDEEPSDEMDE

CODEMDESELF

times105

10minus30

10minus20

10minus10

100

1010

Func

tion

Val

ue

200 400 600 800 1000 1200 1400 1600 1800 20000

Iteration times

SFDEEPSDEMDE

CODEMDESELF


10minus1410minus1210minus1010minus810minus610minus410minus2100102104106

Func

tion

Val

ue

(c) Schwefelrsquos Problem 12

Figure 3 The 30 dimensions and curves convergence for 3 benchmark functions with 5 variants of DE


0

200

400

600

800

1000

1200

1400

1600

1800

2000

Iteration timesSFDEEPSDEMDE

CODEMDESELF


SFDEEPSDEMDE

CODEMDESELF

times105


Func

tion

Val

ue

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue

(a) Rastrigin Function

0

200

400

600

800

1000

1200

1400

1600

1800

2000

Iteration times

SFDEEPSDEMDE

CODEMDESELF


SFDEEPSDEMDE

CODEMDESELF

times105


Func

tion

Val

ue

10minus20

100

1020

1040

1060

1080

10100

Func

tion

Val

ue

(b) Perm Function

0 50 100 150 200 250 300 350 400 450Iteration times

SFDEEPSDEMDE

CODEMDESELF

SFDEEPSDEMDE

CODEMDESELF

0 05 1 15 2 25 3 35 4Number of Function Evaluations (NFE) times105


Func

tion

Val

ue

10minus20

10minus15

10minus10

10minus5

100

105

1010

Func

tion

Val

ue

(c) Sphere Function



0

200

400

600

800

1000

1200

1400

1600

1800

Iteration timesAPDDEEPSDEJADE

MDECODE

100

102

104

106

108

1010

1012

Func

tion

Val

ue

SFDEEPSDEMDE

CODEMDESELF

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue

times105


(a) Rotated Hyper-Ellipsoid

0

200

400

600

800

1000

1200

1400

1600

1800

2000

Iteration times

10minus20

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue


SFDEEPSDEMDE

CODEMDESELF


Func

tion

Val

ue

times105

SFDEEPSDEMDE

CODEMDESELF

(b) Zakharov Function

SFDEEPSDEMDE

CODEMDESELF

SFDEEPSDEMDE

CODEMDESELF

times10505 1 15 2 25 3 35 40

Number of Function Evaluations (NFE)

10minus1100101102103104105106107

Func

tion

Val

ue

200

400

600

800

1000

1200

1400

1600

1800

20000

Iteration times

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue

(c) Dixon-Price Function



Table 2 Experimental data of various DE algorithms on the test functions (30d)

Func Rate SFDE EPSDE MDE CODE MDESELF

1198911(119909) Avg 547E+00 200E+01 207E+01 200E+01 200E+01SD 212E-12 129E-01 337E-02 649E-03 253E-02

1198912(119909) Avg -225E+01 -241E+01 -131E+01 -278E+01 -236E+01SD 499E-01 581E-01 429E-01 110E-02 143E-01

1198913(119909) Avg 416E-31 194E+03 138E-07 442E+01 359E-07SD 716E-31 118E+03 104E-07 834E+00 622E-07

1198914(119909) Avg 476E-21 293E-01 299E-03 326E+01 372E-02SD 106E-20 200E-01 892E-04 704E+00 482E-02

1198915(119909) Avg 120E+01 163E+01 530E-07 119E+01 151E+01SD 114E+00 276E+00 552E-07 698E-01 580E+00

1198916(119909) Avg 998E-94 373E-17 301E-25 118E-10 942E-24SD 160E-93 603E-17 289E-25 118E-10 163E-23

1198917(119909) Avg 547E+03 513E+03 722E+03 408E+03 452E+03SD 314E+02 221E+02 325E+02 352E+02 188E+02


1198919(119909) Avg 000E+00 165E+01 166E+02 571E-06 319E+01SD 000E+00 107E+01 105E+01 546E-06 506E+00

11989110(119909) Avg 380E+00 506E-02 260E+00 266E-01 172E-02SD 534E+00 217E-02 580E+00 367E-01 176E-02


11989112(119909) Avg -126E+04 -126E+04 -126E+04 -126E+04 -117E+04SD 147E-11 186E-05 000E+00 158E-12 199E+02


11989114(119909) Avg 000E+00 347E-58 174E-86 511E-47 808E-67SD 000E+00 775E-58 380E-86 883E-47 181E-66

11989115(119909) Avg -187E+02 -187E+02 -187E+02 -187E+02 -187E+02SD 000E+00 402E-14 000E+00 000E+00 220E-07


11989117(119909) Avg -100E+00 -100E+00 -100E+00 -100E+00 -100E+00SD 000E+00 000E+00 000E+00 000E+00 000E+00




At present Monte Carlo is a common method but itsimplementation is a complex and time-consuming task [15]and the more important point we have noticed is that itcannot alsomeet the real-time requirements It is high time toimprove the sensing time by using the improved DifferentialEvolution algorithm such as good searching performancefewer parameters and faster convergence rate so as tomaximize the system throughput

51 Mathematical Model Based on Energy Detection With-out interfering with the authorized users it is necessaryto determine if they are busy or idle by continuouslydetecting signals received in a certain frequency bandso as to determine whether these resources are accessi-ble or not which is a binary hypothesis testing problemwe assume that the authorized user accesses his reservedfrequency for periodic 1198791 and its disappearance takes


Table 3 The comparison results of function optimization

FRate TF EPSDE MDE DE CODE DE∘ MDESELF DE

F1875T-test 76954E-03 33359E-02 35105E-02 34813E-02F-test 88978E-01 54921E-03 32283E-05 36439E-03TF ++ ++ ++ ++

F2625T-test 22431E-02 33328E-06 31399E-04 58249E-02F-test 54126E-01 52737E-01 42237E-03 13638E-02TF +- +- ++ -+

F375T-test 19592E-01 28839E-02 55096E-03 42232E-01F-test 15253E-33 49760E-23 28585E-31 56612E-24TF -+ ++ ++ -+

F4875T-test 44275E-02 67979E-04 28489E-03 90376E-02F-test 47045E-40 30269E-34 67452E-43 79601E-40TF ++ ++ ++ -+

F550T-test 16634E-02 98894E-06 49342E-01 14166E-01F-test 11582E-01 32658E-25 36254E-01 81762E-03TF +- ++ -- -+

F6625T-test 90588E-02 67503E-02 67318E-03 21129E-01F-test 30342E-147 12115E-130 28959E-159 17384E-146TF -+ -+ ++ -+

F750T-test 80260E-03 50414E-04 82932E-04 14593E-02F-test 29739E-01 29593E-01 63363E-01 19485E-01TF +- +- +- +-


F9100T-test 23766E-02 47325E-08 11628E-02 40496E-07F-test 00000E+00 00000E+00 00000E+00 00000E+00TF ++ ++ ++ ++

F10375T-test 14552E-01 63556E-01 17863E-01 15229E-01F-test 16245E-09 87781E-01 13244E-04 70381E-10TF -+ -- -+ -+

F11100T-test 00000E+00 00000E+00 39290E-02 00000E+00F-test 00000E+00 00000E+00 00000E+00 00000E+00TF ++ ++ ++ ++

F12100T-test 00000E+00 00000E+00 00000E+00 68809E-06F-test 00000E+00 00000E+00 00000E+00 00000E+00TF ++ ++ ++ ++


F14500T-test 12857E-01 29792E-01 68323E-02 42411E-01F-test 00000E+00 00000E+00 00000E+00 00000E+00TF -+ -+ -+ -+

F15100T-test 00000E+00 00000E+00 00000E+00 00000E+00F-test 00000E+00 00000E+00 00000E+00 00000E+00TF ++ ++ ++ ++




Table 3 Continued


F18500T-test 35592E-01 35592E-01 34659E-01 34659E-01F-test 10490E-71 16603E-116 25120E-52 44566E-67TF -+ -+ -+ -+

F19100T-test 13200E-02 54837E-02 15650E-03 33401E-01F-test 00000E+00 57934E-298 00000E+00 13100E-303TF ++ ++ ++ ++


Table 4 Comparison results of function optimization (30d)

Function Dim Algorithm MEAN STD

119891 (119909) = Nsumi=11199092119894 30

SFDE 000E+00 000E+00SaDE 000E+00 000E+00JADE 000E+00 000E+00

DMPSADE 000E+00 000E+00IMMSADE 000E+00 000E+00

119891 (119909) = Nminus1sumi=1(100 (1199092119894 minus 119909119894+1)2 + (119909119894 minus 1)2) 30


DMPSADE 748E-06 224E-05IMMSADE 000E+00 000E+00

119891 (119909) = minus20 exp(minus02radic 1119873119873sum119894=1

1199092119894) minus exp 1119873119873sum119894=1

cos (2120587119909119894) + 20 + 119890 30

SFDE 547E+00 212E-12SaDE 209E+01 426E-03JADE 209E+01 167E-01

DMPSADE 202E+01 160E-01IMMSADE 399E-15 000E+00

1198790 as a cycle the energy detection model is as formula(15)

1198790 z (n) = 120583 (n)1198791 119911 (n) = 119904 (n) + 120583 (n) (15)

In the abovemodel 119911(119899) is the signal received by the cognitiveuser 120583(119899) is a Gaussian noise with a mean of 0 and a varianceof 1205902120583 119904(119899) is the signal belonged to authorized user the meanvalue is 0 and the variance is 1205902

Spectrum sensing concerns two parameters (ie detec-tion probability and false alarm probability) [16] Let 120591 be theduration of observation and while the statistic index denotesas formula (16)

W = 1119873119873sum119899=1

|119911 (119899)|2 (16)

whereN is the amount of those perceived samples and f is thesampling frequency it is obvious that 119873 = 120591119891 Suppose thatprobability density119882 is a random variable with distribution

of 1205942 and a given threshold 120576 the false alarm probability canbe given by the following formula (17)

119875119891 (120576) = 119875120591 (W gt 120576 | T0)= 1radic21205871205900 int

infin

119873119890minus(Wminus1205830)2212059020119889119909

= 119876(( 1205761205902120583) minus radic120591119891)(17)

where 119875119891(120576) refers to the probability of misjudging anauthorized user without hisher perceiving 12057520 is the varianceof119882 and 1205830 is the mean of119882 respectively

However assuming the given 1198791 and a threshold 120576 theprobability density 119882 will be a noncentral 1205942 distributionvariable Then the corresponding detection probability isshown in formula (18)

119875119889 (120576) = 119875120591 (W gt 120576 | T1)= Q(( 1205761205902120583 minus 120574 minus 1)radic 1205911198912120574 + 1)

(18)


Perceivedtime

Data transfer time

t T-t

Perceived time

Data transfer time

t T-t

＄ＮＬＧ1 ＄ＮＬＧＧmiddot middot middot middot middot middot

Figure 6 Period-aware frame structure

where 119875d(120576) refers to the probability of correctly judging theexistence of authorization and 120574 is the signal-to-noise ratiofrom cognitive users to authorized users From formulas (17)and (18) combined we infer that formulas (19) and (20) arecorrect

119875119891 = 119876(radic2120574 + 1Qminus1 (119875119889) + radic120591119891120574) (19)

119875119889 = 119876( 1radic2120574 + 1 (Qminus1 (119875119891) minus radic120591119891120574)) (20)

When the timely requirement of an authorized user isdetected the related cognitive user needs to quickly give away to the authorized user Based on the above formulas (19)and (20) it is obvious that the higher the value of 119875119889 is thebetter the related protection is obtained The lower the 119875119891 isthe higher the reusability of wireless resource is So a goodalgorithm should have high 119875119889 and low 11987511989152 ATrade-Off betweenUserThroughput andPerceivedTimeThe time cost of processing one data frame of cognitiveradio includes two parts ie frame perceived phase anddata transmission phase When the first perception becomeslonger the detection probability becomes larger the proba-bility of false alarm becomes smaller but the cognitive userrsquosdata transmission time will be reduced [17] Therefore howto balance the sensing and transmission time under theprecondition of authorizing users to operate safely and thenimprove the throughput of the cognitive radio system is anurgent problem to be solved In this section the periodicstructure of the radio frame is the basis for research as shownin Figure 6

When the authorized user is not in the channel there is nofalse alarm probability [18] the cognitive userrsquos throughputis C0 = log 2(1 + 119878119873119877119904) if an authorized user exists thecognitive user throughput is C1 = log 2(1+119878119873119877119904(1+119878119873119877119901))Obviously C0 gt C1 and 119878119873119877119904 = 1198751199041198730 where Ps is theaverage cognitive user power and1198730 is the noise powerThen119878119873119877119901 = 1198751199011198730 where 119875119901 is the interference degree of theauthorized user at the cognitive user acceptance point [19]It can be found that in order to protect authorized usersthe probability of 119875119889 is close to 1 At this time the systemthroughput is as formula (21)

119877 (120591) = 1198770 (120576 120591) + R1 (120576 120591) (21)

Among them 1198770(120576 120591) = ((119879 minus 120591)119879)1198620(1 minus 119875119891(120576120591))119875(H0) 1198771(120576 120591) = ((119879 minus 120591)119879)1198621(1 minus 119875119889(120576 120591))119875(H1) 119875(1198670)

and 119875(1198671) denote the probability that the first user will notappear and appear respectively and119875(1198670)+119875(1198671) = 1 SinceC0 gtC1 and119875119889 approximately equal 11198771 is close to zeroThenformula (21) can simplify the following formula (22)

119877 (120591) asymp 1198770 (120576 120591) = 119879 minus 120591119879 1198620 (1 minus 119875119891 (120576 120591)) 119875 (H0) (22)

Since the Q is a decreasing function when the sensing timebecomes larger under the specified detection probabilitythe false alarm probability will be small and the datatransmission time will be smaller That is to say the valueof formula (22) may become larger or smaller The trade-offbetween perceived user throughput and perceived time is tofind the optimal sensing time 120591 under the protection of theauthorized user so that the system arrives at the maximumeffective throughput Therefore the optimization problem oflooking for the optimal perception time is transformed intoformula (23)

max 119877 (120591) = 1198770 (120576 120591)119904119905 119875119889 (120576 120591) ge 119875119889 (23)

To solve problem of the effective throughput of spectrumresource in wireless cognition network we need to findthe best service mode for the personalized users This is aproblem of function optimizationThis section uses the SFDEto find the optimal perception time

53 Specific Solution Based on SFDE Specific implementa-tion steps are as follows which is based on SFDE

Step (1) initializes a population The entire range ofvariables is from 0001 to 1 into 45 intervals The upper limit ofthe i-th segment is bounds (119894 2) and the lower bound is limitedto bounds (119894 1) The specific evaluation process is shown asformula (24)

119887119900119906119899119889119904 (i 2) = 001 + 00002 lowast i119887119900119906119899119889119904 (i 1) = 001 + 00002 lowast (i minus 1) (24)

where each interval assumes as an individual and the wholehas 45 individual vectors The whole population dividethemselves into the three subpopulations each of which has15 individuals Then each individual is initialized as shown informula (25)

119909119895119894 (0) = 119887119900119906119899119889119904 (i 1) + 00002 lowast 119903119886119899119889 (0 1) (25)


Table 5 The parameters used in the simulation experiment

Parameter value DescriptionNP 45 Population sizeD 20 Population individual dimensioniMax 20 The maximum number of iterationsW 5 The maximum number of individuals that the archive set holdsN 15 The number of individuals per sub populationP 01 The step size of the parameters of the parameter poolP(H0) 02 The probability of occurrence of cognitive users119875119889 095 Detection of non-value of probabilityF 6MHz Sampling frequencySNRp -15dB Authorized userrsquos SNRSNRs 20dB Cognitive userrsquos SNR

where the 00002 is the length of itself individual gene in thepopulation

Step (2) finds the optimal individual Xlbest in each sub-population Each gene vector is brought into fitness formula(22)TheXlbest is based on the fitness and themaximum valueof each gene for each individual With randomly selecting theparameters F and CR for each individual from the parametercandidate pool we can get the sniffing values F ad andF de of the parameter F corresponding to each individualare obtained and use the optimal individual to compute thevariation vector

Step (3) chooses sniffing values CR ad and CR de of theparameter CR corresponding to each individual And we cancombine the intermediate vector with the mutation vector ofStep (2)

Step (4) lets the intermediate vector obtained in Step (3)participate in the selection operation and we can computethe fitness values for each gene in each intermediate vectorby formula (22) and compare the fitness value with the targetvector If the fitness is greater than the target vector the genewill replace the gene corresponding to the target individualRepeat Steps (2)ndash(4) until all individuals in the populationhave completed the operation of mutation crossover andselection Then the new population goes into the nextgeneration

Step (5) repeats Steps (2)ndash(4) until the maximum num-ber of iterations is reached The optimal sensing time andthe corresponding maximum effective throughput are ob-tained

54 Parameters Setting In order to prove the effectivenessof the SFDE algorithm in the process of system effectivethroughput optimization the simulation carries out andcompares with the Monte Carlo method In order to fullyreflect the superiority and contrast integrity of the improvedSFDE the experimentwill contrast those brand-new variantssuch as JADE MDE EPSDE and CODE In addition thisexperiment will also join the standard particle swarm algo-rithm to illustrate the Differential Evolution more effectivelyThe simulation in the hardware configuration for the INTERCORE i7 CPU 319GHz memory 198GB running on thecomputer the program written to run the software for the

SFDEMonte CarloPSOJADE

EPSDEMDECODE

2 3 4 5 6 7 8 9 101convergence rate (s)

4

45

5

55

sens

ing

time (

s)

Figure 7 Comparison of SFDE and Monte Carlo for systemeffective throughput

MATLAB 70 The parameters used in the system simulationexperiment are shown in Table 5

The convergence curve obtained by the simulation isshown in Figure 7 From the effective throughput con-vergence charts obtained in Figure 5 it can be seen thatthe optimal sensing time of the SFDE is 367ms and37ms for Monte Carlo The maximum effective throughputof SFDE is 52231bpsHz while Monte Carlorsquos through-put is 51947bpsHz The SFDE achieves better goat thanthe Monte Carlo which is close to the theoretical valueof 53bpsHz For PSO it is the maximum throughputwith 45126bpsHz much worse than that of SFDE JADEis second only to Monte Carlo but its correspondingsensing time is 567ms which is significantly worse Insummary SFDE in the throughput performance is verygood

It can be seen from the experimental results in Figure 8that the convergence rate of SFDE in the optimization processismuch faster than that of others especially Monte CarloTheSFDE spends only 21987s on finding the best sensing timewhile Monte Carlo spends 521423s So the sensing time ofSFDE is 237 times faster than Monte Carlo It is even 569times faster than the EPSDE Monte Carlo is not dominant in


2 3 4 5 6 7 8 9 1010

02

04

06

08

1

12


EPSDEMDECODE

convergence rate (s)

sens

ing

time (

s)

Figure 8 Comparison of SFDE andMonte Carlo convergence rate

the selection of sensing time that is it is not suited to real-time

From the above experimental results SFDE increases thesystem throughput with ensuring the convergence of thepremise Eventually SFDE greatly improve the convergencerate In other words SFDE overcomes the shortcomingsof Monte Carlo and others that are not suitable for real-time which makes it more practical in solving the effectivethroughput optimization of cognitive users

6 Conclusion

In this paper in order to optimize the radio time perceptionso that the system throughput can be maximized a ShuffledFrog-leaping Differential Evolution (SFDE) algorithm is putforward which combines shuffled frog leaping with differen-tial evolutionThe experimental studies show that in the samesituation the proposed SFDE algorithm improves the existingperformance of others This article simulates the effectivethroughput of cognitive users in radio and uses the improvedSFDE to optimize Experimental results show that underthe same situation the SFDE can reach the theoretical valueof throughput optimization accuracy and the convergencespeed is also faster

Data Availability

The experimental Excel data used to support the findings ofthis study are included within the article

Conflicts of Interest

The authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

Financial supports from the National Natural Science Foun-dation of China (no 61572074) the China Scholarship Coun-cil for visiting to UK (Grant no 201706465028) and the2012 Ladder Plan Project of Beijing Key Lab of Knowledge

Engineering forMaterials Science (no Z12110 1002812005) arehighly appreciated

References

[1] Q Fan and X Yan ldquoSelf-adaptive differential evolution algo-rithm with discrete mutation control parametersrdquo Expert Sys-tems with Applications vol 42 no 3 pp 1551ndash1572 2015

[2] POchoa O Castillo and J Soria ldquoA fuzzy differential evolutionmethod with dynamic adaptation of parameters for the opti-mization of fuzzy controllersrdquo in Proceedings of the 2014 IEEEConference on Norbert Wiener in the 21st Century (21CW) pp1ndash6 Boston Mass USA June 2014

[3] W-J Yu M Shen W-N Chen et al ldquoDifferential evolutionwith two-level parameter adaptationrdquo IEEE Transactions onCybernetics vol 44 no 7 pp 1080ndash1099 2014

[4] J Liang B Qu X Mao and T Chen ldquoDifferential evolutionbased on fitness euclidean-distance ratio for multimodal opti-mizationrdquo in Emerging Intelligent Computing Technology andApplications pp 252ndash260 Springer Berlin Germany 2012

[5] S Wang Y Duan W Shu D Xie Y Hu and Z GuoldquoDifferential evolution with elite mutation strategyrdquo Journal ofComputational Information Systems vol 9 no 3 pp 855ndash8622013

[6] M Ali M Pant and A Abraham ldquoImproving differentialevolution algorithm by synergizing different improvementmechanismsrdquo ACM Transactions on Autonomous and AdaptiveSystems (TAAS) vol 7 no 2 pp 1ndash32 2012

[7] S-WWangW-S Zhang L-XDing et al ldquoResearch on param-eter self-selection strategy of differential evolutionrdquo ComputerScience vol 42 no 1 pp 256ndash259 2015

[8] Z-W Li X-G Zhou G-J Zhang et al ldquoDynamic adaptivedifferential evolution algorithmrdquo Computer Science vol 42 noz1 pp 52ndash56 2015

[9] MM Eusuff and K E Lansey ldquoOptimization of water distribu-tion network design using the shuffled frog leaping algorithmrdquoJournal of Water Resources Planning and Management vol 129no 3 pp 210ndash225 2003

[10] J Luo and M-R Chen ldquoImproved shuffled Frog Leapingalgorithm and its multi-phase model for multi-depot vehiclerouting problemrdquo Expert Systems with Applications vol 41 no5 pp 2535ndash2545 2014

[11] Q Zhang L Liu and H Guo ldquoImproved shuffled flog leapingalgorithm based on keeping the diversity of populationrdquo Journalof Thermal Analysis and Calorimetry vol 105 no 1 pp 53ndash592009

[12] H Li ldquoCrossing and variation frog leaping algorithmrdquo Journalof Ludong University (Natural Science Edition) no 1 pp 16ndash202015

[13] SWang Y Li andH Yang ldquoSelf-adaptive differential evolutionalgorithm with improved mutation moderdquo Applied Intelligencevol 47 no 3 pp 644ndash658 2017

[14] Z Quan S Cui A H Sayed and H V Poor ldquoWidebandspectrum sensing in cognitive radio networksrdquo in Proceedingsof the IEEE International Conference on Communications (ICCrsquo08) pp 901ndash906 Beijing China May 2008

[15] E C Y Peh Y Liang Y L Guan and Y Zeng ldquoOptimizationof cooperative sensing in cognitive radio networks a sensing-throughput tradeoff viewrdquo IEEE Transactions on VehicularTechnology vol 58 no 9 pp 5294ndash5299 2009


[16] X Zhang H Bie Q Ye C Lei and X Tang ldquodual-mode indexmodulation aided OFDM with constellation power allocationand low-complexity detector designrdquo IEEE Access vol 5 pp23871ndash23880 2017

[17] J Svenson and T Santner ldquoMultiobjective optimization ofexpensive-to-evaluate deterministic computer simulator mod-elsrdquo Computational Statistics amp Data Analysis vol 94 pp 250ndash264 2016

[18] J Zhou E Dutkiewicz R P Liu X Huang G Fang and Y LiuldquoAmodified shuffled frog leaping algorithm for PAPR reductionin OFDM systemsrdquo IEEE Transactions on Broadcasting vol 61no 4 pp 698ndash709 2015

[19] Y Yu P Zhang Z Song and F Chai ldquoComposite differentialevolution algorithm for SHM with low carrier ratiordquo IET PowerElectronics vol 11 no 6 pp 1101ndash1109 2018

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Submit your manuscripts atwwwhindawicom


(DADE) is proposed in [8] Shuffled Frog Leaping Algorithm(SFLA) is proposed in [9] which is inspired by the individualslearning from each other during the foraging behaviour offrogs In [10] a multiphase hybrid algorithm implements alocal depth search using SFLA for every cluster and readjustsits global solutions An improved hybrid bifurcation algo-rithmbased on cloudmodel is proposed in [11] which focuseson the transformation between qualitative and quantitativecomputing Reference [12] proposed crossing and variationfrog leaping algorithm (KSFLA) where the individuals of thesubpopulations vary from the ranking list before producingnew individuals instead of the poor ones Reference [13] pro-posed a Self-adaptive Differential Evolution algorithm withImproved Mutation Mode (IMMSADE) which improves themutation model of DE and introduces some new controlparameters

Based on the above discussion SFLA has slow the con-vergence low efficiency and precision in the high dimensioncontinuous optimization problems in that its core strategy isto continuously update the location of the worst individualBut DE does not do anything with the worst individualA hybrid algorithm based on frog leaping algorithm andDifferential Evolution is suggested in this article whichcombines the advantages of SFLA and DE in order to obtaina significant performance on convergence speed and theaccuracy

The rest of this paper is organized as follows In order toensure the readability the related mathematics description ofDifferential Evolution and Shuffled Frog Leaping Algorithmis summarized in Section 2 Section 3 formally definesmodelsof an improvement in a Shuffled Frog-leaping Differen-tial Evolutionary algorithm (SFDE) Section 4 designs thecomparative experiments of well-known public benchmarkfunctions and analyses the related T-test and F-test resultsfor proof of the effective SFDE The analysis of convergencein SFDE is described in detail in Section 4 Simulation exper-iments on the problem of effective throughput optimizationfor cognitive users are given in Section 5 Section 6 concludesthis article with a summary and future direction

2 The Related Work

21 About Differential Evolution DE is a random searchbased on population and also a heuristic swarm intelligencealgorithm It mainly uses mutation crossover and selectionoperations to perform an intelligent evolutionary search DEhas five operations which are described as follows

(1) Initialization Operation Initializing a population ran-domly in the search space the j-th parameter of the i-thindividual in the 0-th generation is initialized by formula (1)

119909119895119894 (0) = 119909119871119900119908119895119894 + 119903119886119899119889 (0 1) sdot (119909119880119901119895119894 minus 119909119871119900119908119895119894 ) (1)

In formula (1) xUp and xLow are the upper and lower boundaryof the j-th parameter of the i-th individual respectively119903119886119899119889(0 1) denotes a random number which is limitedbetween 0 to 1

(2) Mutation Operation In DE the most common in muta-tion operations isDErand1 which selects two individuals atrandom in a population Then the vectors are combined withthe target vector for mutating into an intermediate vectorV119894(119892) The process can be expressed as follows in formula (2)

V119894 (119892) = 1199091199031 (119892) + 119865 sdot (1199091199032 (119892) minus 1199091199033 (119892)) (2)

Obviously the smaller the difference between 1199091199032(119892) and1199091199033(119892) is the smaller the difference between 1199091199031(119892) and V119894(119892)is This means that in the initial stage the disturbancesare large because of the far distance between individualsand the search range of the algorithm is large But in thelater period of the iteration the detective range will be ashrink Several commonmutation strategies are shown in thefollowing formulas (3) (4) and (5)

A DErand2

V119894 (119892) = 1199091199031 (119892) + 119865 (1199091199032 (119892) minus 1199091199033 (119892))+ 119865 (1199091199034 (119892) minus 1199091199035 (119892)) (3)

B DEcurrent-to-best1

V119894 (119892) = 119909119894 (119892) + 119865 (119909119887119890119904119905 (119892) minus 119909119894 (119892))+ 119865 (1199091199031 (119892) minus 1199091199032 (119892)) (4)

C DEbest1

V119894 (119892) = 119909119887119890119904119905 (119892) + 119865 (1199091199032 (119892) minus 1199091199033 (119892)) (5)

Among them the subscript variables 1199031 1199032 1199033 1199034 and 1199035represent different individuals and 119909119887119890119904119905(119892) represents theoptimal vector in the 119892-th generation(3) Correcting Operation After the mutation operation thealgorithm must ensure that each component (gene) of theintermediate vector satisfies the predefined boundary con-straints If a component (gene) of an intermediate vectorexceeds the scope the vector individual must be correctedThe following formula (6) is a simple but most frequentlyused correction strategy

V119894 (119892)=

min 119909119880119901119895119894 2119909119871119900119908119895119894 minus V119894 (119892) 119894119891 V119894 (119892) lt 119909119871119900119908119895119894max 119909119871119900119908119895119894 2119909119880119901119895119894 minus V119894 (119892) 119894119891 V119894 (119892) gt 119909119880119901119895119894

(6)

(4) Crossover Crossover is tomixture the 119909119895119894(119892) and V119895119894(119892) inthe 119892-th generation producing test vectors The process canbe expressed as follows in formula (7)

119906119895119894 (119892)=

V119895119894 (119892) 119894119891 119903119886119899119889 (0 1) le 119862119877 119900119903 119895 = 119895119903119886119899119889119909119895119894 (119892) 119900119905ℎ119890119903119908119894119904119890(7)



119909119894 (119892 + 1) = 119906119894 (119892) 119894119891 119891 (119906119894 (119892)) le 119891 (119909119894 (119892))119909119894 (119892) 119900119905ℎ119890119903119908119894119904119890 (8)




119901119887119890119904119905119894 (119905) 119894119891 119891 (119883119894 (119905 + 1)) ge 119891 (119901119887119890119904119905119894 (119905))119883119894 (119905 + 1) 119894119891 119891 (119883119894 (119905 + 1)) lt 119891 (119901119887119890119904119905119894 (119905))(9)


119892119887119890119904119905 (119905) = min 119891 (1199011198871198901199041199051 (119905)) 119891 (1199011198871198901199041199052 (119905)) 119891 (119901119887119890119904119905119898 (119905)) (10)



119901119898119900V119890119894 = 119903119886119899119889 lowast (119901119887119890119904119905119894 minus 119901119908119900119903119904119905119894) (11)


119901119908119900119903119904119905119894= 119901119908119900119903119904119905119894+ 119901119898119900V119890119894 (minus119901119898119900V119890119898119886119909 ≪ 119901119898119900V119890119894 ≪ 119901119898119900V119890119898119886119909)

(12)



119901119908119900119903119904119905119894 = 119901119908119900119903119904119905119894 + 119901119898119900V119890119894(minus119901119898119900V119890119898119886119909 ≪ 119901119898119900V119890119894 ≪ 119901119898119900V119890119898119886119909) (14)
















pworst

pbestUpdated pworst

pmove







4 Experimentation






fw

fb

Group_1

fb

fw

Group_2

fb

fwGroup_3

gb

1 group computing


3 selection

SFLA DE




























Table1Detaileddefin

ition

softhe

testfunctio

nF

Nam

eDescriptio

nDim

Ra

nge

Opt

119891 1(119909)

Ackle

119891 1(119909)=minus

20exp(minus0

2radic1 119873119873 sum 119894=11199092 119894

)minusexp1 119873119873 sum 119894=1co

s (2120587119909 119894)+

20+119890

30[minus60

0600]

0

119891 2(119909)

Michalewicz

119891 2(119909)=minus

119873 sum 119894=1sin(119909 119894)

sin2119898(1198941199092 119894 120587

)119898=10

30[0120587

]-966

119891 3(119909)

Schw

efelrsquos

prob

lem

12119891 3(119909

)=119873 sum 119894=1

(119894 sum 119895119909 119894)2

30[minus50

0500]

0

119891 4(119909)

Sphere

119891 4(119909)=

N sum i=1

1199092 11989430

[minus50050

0]0

119891 5(119909)

Rosenb

rock

119891 5(119909)=Nminus1 sum i=1

(100(1199092 119894minus

119909 119894+1)2+(119909119894minus1)2

)30

[minus10010

0]0

119891 6(119909)

Rotated

Hyper-Ellipsoid

119891 6(119909)=119899 sum 119894=1119894 sum 119895=11199092 119895

30[minus65

536553]

0

119891 7(119909)

Shifted

and

Rotated

Schw

efelrsquos

Functio

n

119891 7(119909)=5

00+4189

829times119899minus119899 sum 119894=1119892(119910 119894)

119910 119894=119911 119894+

42096873

6119890+002

119892(119910 119894)=

119910 119894sin(1003816 1003816 1003816 1003816119910 1198941003816 1003816 1003816 100381612)

1198941198911003816 1003816 1003816 10038161199101198941003816 1003816 1003816 1003816le5

00((50

0minusmod(119910 1198945

00))sin(radic1003816 1003816 1003816 10038165

00minusmod(119910 1198945

00)1003816 1003816 1003816 1003816))minus

(119910 119894minus500)2

10000119899

119894119891119910 119894gt50

0((m

od(1003816 1003816 1003816 1003816119910 1198941003816 1003816 1003816 1003816

500)minus5

00)sin(radic1003816 1003816 1003816 10038165

00minusmod(1003816 1003816 1003816 1003816119910 1198941003816 1003816 1003816 1003816

500)1003816 1003816 1003816 1003816))

minus(119910119894+50

0)21000

0119899119894119891119910 119894

ltminus500

119911=1198725(10

00(119909minus119900 5) 100

)119900 3=

[119900 31119900 32

119900 3n]

30[minus10

0100]

500


Table1Con

tinued

FNam

eDescriptio

nDim

Ra

nge

Opt

119891 8(119909)

Zakh

arov

119891 8=119873 sum 119894=1119909 1198942+ (119873 sum 119894=105119894times

119909 1198942 )2

+ (119873 sum 119894=105119894times

119909 1198942 )4

30[minus10

10]0

119891 9(119909)

Dixon

-Pric

e119891 9=

119873 sum 119894=2119894(2119909 1198942

minus119909 119894minus1)2 +

(119909 119894minus1)2

30[minus10

10]0

119891 10(119909)

Perm

119891 10=119889 sum 119894=1(119889 sum 119895=1(119895119894+120573 )

((119909119895 119895)119894minus1 )

)230

[0120587]

-966

119891 11(119909)

Grie

wank

119891 11=1 4000119873 sum 119894=11199092


30[minus60

0600]

0

119891 12(119909)

Schw

efel

119891 12=119873 sum 119894=1[minus

119909 119894sin(radic1003816 1003816 1003816 1003816119909

1198941003816 1003816 1003816 1003816)]30

[minus50050

0]-418982d

119891 13(119909)

Rastr

igin

119891 13=119873 sum 119894=1(1199091198942minus10

cos(2120587

119909 119894)+10)

30[minus51

2512]

0

119891 14(119909)

Sum

ofdifferent

powe

rs119891 14=

(119873 sum 119894=11003816 1003816 1003816 1003816119909 1198941003816 1003816 1003816 1003816119894+1)

30[minus1

1]0

119891 15(119909)

Shub

ert

119891 15=(5 sum 119894=1119894

cos( (119894

+1 )119909 1+

119894))+(5 sum 119894=1119894

cos( (119894

+1 )119909 2+

119894))2

[minus1010]

-1867309

119891 16(119909)

Powe

ll119891 16=

1198894 sum 119894=1[(119909 4119894minus3

+10119909 4119894minus2

)2 +5(119909 4119894minus1minus119909 4119894


10(1199094119894minus3minus21199094119894)4 ]

30[minus4

5]0

119891 17(119909)

Drop-Wave

119891 17=1+c

os(12radic

119909 12 +119909 22 )

05(119909 12 +

119909 22 )+2

2[minus51

2512]

-1

119891 18(119909)

Levy

119891 18=sin2(120587120596 1

)+119889minus1 sum 119894=1(1205961minus1)2

[1+10sin2(120587120596 1

+1)]+(120596119889minus1)2

[1+10sin

2(2120587120596119889)]

30[minus10

10]0

119891 19(119909)

SumSquares

119891 19=119889 sum 119894=11198941199091198942

30[minus10

10]0

119891 20(119909)

Weierstr

ass

119891 20=119873 sum 119894=1(119896max sum 119896=0[119886119896 co

s(2120587119887119896 (119909119894+05

))]minus119899119896max sum 119896=0[

119886119896 cos(2120587

119887119896 times05)]

)30

[minus0505]

0


SFDEEPSDEMDE

CODEMDESELF


SFDEEPSDEMDE

CODEMDESELF

times105

10minus120

10minus100

10minus80

10minus60

10minus40

10minus20

100

1020Fu

nctio

n V

alue

200 400 600 800 1000 1200 1400 1600 1800 20000Iteration times

10minus15

10minus10

10minus5

100

105

1010

Func

tion

Val

ue

(a) Ackle Function

SFDEEPSDEMDE

CODEMDESELF

SFDEEPSDEMDE

CODEMDESELF

times105

minus102

minus101

minus100

Func

tion

Val

ue

200 400 600 800 1000 1200 1400 1600 1800 20000Iteration times

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue



SFDEEPSDEMDE

CODEMDESELF

times105

10minus30

10minus20

10minus10

100

1010

Func

tion

Val

ue

200 400 600 800 1000 1200 1400 1600 1800 20000

Iteration times

SFDEEPSDEMDE

CODEMDESELF



Func

tion

Val

ue




0

200

400

600

800

1000

1200

1400

1600

1800

2000


CODEMDESELF


SFDEEPSDEMDE

CODEMDESELF

times105


Func

tion

Val

ue

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue


0

200

400

600

800

1000

1200

1400

1600

1800

2000

Iteration times

SFDEEPSDEMDE

CODEMDESELF


SFDEEPSDEMDE

CODEMDESELF

times105


Func

tion

Val

ue

10minus20

100

1020

1040

1060

1080

10100

Func

tion

Val

ue

(b) Perm Function

0 50 100 150 200 250 300 350 400 450Iteration times

SFDEEPSDEMDE

CODEMDESELF

SFDEEPSDEMDE

CODEMDESELF



Func

tion

Val

ue

10minus20

10minus15

10minus10

10minus5

100

105

1010

Func

tion

Val

ue

(c) Sphere Function



0

200

400

600

800

1000

1200

1400

1600

1800


MDECODE

100

102

104

106

108

1010

1012

Func

tion

Val

ue

SFDEEPSDEMDE

CODEMDESELF

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue

times105



0

200

400

600

800

1000

1200

1400

1600

1800

2000

Iteration times

10minus20

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue


SFDEEPSDEMDE

CODEMDESELF


Func

tion

Val

ue

times105

SFDEEPSDEMDE

CODEMDESELF


SFDEEPSDEMDE

CODEMDESELF

SFDEEPSDEMDE

CODEMDESELF

times10505 1 15 2 25 3 35 40


10minus1100101102103104105106107

Func

tion

Val

ue

200

400

600

800

1000

1200

1400

1600

1800

20000

Iteration times

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue

















































Table 3 Continued







119891 (119909) = Nsumi=11199092119894 30







1199092119894) minus exp 1119873119873sum119894=1

cos (2120587119909119894) + 20 + 119890 30




1198790 z (n) = 120583 (n)1198791 119911 (n) = 119904 (n) + 120583 (n) (15)



W = 1119873119873sum119899=1

|119911 (119899)|2 (16)



119875119891 (120576) = 119875120591 (W gt 120576 | T0)= 1radic21205871205900 int

infin

119873119890minus(Wminus1205830)2212059020119889119909

= 119876(( 1205761205902120583) minus radic120591119891)(17)




(18)


Perceivedtime

Data transfer time

t T-t

Perceived time

Data transfer time

t T-t








119877 (120591) = 1198770 (120576 120591) + R1 (120576 120591) (21)





max 119877 (120591) = 1198770 (120576 120591)119904119905 119875119889 (120576 120591) ge 119875119889 (23)






119909119895119894 (0) = 119887119900119906119899119889119904 (i 1) + 00002 lowast 119903119886119899119889 (0 1) (25)











EPSDEMDECODE


4

45

5

55

sens

ing

time (

s)






2 3 4 5 6 7 8 9 1010

02

04

06

08

1

12


EPSDEMDECODE


sens

ing

time (

s)




6 Conclusion


Data Availability




Acknowledgments



References























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




119909119894 (119892 + 1) = 119906119894 (119892) 119894119891 119891 (119906119894 (119892)) le 119891 (119909119894 (119892))119909119894 (119892) 119900119905ℎ119890119903119908119894119904119890 (8)




119901119887119890119904119905119894 (119905) 119894119891 119891 (119883119894 (119905 + 1)) ge 119891 (119901119887119890119904119905119894 (119905))119883119894 (119905 + 1) 119894119891 119891 (119883119894 (119905 + 1)) lt 119891 (119901119887119890119904119905119894 (119905))(9)


119892119887119890119904119905 (119905) = min 119891 (1199011198871198901199041199051 (119905)) 119891 (1199011198871198901199041199052 (119905)) 119891 (119901119887119890119904119905119898 (119905)) (10)



119901119898119900V119890119894 = 119903119886119899119889 lowast (119901119887119890119904119905119894 minus 119901119908119900119903119904119905119894) (11)


119901119908119900119903119904119905119894= 119901119908119900119903119904119905119894+ 119901119898119900V119890119894 (minus119901119898119900V119890119898119886119909 ≪ 119901119898119900V119890119894 ≪ 119901119898119900V119890119898119886119909)

(12)



119901119908119900119903119904119905119894 = 119901119908119900119903119904119905119894 + 119901119898119900V119890119894(minus119901119898119900V119890119898119886119909 ≪ 119901119898119900V119890119894 ≪ 119901119898119900V119890119898119886119909) (14)
















pworst

pbestUpdated pworst

pmove







4 Experimentation






fw

fb

Group_1

fb

fw

Group_2

fb

fwGroup_3

gb

1 group computing


3 selection

SFLA DE




























Table1Detaileddefin

ition

softhe

testfunctio

nF

Nam

eDescriptio

nDim

Ra

nge

Opt

119891 1(119909)

Ackle

119891 1(119909)=minus

20exp(minus0

2radic1 119873119873 sum 119894=11199092 119894

)minusexp1 119873119873 sum 119894=1co

s (2120587119909 119894)+

20+119890

30[minus60

0600]

0

119891 2(119909)

Michalewicz

119891 2(119909)=minus

119873 sum 119894=1sin(119909 119894)

sin2119898(1198941199092 119894 120587

)119898=10

30[0120587

]-966

119891 3(119909)

Schw

efelrsquos

prob

lem

12119891 3(119909

)=119873 sum 119894=1

(119894 sum 119895119909 119894)2

30[minus50

0500]

0

119891 4(119909)

Sphere

119891 4(119909)=

N sum i=1

1199092 11989430

[minus50050

0]0

119891 5(119909)

Rosenb

rock

119891 5(119909)=Nminus1 sum i=1

(100(1199092 119894minus

119909 119894+1)2+(119909119894minus1)2

)30

[minus10010

0]0

119891 6(119909)

Rotated

Hyper-Ellipsoid

119891 6(119909)=119899 sum 119894=1119894 sum 119895=11199092 119895

30[minus65

536553]

0

119891 7(119909)

Shifted

and

Rotated

Schw

efelrsquos

Functio

n

119891 7(119909)=5

00+4189

829times119899minus119899 sum 119894=1119892(119910 119894)

119910 119894=119911 119894+

42096873

6119890+002

119892(119910 119894)=

119910 119894sin(1003816 1003816 1003816 1003816119910 1198941003816 1003816 1003816 100381612)

1198941198911003816 1003816 1003816 10038161199101198941003816 1003816 1003816 1003816le5

00((50

0minusmod(119910 1198945

00))sin(radic1003816 1003816 1003816 10038165

00minusmod(119910 1198945

00)1003816 1003816 1003816 1003816))minus

(119910 119894minus500)2

10000119899

119894119891119910 119894gt50

0((m

od(1003816 1003816 1003816 1003816119910 1198941003816 1003816 1003816 1003816

500)minus5

00)sin(radic1003816 1003816 1003816 10038165

00minusmod(1003816 1003816 1003816 1003816119910 1198941003816 1003816 1003816 1003816

500)1003816 1003816 1003816 1003816))

minus(119910119894+50

0)21000

0119899119894119891119910 119894

ltminus500

119911=1198725(10

00(119909minus119900 5) 100

)119900 3=

[119900 31119900 32

119900 3n]

30[minus10

0100]

500


Table1Con

tinued

FNam

eDescriptio

nDim

Ra

nge

Opt

119891 8(119909)

Zakh

arov

119891 8=119873 sum 119894=1119909 1198942+ (119873 sum 119894=105119894times

119909 1198942 )2

+ (119873 sum 119894=105119894times

119909 1198942 )4

30[minus10

10]0

119891 9(119909)

Dixon

-Pric

e119891 9=

119873 sum 119894=2119894(2119909 1198942

minus119909 119894minus1)2 +

(119909 119894minus1)2

30[minus10

10]0

119891 10(119909)

Perm

119891 10=119889 sum 119894=1(119889 sum 119895=1(119895119894+120573 )

((119909119895 119895)119894minus1 )

)230

[0120587]

-966

119891 11(119909)

Grie

wank

119891 11=1 4000119873 sum 119894=11199092


30[minus60

0600]

0

119891 12(119909)

Schw

efel

119891 12=119873 sum 119894=1[minus

119909 119894sin(radic1003816 1003816 1003816 1003816119909

1198941003816 1003816 1003816 1003816)]30

[minus50050

0]-418982d

119891 13(119909)

Rastr

igin

119891 13=119873 sum 119894=1(1199091198942minus10

cos(2120587

119909 119894)+10)

30[minus51

2512]

0

119891 14(119909)

Sum

ofdifferent

powe

rs119891 14=

(119873 sum 119894=11003816 1003816 1003816 1003816119909 1198941003816 1003816 1003816 1003816119894+1)

30[minus1

1]0

119891 15(119909)

Shub

ert

119891 15=(5 sum 119894=1119894

cos( (119894

+1 )119909 1+

119894))+(5 sum 119894=1119894

cos( (119894

+1 )119909 2+

119894))2

[minus1010]

-1867309

119891 16(119909)

Powe

ll119891 16=

1198894 sum 119894=1[(119909 4119894minus3

+10119909 4119894minus2

)2 +5(119909 4119894minus1minus119909 4119894


10(1199094119894minus3minus21199094119894)4 ]

30[minus4

5]0

119891 17(119909)

Drop-Wave

119891 17=1+c

os(12radic

119909 12 +119909 22 )

05(119909 12 +

119909 22 )+2

2[minus51

2512]

-1

119891 18(119909)

Levy

119891 18=sin2(120587120596 1

)+119889minus1 sum 119894=1(1205961minus1)2

[1+10sin2(120587120596 1

+1)]+(120596119889minus1)2

[1+10sin

2(2120587120596119889)]

30[minus10

10]0

119891 19(119909)

SumSquares

119891 19=119889 sum 119894=11198941199091198942

30[minus10

10]0

119891 20(119909)

Weierstr

ass

119891 20=119873 sum 119894=1(119896max sum 119896=0[119886119896 co

s(2120587119887119896 (119909119894+05

))]minus119899119896max sum 119896=0[

119886119896 cos(2120587

119887119896 times05)]

)30

[minus0505]

0


SFDEEPSDEMDE

CODEMDESELF


SFDEEPSDEMDE

CODEMDESELF

times105

10minus120

10minus100

10minus80

10minus60

10minus40

10minus20

100

1020Fu

nctio

n V

alue

200 400 600 800 1000 1200 1400 1600 1800 20000Iteration times

10minus15

10minus10

10minus5

100

105

1010

Func

tion

Val

ue

(a) Ackle Function

SFDEEPSDEMDE

CODEMDESELF

SFDEEPSDEMDE

CODEMDESELF

times105

minus102

minus101

minus100

Func

tion

Val

ue

200 400 600 800 1000 1200 1400 1600 1800 20000Iteration times

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue



SFDEEPSDEMDE

CODEMDESELF

times105

10minus30

10minus20

10minus10

100

1010

Func

tion

Val

ue

200 400 600 800 1000 1200 1400 1600 1800 20000

Iteration times

SFDEEPSDEMDE

CODEMDESELF



Func

tion

Val

ue




0

200

400

600

800

1000

1200

1400

1600

1800

2000


CODEMDESELF


SFDEEPSDEMDE

CODEMDESELF

times105


Func

tion

Val

ue

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue


0

200

400

600

800

1000

1200

1400

1600

1800

2000

Iteration times

SFDEEPSDEMDE

CODEMDESELF


SFDEEPSDEMDE

CODEMDESELF

times105


Func

tion

Val

ue

10minus20

100

1020

1040

1060

1080

10100

Func

tion

Val

ue

(b) Perm Function

0 50 100 150 200 250 300 350 400 450Iteration times

SFDEEPSDEMDE

CODEMDESELF

SFDEEPSDEMDE

CODEMDESELF



Func

tion

Val

ue

10minus20

10minus15

10minus10

10minus5

100

105

1010

Func

tion

Val

ue

(c) Sphere Function



0

200

400

600

800

1000

1200

1400

1600

1800


MDECODE

100

102

104

106

108

1010

1012

Func

tion

Val

ue

SFDEEPSDEMDE

CODEMDESELF

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue

times105



0

200

400

600

800

1000

1200

1400

1600

1800

2000

Iteration times

10minus20

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue


SFDEEPSDEMDE

CODEMDESELF


Func

tion

Val

ue

times105

SFDEEPSDEMDE

CODEMDESELF


SFDEEPSDEMDE

CODEMDESELF

SFDEEPSDEMDE

CODEMDESELF

times10505 1 15 2 25 3 35 40


10minus1100101102103104105106107

Func

tion

Val

ue

200

400

600

800

1000

1200

1400

1600

1800

20000

Iteration times

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue

















































Table 3 Continued







119891 (119909) = Nsumi=11199092119894 30







1199092119894) minus exp 1119873119873sum119894=1

cos (2120587119909119894) + 20 + 119890 30




1198790 z (n) = 120583 (n)1198791 119911 (n) = 119904 (n) + 120583 (n) (15)



W = 1119873119873sum119899=1

|119911 (119899)|2 (16)



119875119891 (120576) = 119875120591 (W gt 120576 | T0)= 1radic21205871205900 int

infin

119873119890minus(Wminus1205830)2212059020119889119909

= 119876(( 1205761205902120583) minus radic120591119891)(17)




(18)


Perceivedtime

Data transfer time

t T-t

Perceived time

Data transfer time

t T-t








119877 (120591) = 1198770 (120576 120591) + R1 (120576 120591) (21)





max 119877 (120591) = 1198770 (120576 120591)119904119905 119875119889 (120576 120591) ge 119875119889 (23)






119909119895119894 (0) = 119887119900119906119899119889119904 (i 1) + 00002 lowast 119903119886119899119889 (0 1) (25)











EPSDEMDECODE


4

45

5

55

sens

ing

time (

s)






2 3 4 5 6 7 8 9 1010

02

04

06

08

1

12


EPSDEMDECODE


sens

ing

time (

s)




6 Conclusion


Data Availability




Acknowledgments



References























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia













pworst

pbestUpdated pworst

pmove







4 Experimentation






fw

fb

Group_1

fb

fw

Group_2

fb

fwGroup_3

gb

1 group computing


3 selection

SFLA DE




























Table1Detaileddefin

ition

softhe

testfunctio

nF

Nam

eDescriptio

nDim

Ra

nge

Opt

119891 1(119909)

Ackle

119891 1(119909)=minus

20exp(minus0

2radic1 119873119873 sum 119894=11199092 119894

)minusexp1 119873119873 sum 119894=1co

s (2120587119909 119894)+

20+119890

30[minus60

0600]

0

119891 2(119909)

Michalewicz

119891 2(119909)=minus

119873 sum 119894=1sin(119909 119894)

sin2119898(1198941199092 119894 120587

)119898=10

30[0120587

]-966

119891 3(119909)

Schw

efelrsquos

prob

lem

12119891 3(119909

)=119873 sum 119894=1

(119894 sum 119895119909 119894)2

30[minus50

0500]

0

119891 4(119909)

Sphere

119891 4(119909)=

N sum i=1

1199092 11989430

[minus50050

0]0

119891 5(119909)

Rosenb

rock

119891 5(119909)=Nminus1 sum i=1

(100(1199092 119894minus

119909 119894+1)2+(119909119894minus1)2

)30

[minus10010

0]0

119891 6(119909)

Rotated

Hyper-Ellipsoid

119891 6(119909)=119899 sum 119894=1119894 sum 119895=11199092 119895

30[minus65

536553]

0

119891 7(119909)

Shifted

and

Rotated

Schw

efelrsquos

Functio

n

119891 7(119909)=5

00+4189

829times119899minus119899 sum 119894=1119892(119910 119894)

119910 119894=119911 119894+

42096873

6119890+002

119892(119910 119894)=

119910 119894sin(1003816 1003816 1003816 1003816119910 1198941003816 1003816 1003816 100381612)

1198941198911003816 1003816 1003816 10038161199101198941003816 1003816 1003816 1003816le5

00((50

0minusmod(119910 1198945

00))sin(radic1003816 1003816 1003816 10038165

00minusmod(119910 1198945

00)1003816 1003816 1003816 1003816))minus

(119910 119894minus500)2

10000119899

119894119891119910 119894gt50

0((m

od(1003816 1003816 1003816 1003816119910 1198941003816 1003816 1003816 1003816

500)minus5

00)sin(radic1003816 1003816 1003816 10038165

00minusmod(1003816 1003816 1003816 1003816119910 1198941003816 1003816 1003816 1003816

500)1003816 1003816 1003816 1003816))

minus(119910119894+50

0)21000

0119899119894119891119910 119894

ltminus500

119911=1198725(10

00(119909minus119900 5) 100

)119900 3=

[119900 31119900 32

119900 3n]

30[minus10

0100]

500


Table1Con

tinued

FNam

eDescriptio

nDim

Ra

nge

Opt

119891 8(119909)

Zakh

arov

119891 8=119873 sum 119894=1119909 1198942+ (119873 sum 119894=105119894times

119909 1198942 )2

+ (119873 sum 119894=105119894times

119909 1198942 )4

30[minus10

10]0

119891 9(119909)

Dixon

-Pric

e119891 9=

119873 sum 119894=2119894(2119909 1198942

minus119909 119894minus1)2 +

(119909 119894minus1)2

30[minus10

10]0

119891 10(119909)

Perm

119891 10=119889 sum 119894=1(119889 sum 119895=1(119895119894+120573 )

((119909119895 119895)119894minus1 )

)230

[0120587]

-966

119891 11(119909)

Grie

wank

119891 11=1 4000119873 sum 119894=11199092


30[minus60

0600]

0

119891 12(119909)

Schw

efel

119891 12=119873 sum 119894=1[minus

119909 119894sin(radic1003816 1003816 1003816 1003816119909

1198941003816 1003816 1003816 1003816)]30

[minus50050

0]-418982d

119891 13(119909)

Rastr

igin

119891 13=119873 sum 119894=1(1199091198942minus10

cos(2120587

119909 119894)+10)

30[minus51

2512]

0

119891 14(119909)

Sum

ofdifferent

powe

rs119891 14=

(119873 sum 119894=11003816 1003816 1003816 1003816119909 1198941003816 1003816 1003816 1003816119894+1)

30[minus1

1]0

119891 15(119909)

Shub

ert

119891 15=(5 sum 119894=1119894

cos( (119894

+1 )119909 1+

119894))+(5 sum 119894=1119894

cos( (119894

+1 )119909 2+

119894))2

[minus1010]

-1867309

119891 16(119909)

Powe

ll119891 16=

1198894 sum 119894=1[(119909 4119894minus3

+10119909 4119894minus2

)2 +5(119909 4119894minus1minus119909 4119894


10(1199094119894minus3minus21199094119894)4 ]

30[minus4

5]0

119891 17(119909)

Drop-Wave

119891 17=1+c

os(12radic

119909 12 +119909 22 )

05(119909 12 +

119909 22 )+2

2[minus51

2512]

-1

119891 18(119909)

Levy

119891 18=sin2(120587120596 1

)+119889minus1 sum 119894=1(1205961minus1)2

[1+10sin2(120587120596 1

+1)]+(120596119889minus1)2

[1+10sin

2(2120587120596119889)]

30[minus10

10]0

119891 19(119909)

SumSquares

119891 19=119889 sum 119894=11198941199091198942

30[minus10

10]0

119891 20(119909)

Weierstr

ass

119891 20=119873 sum 119894=1(119896max sum 119896=0[119886119896 co

s(2120587119887119896 (119909119894+05

))]minus119899119896max sum 119896=0[

119886119896 cos(2120587

119887119896 times05)]

)30

[minus0505]

0


SFDEEPSDEMDE

CODEMDESELF


SFDEEPSDEMDE

CODEMDESELF

times105

10minus120

10minus100

10minus80

10minus60

10minus40

10minus20

100

1020Fu

nctio

n V

alue

200 400 600 800 1000 1200 1400 1600 1800 20000Iteration times

10minus15

10minus10

10minus5

100

105

1010

Func

tion

Val

ue

(a) Ackle Function

SFDEEPSDEMDE

CODEMDESELF

SFDEEPSDEMDE

CODEMDESELF

times105

minus102

minus101

minus100

Func

tion

Val

ue

200 400 600 800 1000 1200 1400 1600 1800 20000Iteration times

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue



SFDEEPSDEMDE

CODEMDESELF

times105

10minus30

10minus20

10minus10

100

1010

Func

tion

Val

ue

200 400 600 800 1000 1200 1400 1600 1800 20000

Iteration times

SFDEEPSDEMDE

CODEMDESELF



Func

tion

Val

ue




0

200

400

600

800

1000

1200

1400

1600

1800

2000


CODEMDESELF


SFDEEPSDEMDE

CODEMDESELF

times105


Func

tion

Val

ue

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue


0

200

400

600

800

1000

1200

1400

1600

1800

2000

Iteration times

SFDEEPSDEMDE

CODEMDESELF


SFDEEPSDEMDE

CODEMDESELF

times105


Func

tion

Val

ue

10minus20

100

1020

1040

1060

1080

10100

Func

tion

Val

ue

(b) Perm Function

0 50 100 150 200 250 300 350 400 450Iteration times

SFDEEPSDEMDE

CODEMDESELF

SFDEEPSDEMDE

CODEMDESELF



Func

tion

Val

ue

10minus20

10minus15

10minus10

10minus5

100

105

1010

Func

tion

Val

ue

(c) Sphere Function



0

200

400

600

800

1000

1200

1400

1600

1800


MDECODE

100

102

104

106

108

1010

1012

Func

tion

Val

ue

SFDEEPSDEMDE

CODEMDESELF

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue

times105



0

200

400

600

800

1000

1200

1400

1600

1800

2000

Iteration times

10minus20

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue


SFDEEPSDEMDE

CODEMDESELF


Func

tion

Val

ue

times105

SFDEEPSDEMDE

CODEMDESELF


SFDEEPSDEMDE

CODEMDESELF

SFDEEPSDEMDE

CODEMDESELF

times10505 1 15 2 25 3 35 40


10minus1100101102103104105106107

Func

tion

Val

ue

200

400

600

800

1000

1200

1400

1600

1800

20000

Iteration times

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue

















































Table 3 Continued







119891 (119909) = Nsumi=11199092119894 30







1199092119894) minus exp 1119873119873sum119894=1

cos (2120587119909119894) + 20 + 119890 30




1198790 z (n) = 120583 (n)1198791 119911 (n) = 119904 (n) + 120583 (n) (15)



W = 1119873119873sum119899=1

|119911 (119899)|2 (16)



119875119891 (120576) = 119875120591 (W gt 120576 | T0)= 1radic21205871205900 int

infin

119873119890minus(Wminus1205830)2212059020119889119909

= 119876(( 1205761205902120583) minus radic120591119891)(17)




(18)


Perceivedtime

Data transfer time

t T-t

Perceived time

Data transfer time

t T-t








119877 (120591) = 1198770 (120576 120591) + R1 (120576 120591) (21)





max 119877 (120591) = 1198770 (120576 120591)119904119905 119875119889 (120576 120591) ge 119875119889 (23)






119909119895119894 (0) = 119887119900119906119899119889119904 (i 1) + 00002 lowast 119903119886119899119889 (0 1) (25)











EPSDEMDECODE


4

45

5

55

sens

ing

time (

s)






2 3 4 5 6 7 8 9 1010

02

04

06

08

1

12


EPSDEMDECODE


sens

ing

time (

s)




6 Conclusion


Data Availability




Acknowledgments



References























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



fw

fb

Group_1

fb

fw

Group_2

fb

fwGroup_3

gb

1 group computing


3 selection

SFLA DE




























Table1Detaileddefin

ition

softhe

testfunctio

nF

Nam

eDescriptio

nDim

Ra

nge

Opt

119891 1(119909)

Ackle

119891 1(119909)=minus

20exp(minus0

2radic1 119873119873 sum 119894=11199092 119894

)minusexp1 119873119873 sum 119894=1co

s (2120587119909 119894)+

20+119890

30[minus60

0600]

0

119891 2(119909)

Michalewicz

119891 2(119909)=minus

119873 sum 119894=1sin(119909 119894)

sin2119898(1198941199092 119894 120587

)119898=10

30[0120587

]-966

119891 3(119909)

Schw

efelrsquos

prob

lem

12119891 3(119909

)=119873 sum 119894=1

(119894 sum 119895119909 119894)2

30[minus50

0500]

0

119891 4(119909)

Sphere

119891 4(119909)=

N sum i=1

1199092 11989430

[minus50050

0]0

119891 5(119909)

Rosenb

rock

119891 5(119909)=Nminus1 sum i=1

(100(1199092 119894minus

119909 119894+1)2+(119909119894minus1)2

)30

[minus10010

0]0

119891 6(119909)

Rotated

Hyper-Ellipsoid

119891 6(119909)=119899 sum 119894=1119894 sum 119895=11199092 119895

30[minus65

536553]

0

119891 7(119909)

Shifted

and

Rotated

Schw

efelrsquos

Functio

n

119891 7(119909)=5

00+4189

829times119899minus119899 sum 119894=1119892(119910 119894)

119910 119894=119911 119894+

42096873

6119890+002

119892(119910 119894)=

119910 119894sin(1003816 1003816 1003816 1003816119910 1198941003816 1003816 1003816 100381612)

1198941198911003816 1003816 1003816 10038161199101198941003816 1003816 1003816 1003816le5

00((50

0minusmod(119910 1198945

00))sin(radic1003816 1003816 1003816 10038165

00minusmod(119910 1198945

00)1003816 1003816 1003816 1003816))minus

(119910 119894minus500)2

10000119899

119894119891119910 119894gt50

0((m

od(1003816 1003816 1003816 1003816119910 1198941003816 1003816 1003816 1003816

500)minus5

00)sin(radic1003816 1003816 1003816 10038165

00minusmod(1003816 1003816 1003816 1003816119910 1198941003816 1003816 1003816 1003816

500)1003816 1003816 1003816 1003816))

minus(119910119894+50

0)21000

0119899119894119891119910 119894

ltminus500

119911=1198725(10

00(119909minus119900 5) 100

)119900 3=

[119900 31119900 32

119900 3n]

30[minus10

0100]

500


Table1Con

tinued

FNam

eDescriptio

nDim

Ra

nge

Opt

119891 8(119909)

Zakh

arov

119891 8=119873 sum 119894=1119909 1198942+ (119873 sum 119894=105119894times

119909 1198942 )2

+ (119873 sum 119894=105119894times

119909 1198942 )4

30[minus10

10]0

119891 9(119909)

Dixon

-Pric

e119891 9=

119873 sum 119894=2119894(2119909 1198942

minus119909 119894minus1)2 +

(119909 119894minus1)2

30[minus10

10]0

119891 10(119909)

Perm

119891 10=119889 sum 119894=1(119889 sum 119895=1(119895119894+120573 )

((119909119895 119895)119894minus1 )

)230

[0120587]

-966

119891 11(119909)

Grie

wank

119891 11=1 4000119873 sum 119894=11199092


30[minus60

0600]

0

119891 12(119909)

Schw

efel

119891 12=119873 sum 119894=1[minus

119909 119894sin(radic1003816 1003816 1003816 1003816119909

1198941003816 1003816 1003816 1003816)]30

[minus50050

0]-418982d

119891 13(119909)

Rastr

igin

119891 13=119873 sum 119894=1(1199091198942minus10

cos(2120587

119909 119894)+10)

30[minus51

2512]

0

119891 14(119909)

Sum

ofdifferent

powe

rs119891 14=

(119873 sum 119894=11003816 1003816 1003816 1003816119909 1198941003816 1003816 1003816 1003816119894+1)

30[minus1

1]0

119891 15(119909)

Shub

ert

119891 15=(5 sum 119894=1119894

cos( (119894

+1 )119909 1+

119894))+(5 sum 119894=1119894

cos( (119894

+1 )119909 2+

119894))2

[minus1010]

-1867309

119891 16(119909)

Powe

ll119891 16=

1198894 sum 119894=1[(119909 4119894minus3

+10119909 4119894minus2

)2 +5(119909 4119894minus1minus119909 4119894


10(1199094119894minus3minus21199094119894)4 ]

30[minus4

5]0

119891 17(119909)

Drop-Wave

119891 17=1+c

os(12radic

119909 12 +119909 22 )

05(119909 12 +

119909 22 )+2

2[minus51

2512]

-1

119891 18(119909)

Levy

119891 18=sin2(120587120596 1

)+119889minus1 sum 119894=1(1205961minus1)2

[1+10sin2(120587120596 1

+1)]+(120596119889minus1)2

[1+10sin

2(2120587120596119889)]

30[minus10

10]0

119891 19(119909)

SumSquares

119891 19=119889 sum 119894=11198941199091198942

30[minus10

10]0

119891 20(119909)

Weierstr

ass

119891 20=119873 sum 119894=1(119896max sum 119896=0[119886119896 co

s(2120587119887119896 (119909119894+05

))]minus119899119896max sum 119896=0[

119886119896 cos(2120587

119887119896 times05)]

)30

[minus0505]

0


SFDEEPSDEMDE

CODEMDESELF


SFDEEPSDEMDE

CODEMDESELF

times105

10minus120

10minus100

10minus80

10minus60

10minus40

10minus20

100

1020Fu

nctio

n V

alue

200 400 600 800 1000 1200 1400 1600 1800 20000Iteration times

10minus15

10minus10

10minus5

100

105

1010

Func

tion

Val

ue

(a) Ackle Function

SFDEEPSDEMDE

CODEMDESELF

SFDEEPSDEMDE

CODEMDESELF

times105

minus102

minus101

minus100

Func

tion

Val

ue

200 400 600 800 1000 1200 1400 1600 1800 20000Iteration times

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue



SFDEEPSDEMDE

CODEMDESELF

times105

10minus30

10minus20

10minus10

100

1010

Func

tion

Val

ue

200 400 600 800 1000 1200 1400 1600 1800 20000

Iteration times

SFDEEPSDEMDE

CODEMDESELF



Func

tion

Val

ue




0

200

400

600

800

1000

1200

1400

1600

1800

2000


CODEMDESELF


SFDEEPSDEMDE

CODEMDESELF

times105


Func

tion

Val

ue

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue


0

200

400

600

800

1000

1200

1400

1600

1800

2000

Iteration times

SFDEEPSDEMDE

CODEMDESELF


SFDEEPSDEMDE

CODEMDESELF

times105


Func

tion

Val

ue

10minus20

100

1020

1040

1060

1080

10100

Func

tion

Val

ue

(b) Perm Function

0 50 100 150 200 250 300 350 400 450Iteration times

SFDEEPSDEMDE

CODEMDESELF

SFDEEPSDEMDE

CODEMDESELF



Func

tion

Val

ue

10minus20

10minus15

10minus10

10minus5

100

105

1010

Func

tion

Val

ue

(c) Sphere Function



0

200

400

600

800

1000

1200

1400

1600

1800


MDECODE

100

102

104

106

108

1010

1012

Func

tion

Val

ue

SFDEEPSDEMDE

CODEMDESELF

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue

times105



0

200

400

600

800

1000

1200

1400

1600

1800

2000

Iteration times

10minus20

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue


SFDEEPSDEMDE

CODEMDESELF


Func

tion

Val

ue

times105

SFDEEPSDEMDE

CODEMDESELF


SFDEEPSDEMDE

CODEMDESELF

SFDEEPSDEMDE

CODEMDESELF

times10505 1 15 2 25 3 35 40


10minus1100101102103104105106107

Func

tion

Val

ue

200

400

600

800

1000

1200

1400

1600

1800

20000

Iteration times

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue

















































Table 3 Continued







119891 (119909) = Nsumi=11199092119894 30







1199092119894) minus exp 1119873119873sum119894=1

cos (2120587119909119894) + 20 + 119890 30




1198790 z (n) = 120583 (n)1198791 119911 (n) = 119904 (n) + 120583 (n) (15)



W = 1119873119873sum119899=1

|119911 (119899)|2 (16)



119875119891 (120576) = 119875120591 (W gt 120576 | T0)= 1radic21205871205900 int

infin

119873119890minus(Wminus1205830)2212059020119889119909

= 119876(( 1205761205902120583) minus radic120591119891)(17)




(18)


Perceivedtime

Data transfer time

t T-t

Perceived time

Data transfer time

t T-t








119877 (120591) = 1198770 (120576 120591) + R1 (120576 120591) (21)





max 119877 (120591) = 1198770 (120576 120591)119904119905 119875119889 (120576 120591) ge 119875119889 (23)






119909119895119894 (0) = 119887119900119906119899119889119904 (i 1) + 00002 lowast 119903119886119899119889 (0 1) (25)











EPSDEMDECODE


4

45

5

55

sens

ing

time (

s)






2 3 4 5 6 7 8 9 1010

02

04

06

08

1

12


EPSDEMDECODE


sens

ing

time (

s)




6 Conclusion


Data Availability




Acknowledgments



References























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


















Table1Detaileddefin

ition

softhe

testfunctio

nF

Nam

eDescriptio

nDim

Ra

nge

Opt

119891 1(119909)

Ackle

119891 1(119909)=minus

20exp(minus0

2radic1 119873119873 sum 119894=11199092 119894

)minusexp1 119873119873 sum 119894=1co

s (2120587119909 119894)+

20+119890

30[minus60

0600]

0

119891 2(119909)

Michalewicz

119891 2(119909)=minus

119873 sum 119894=1sin(119909 119894)

sin2119898(1198941199092 119894 120587

)119898=10

30[0120587

]-966

119891 3(119909)

Schw

efelrsquos

prob

lem

12119891 3(119909

)=119873 sum 119894=1

(119894 sum 119895119909 119894)2

30[minus50

0500]

0

119891 4(119909)

Sphere

119891 4(119909)=

N sum i=1

1199092 11989430

[minus50050

0]0

119891 5(119909)

Rosenb

rock

119891 5(119909)=Nminus1 sum i=1

(100(1199092 119894minus

119909 119894+1)2+(119909119894minus1)2

)30

[minus10010

0]0

119891 6(119909)

Rotated

Hyper-Ellipsoid

119891 6(119909)=119899 sum 119894=1119894 sum 119895=11199092 119895

30[minus65

536553]

0

119891 7(119909)

Shifted

and

Rotated

Schw

efelrsquos

Functio

n

119891 7(119909)=5

00+4189

829times119899minus119899 sum 119894=1119892(119910 119894)

119910 119894=119911 119894+

42096873

6119890+002

119892(119910 119894)=

119910 119894sin(1003816 1003816 1003816 1003816119910 1198941003816 1003816 1003816 100381612)

1198941198911003816 1003816 1003816 10038161199101198941003816 1003816 1003816 1003816le5

00((50

0minusmod(119910 1198945

00))sin(radic1003816 1003816 1003816 10038165

00minusmod(119910 1198945

00)1003816 1003816 1003816 1003816))minus

(119910 119894minus500)2

10000119899

119894119891119910 119894gt50

0((m

od(1003816 1003816 1003816 1003816119910 1198941003816 1003816 1003816 1003816

500)minus5

00)sin(radic1003816 1003816 1003816 10038165

00minusmod(1003816 1003816 1003816 1003816119910 1198941003816 1003816 1003816 1003816

500)1003816 1003816 1003816 1003816))

minus(119910119894+50

0)21000

0119899119894119891119910 119894

ltminus500

119911=1198725(10

00(119909minus119900 5) 100

)119900 3=

[119900 31119900 32

119900 3n]

30[minus10

0100]

500


Table1Con

tinued

FNam

eDescriptio

nDim

Ra

nge

Opt

119891 8(119909)

Zakh

arov

119891 8=119873 sum 119894=1119909 1198942+ (119873 sum 119894=105119894times

119909 1198942 )2

+ (119873 sum 119894=105119894times

119909 1198942 )4

30[minus10

10]0

119891 9(119909)

Dixon

-Pric

e119891 9=

119873 sum 119894=2119894(2119909 1198942

minus119909 119894minus1)2 +

(119909 119894minus1)2

30[minus10

10]0

119891 10(119909)

Perm

119891 10=119889 sum 119894=1(119889 sum 119895=1(119895119894+120573 )

((119909119895 119895)119894minus1 )

)230

[0120587]

-966

119891 11(119909)

Grie

wank

119891 11=1 4000119873 sum 119894=11199092


30[minus60

0600]

0

119891 12(119909)

Schw

efel

119891 12=119873 sum 119894=1[minus

119909 119894sin(radic1003816 1003816 1003816 1003816119909

1198941003816 1003816 1003816 1003816)]30

[minus50050

0]-418982d

119891 13(119909)

Rastr

igin

119891 13=119873 sum 119894=1(1199091198942minus10

cos(2120587

119909 119894)+10)

30[minus51

2512]

0

119891 14(119909)

Sum

ofdifferent

powe

rs119891 14=

(119873 sum 119894=11003816 1003816 1003816 1003816119909 1198941003816 1003816 1003816 1003816119894+1)

30[minus1

1]0

119891 15(119909)

Shub

ert

119891 15=(5 sum 119894=1119894

cos( (119894

+1 )119909 1+

119894))+(5 sum 119894=1119894

cos( (119894

+1 )119909 2+

119894))2

[minus1010]

-1867309

119891 16(119909)

Powe

ll119891 16=

1198894 sum 119894=1[(119909 4119894minus3

+10119909 4119894minus2

)2 +5(119909 4119894minus1minus119909 4119894


10(1199094119894minus3minus21199094119894)4 ]

30[minus4

5]0

119891 17(119909)

Drop-Wave

119891 17=1+c

os(12radic

119909 12 +119909 22 )

05(119909 12 +

119909 22 )+2

2[minus51

2512]

-1

119891 18(119909)

Levy

119891 18=sin2(120587120596 1

)+119889minus1 sum 119894=1(1205961minus1)2

[1+10sin2(120587120596 1

+1)]+(120596119889minus1)2

[1+10sin

2(2120587120596119889)]

30[minus10

10]0

119891 19(119909)

SumSquares

119891 19=119889 sum 119894=11198941199091198942

30[minus10

10]0

119891 20(119909)

Weierstr

ass

119891 20=119873 sum 119894=1(119896max sum 119896=0[119886119896 co

s(2120587119887119896 (119909119894+05

))]minus119899119896max sum 119896=0[

119886119896 cos(2120587

119887119896 times05)]

)30

[minus0505]

0


SFDEEPSDEMDE

CODEMDESELF


SFDEEPSDEMDE

CODEMDESELF

times105

10minus120

10minus100

10minus80

10minus60

10minus40

10minus20

100

1020Fu

nctio

n V

alue

200 400 600 800 1000 1200 1400 1600 1800 20000Iteration times

10minus15

10minus10

10minus5

100

105

1010

Func

tion

Val

ue

(a) Ackle Function

SFDEEPSDEMDE

CODEMDESELF

SFDEEPSDEMDE

CODEMDESELF

times105

minus102

minus101

minus100

Func

tion

Val

ue

200 400 600 800 1000 1200 1400 1600 1800 20000Iteration times

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue



SFDEEPSDEMDE

CODEMDESELF

times105

10minus30

10minus20

10minus10

100

1010

Func

tion

Val

ue

200 400 600 800 1000 1200 1400 1600 1800 20000

Iteration times

SFDEEPSDEMDE

CODEMDESELF



Func

tion

Val

ue




0

200

400

600

800

1000

1200

1400

1600

1800

2000


CODEMDESELF


SFDEEPSDEMDE

CODEMDESELF

times105


Func

tion

Val

ue

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue


0

200

400

600

800

1000

1200

1400

1600

1800

2000

Iteration times

SFDEEPSDEMDE

CODEMDESELF


SFDEEPSDEMDE

CODEMDESELF

times105


Func

tion

Val

ue

10minus20

100

1020

1040

1060

1080

10100

Func

tion

Val

ue

(b) Perm Function

0 50 100 150 200 250 300 350 400 450Iteration times

SFDEEPSDEMDE

CODEMDESELF

SFDEEPSDEMDE

CODEMDESELF



Func

tion

Val

ue

10minus20

10minus15

10minus10

10minus5

100

105

1010

Func

tion

Val

ue

(c) Sphere Function



0

200

400

600

800

1000

1200

1400

1600

1800


MDECODE

100

102

104

106

108

1010

1012

Func

tion

Val

ue

SFDEEPSDEMDE

CODEMDESELF

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue

times105



0

200

400

600

800

1000

1200

1400

1600

1800

2000

Iteration times

10minus20

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue


SFDEEPSDEMDE

CODEMDESELF


Func

tion

Val

ue

times105

SFDEEPSDEMDE

CODEMDESELF


SFDEEPSDEMDE

CODEMDESELF

SFDEEPSDEMDE

CODEMDESELF

times10505 1 15 2 25 3 35 40


10minus1100101102103104105106107

Func

tion

Val

ue

200

400

600

800

1000

1200

1400

1600

1800

20000

Iteration times

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue

















































Table 3 Continued







119891 (119909) = Nsumi=11199092119894 30







1199092119894) minus exp 1119873119873sum119894=1

cos (2120587119909119894) + 20 + 119890 30




1198790 z (n) = 120583 (n)1198791 119911 (n) = 119904 (n) + 120583 (n) (15)



W = 1119873119873sum119899=1

|119911 (119899)|2 (16)



119875119891 (120576) = 119875120591 (W gt 120576 | T0)= 1radic21205871205900 int

infin

119873119890minus(Wminus1205830)2212059020119889119909

= 119876(( 1205761205902120583) minus radic120591119891)(17)




(18)


Perceivedtime

Data transfer time

t T-t

Perceived time

Data transfer time

t T-t








119877 (120591) = 1198770 (120576 120591) + R1 (120576 120591) (21)





max 119877 (120591) = 1198770 (120576 120591)119904119905 119875119889 (120576 120591) ge 119875119889 (23)






119909119895119894 (0) = 119887119900119906119899119889119904 (i 1) + 00002 lowast 119903119886119899119889 (0 1) (25)











EPSDEMDECODE


4

45

5

55

sens

ing

time (

s)






2 3 4 5 6 7 8 9 1010

02

04

06

08

1

12


EPSDEMDECODE


sens

ing

time (

s)




6 Conclusion


Data Availability




Acknowledgments



References























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Table1Con

tinued

FNam

eDescriptio

nDim

Ra

nge

Opt

119891 8(119909)

Zakh

arov

119891 8=119873 sum 119894=1119909 1198942+ (119873 sum 119894=105119894times

119909 1198942 )2

+ (119873 sum 119894=105119894times

119909 1198942 )4

30[minus10

10]0

119891 9(119909)

Dixon

-Pric

e119891 9=

119873 sum 119894=2119894(2119909 1198942

minus119909 119894minus1)2 +

(119909 119894minus1)2

30[minus10

10]0

119891 10(119909)

Perm

119891 10=119889 sum 119894=1(119889 sum 119895=1(119895119894+120573 )

((119909119895 119895)119894minus1 )

)230

[0120587]

-966

119891 11(119909)

Grie

wank

119891 11=1 4000119873 sum 119894=11199092


30[minus60

0600]

0

119891 12(119909)

Schw

efel

119891 12=119873 sum 119894=1[minus

119909 119894sin(radic1003816 1003816 1003816 1003816119909

1198941003816 1003816 1003816 1003816)]30

[minus50050

0]-418982d

119891 13(119909)

Rastr

igin

119891 13=119873 sum 119894=1(1199091198942minus10

cos(2120587

119909 119894)+10)

30[minus51

2512]

0

119891 14(119909)

Sum

ofdifferent

powe

rs119891 14=

(119873 sum 119894=11003816 1003816 1003816 1003816119909 1198941003816 1003816 1003816 1003816119894+1)

30[minus1

1]0

119891 15(119909)

Shub

ert

119891 15=(5 sum 119894=1119894

cos( (119894

+1 )119909 1+

119894))+(5 sum 119894=1119894

cos( (119894

+1 )119909 2+

119894))2

[minus1010]

-1867309

119891 16(119909)

Powe

ll119891 16=

1198894 sum 119894=1[(119909 4119894minus3

+10119909 4119894minus2

)2 +5(119909 4119894minus1minus119909 4119894


10(1199094119894minus3minus21199094119894)4 ]

30[minus4

5]0

119891 17(119909)

Drop-Wave

119891 17=1+c

os(12radic

119909 12 +119909 22 )

05(119909 12 +

119909 22 )+2

2[minus51

2512]

-1

119891 18(119909)

Levy

119891 18=sin2(120587120596 1

)+119889minus1 sum 119894=1(1205961minus1)2

[1+10sin2(120587120596 1

+1)]+(120596119889minus1)2

[1+10sin

2(2120587120596119889)]

30[minus10

10]0

119891 19(119909)

SumSquares

119891 19=119889 sum 119894=11198941199091198942

30[minus10

10]0

119891 20(119909)

Weierstr

ass

119891 20=119873 sum 119894=1(119896max sum 119896=0[119886119896 co

s(2120587119887119896 (119909119894+05

))]minus119899119896max sum 119896=0[

119886119896 cos(2120587

119887119896 times05)]

)30

[minus0505]

0


SFDEEPSDEMDE

CODEMDESELF


SFDEEPSDEMDE

CODEMDESELF

times105

10minus120

10minus100

10minus80

10minus60

10minus40

10minus20

100

1020Fu

nctio

n V

alue

200 400 600 800 1000 1200 1400 1600 1800 20000Iteration times

10minus15

10minus10

10minus5

100

105

1010

Func

tion

Val

ue

(a) Ackle Function

SFDEEPSDEMDE

CODEMDESELF

SFDEEPSDEMDE

CODEMDESELF

times105

minus102

minus101

minus100

Func

tion

Val

ue

200 400 600 800 1000 1200 1400 1600 1800 20000Iteration times

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue



SFDEEPSDEMDE

CODEMDESELF

times105

10minus30

10minus20

10minus10

100

1010

Func

tion

Val

ue

200 400 600 800 1000 1200 1400 1600 1800 20000

Iteration times

SFDEEPSDEMDE

CODEMDESELF



Func

tion

Val

ue




0

200

400

600

800

1000

1200

1400

1600

1800

2000


CODEMDESELF


SFDEEPSDEMDE

CODEMDESELF

times105


Func

tion

Val

ue

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue


0

200

400

600

800

1000

1200

1400

1600

1800

2000

Iteration times

SFDEEPSDEMDE

CODEMDESELF


SFDEEPSDEMDE

CODEMDESELF

times105


Func

tion

Val

ue

10minus20

100

1020

1040

1060

1080

10100

Func

tion

Val

ue

(b) Perm Function

0 50 100 150 200 250 300 350 400 450Iteration times

SFDEEPSDEMDE

CODEMDESELF

SFDEEPSDEMDE

CODEMDESELF



Func

tion

Val

ue

10minus20

10minus15

10minus10

10minus5

100

105

1010

Func

tion

Val

ue

(c) Sphere Function



0

200

400

600

800

1000

1200

1400

1600

1800


MDECODE

100

102

104

106

108

1010

1012

Func

tion

Val

ue

SFDEEPSDEMDE

CODEMDESELF

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue

times105



0

200

400

600

800

1000

1200

1400

1600

1800

2000

Iteration times

10minus20

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue


SFDEEPSDEMDE

CODEMDESELF


Func

tion

Val

ue

times105

SFDEEPSDEMDE

CODEMDESELF


SFDEEPSDEMDE

CODEMDESELF

SFDEEPSDEMDE

CODEMDESELF

times10505 1 15 2 25 3 35 40


10minus1100101102103104105106107

Func

tion

Val

ue

200

400

600

800

1000

1200

1400

1600

1800

20000

Iteration times

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue

















































Table 3 Continued







119891 (119909) = Nsumi=11199092119894 30







1199092119894) minus exp 1119873119873sum119894=1

cos (2120587119909119894) + 20 + 119890 30




1198790 z (n) = 120583 (n)1198791 119911 (n) = 119904 (n) + 120583 (n) (15)



W = 1119873119873sum119899=1

|119911 (119899)|2 (16)



119875119891 (120576) = 119875120591 (W gt 120576 | T0)= 1radic21205871205900 int

infin

119873119890minus(Wminus1205830)2212059020119889119909

= 119876(( 1205761205902120583) minus radic120591119891)(17)




(18)


Perceivedtime

Data transfer time

t T-t

Perceived time

Data transfer time

t T-t








119877 (120591) = 1198770 (120576 120591) + R1 (120576 120591) (21)





max 119877 (120591) = 1198770 (120576 120591)119904119905 119875119889 (120576 120591) ge 119875119889 (23)






119909119895119894 (0) = 119887119900119906119899119889119904 (i 1) + 00002 lowast 119903119886119899119889 (0 1) (25)











EPSDEMDECODE


4

45

5

55

sens

ing

time (

s)






2 3 4 5 6 7 8 9 1010

02

04

06

08

1

12


EPSDEMDECODE


sens

ing

time (

s)




6 Conclusion


Data Availability




Acknowledgments



References























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



SFDEEPSDEMDE

CODEMDESELF


SFDEEPSDEMDE

CODEMDESELF

times105

10minus120

10minus100

10minus80

10minus60

10minus40

10minus20

100

1020Fu

nctio

n V

alue

200 400 600 800 1000 1200 1400 1600 1800 20000Iteration times

10minus15

10minus10

10minus5

100

105

1010

Func

tion

Val

ue

(a) Ackle Function

SFDEEPSDEMDE

CODEMDESELF

SFDEEPSDEMDE

CODEMDESELF

times105

minus102

minus101

minus100

Func

tion

Val

ue

200 400 600 800 1000 1200 1400 1600 1800 20000Iteration times

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue



SFDEEPSDEMDE

CODEMDESELF

times105

10minus30

10minus20

10minus10

100

1010

Func

tion

Val

ue

200 400 600 800 1000 1200 1400 1600 1800 20000

Iteration times

SFDEEPSDEMDE

CODEMDESELF



Func

tion

Val

ue




0

200

400

600

800

1000

1200

1400

1600

1800

2000


CODEMDESELF


SFDEEPSDEMDE

CODEMDESELF

times105


Func

tion

Val

ue

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue


0

200

400

600

800

1000

1200

1400

1600

1800

2000

Iteration times

SFDEEPSDEMDE

CODEMDESELF


SFDEEPSDEMDE

CODEMDESELF

times105


Func

tion

Val

ue

10minus20

100

1020

1040

1060

1080

10100

Func

tion

Val

ue

(b) Perm Function

0 50 100 150 200 250 300 350 400 450Iteration times

SFDEEPSDEMDE

CODEMDESELF

SFDEEPSDEMDE

CODEMDESELF



Func

tion

Val

ue

10minus20

10minus15

10minus10

10minus5

100

105

1010

Func

tion

Val

ue

(c) Sphere Function



0

200

400

600

800

1000

1200

1400

1600

1800


MDECODE

100

102

104

106

108

1010

1012

Func

tion

Val

ue

SFDEEPSDEMDE

CODEMDESELF

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue

times105



0

200

400

600

800

1000

1200

1400

1600

1800

2000

Iteration times

10minus20

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue


SFDEEPSDEMDE

CODEMDESELF


Func

tion

Val

ue

times105

SFDEEPSDEMDE

CODEMDESELF


SFDEEPSDEMDE

CODEMDESELF

SFDEEPSDEMDE

CODEMDESELF

times10505 1 15 2 25 3 35 40


10minus1100101102103104105106107

Func

tion

Val

ue

200

400

600

800

1000

1200

1400

1600

1800

20000

Iteration times

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue

















































Table 3 Continued







119891 (119909) = Nsumi=11199092119894 30







1199092119894) minus exp 1119873119873sum119894=1

cos (2120587119909119894) + 20 + 119890 30




1198790 z (n) = 120583 (n)1198791 119911 (n) = 119904 (n) + 120583 (n) (15)



W = 1119873119873sum119899=1

|119911 (119899)|2 (16)



119875119891 (120576) = 119875120591 (W gt 120576 | T0)= 1radic21205871205900 int

infin

119873119890minus(Wminus1205830)2212059020119889119909

= 119876(( 1205761205902120583) minus radic120591119891)(17)




(18)


Perceivedtime

Data transfer time

t T-t

Perceived time

Data transfer time

t T-t








119877 (120591) = 1198770 (120576 120591) + R1 (120576 120591) (21)





max 119877 (120591) = 1198770 (120576 120591)119904119905 119875119889 (120576 120591) ge 119875119889 (23)






119909119895119894 (0) = 119887119900119906119899119889119904 (i 1) + 00002 lowast 119903119886119899119889 (0 1) (25)











EPSDEMDECODE


4

45

5

55

sens

ing

time (

s)






2 3 4 5 6 7 8 9 1010

02

04

06

08

1

12


EPSDEMDECODE


sens

ing

time (

s)




6 Conclusion


Data Availability




Acknowledgments



References























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



0

200

400

600

800

1000

1200

1400

1600

1800

2000


CODEMDESELF


SFDEEPSDEMDE

CODEMDESELF

times105


Func

tion

Val

ue

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue


0

200

400

600

800

1000

1200

1400

1600

1800

2000

Iteration times

SFDEEPSDEMDE

CODEMDESELF


SFDEEPSDEMDE

CODEMDESELF

times105


Func

tion

Val

ue

10minus20

100

1020

1040

1060

1080

10100

Func

tion

Val

ue

(b) Perm Function

0 50 100 150 200 250 300 350 400 450Iteration times

SFDEEPSDEMDE

CODEMDESELF

SFDEEPSDEMDE

CODEMDESELF



Func

tion

Val

ue

10minus20

10minus15

10minus10

10minus5

100

105

1010

Func

tion

Val

ue

(c) Sphere Function



0

200

400

600

800

1000

1200

1400

1600

1800


MDECODE

100

102

104

106

108

1010

1012

Func

tion

Val

ue

SFDEEPSDEMDE

CODEMDESELF

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue

times105



0

200

400

600

800

1000

1200

1400

1600

1800

2000

Iteration times

10minus20

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue


SFDEEPSDEMDE

CODEMDESELF


Func

tion

Val

ue

times105

SFDEEPSDEMDE

CODEMDESELF


SFDEEPSDEMDE

CODEMDESELF

SFDEEPSDEMDE

CODEMDESELF

times10505 1 15 2 25 3 35 40


10minus1100101102103104105106107

Func

tion

Val

ue

200

400

600

800

1000

1200

1400

1600

1800

20000

Iteration times

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue

















































Table 3 Continued







119891 (119909) = Nsumi=11199092119894 30







1199092119894) minus exp 1119873119873sum119894=1

cos (2120587119909119894) + 20 + 119890 30




1198790 z (n) = 120583 (n)1198791 119911 (n) = 119904 (n) + 120583 (n) (15)



W = 1119873119873sum119899=1

|119911 (119899)|2 (16)



119875119891 (120576) = 119875120591 (W gt 120576 | T0)= 1radic21205871205900 int

infin

119873119890minus(Wminus1205830)2212059020119889119909

= 119876(( 1205761205902120583) minus radic120591119891)(17)




(18)


Perceivedtime

Data transfer time

t T-t

Perceived time

Data transfer time

t T-t








119877 (120591) = 1198770 (120576 120591) + R1 (120576 120591) (21)





max 119877 (120591) = 1198770 (120576 120591)119904119905 119875119889 (120576 120591) ge 119875119889 (23)






119909119895119894 (0) = 119887119900119906119899119889119904 (i 1) + 00002 lowast 119903119886119899119889 (0 1) (25)











EPSDEMDECODE


4

45

5

55

sens

ing

time (

s)






2 3 4 5 6 7 8 9 1010

02

04

06

08

1

12


EPSDEMDECODE


sens

ing

time (

s)




6 Conclusion


Data Availability




Acknowledgments



References























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



0

200

400

600

800

1000

1200

1400

1600

1800


MDECODE

100

102

104

106

108

1010

1012

Func

tion

Val

ue

SFDEEPSDEMDE

CODEMDESELF

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue

times105



0

200

400

600

800

1000

1200

1400

1600

1800

2000

Iteration times

10minus20

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue


SFDEEPSDEMDE

CODEMDESELF


Func

tion

Val

ue

times105

SFDEEPSDEMDE

CODEMDESELF


SFDEEPSDEMDE

CODEMDESELF

SFDEEPSDEMDE

CODEMDESELF

times10505 1 15 2 25 3 35 40


10minus1100101102103104105106107

Func

tion

Val

ue

200

400

600

800

1000

1200

1400

1600

1800

20000

Iteration times

10minus15

10minus10

10minus5

100

105

Func

tion

Val

ue

















































Table 3 Continued







119891 (119909) = Nsumi=11199092119894 30







1199092119894) minus exp 1119873119873sum119894=1

cos (2120587119909119894) + 20 + 119890 30




1198790 z (n) = 120583 (n)1198791 119911 (n) = 119904 (n) + 120583 (n) (15)



W = 1119873119873sum119899=1

|119911 (119899)|2 (16)



119875119891 (120576) = 119875120591 (W gt 120576 | T0)= 1radic21205871205900 int

infin

119873119890minus(Wminus1205830)2212059020119889119909

= 119876(( 1205761205902120583) minus radic120591119891)(17)




(18)


Perceivedtime

Data transfer time

t T-t

Perceived time

Data transfer time

t T-t








119877 (120591) = 1198770 (120576 120591) + R1 (120576 120591) (21)





max 119877 (120591) = 1198770 (120576 120591)119904119905 119875119889 (120576 120591) ge 119875119889 (23)






119909119895119894 (0) = 119887119900119906119899119889119904 (i 1) + 00002 lowast 119903119886119899119889 (0 1) (25)











EPSDEMDECODE


4

45

5

55

sens

ing

time (

s)






2 3 4 5 6 7 8 9 1010

02

04

06

08

1

12


EPSDEMDECODE


sens

ing

time (

s)




6 Conclusion


Data Availability




Acknowledgments



References























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia
















































Table 3 Continued







119891 (119909) = Nsumi=11199092119894 30







1199092119894) minus exp 1119873119873sum119894=1

cos (2120587119909119894) + 20 + 119890 30




1198790 z (n) = 120583 (n)1198791 119911 (n) = 119904 (n) + 120583 (n) (15)



W = 1119873119873sum119899=1

|119911 (119899)|2 (16)



119875119891 (120576) = 119875120591 (W gt 120576 | T0)= 1radic21205871205900 int

infin

119873119890minus(Wminus1205830)2212059020119889119909

= 119876(( 1205761205902120583) minus radic120591119891)(17)




(18)


Perceivedtime

Data transfer time

t T-t

Perceived time

Data transfer time

t T-t








119877 (120591) = 1198770 (120576 120591) + R1 (120576 120591) (21)





max 119877 (120591) = 1198770 (120576 120591)119904119905 119875119889 (120576 120591) ge 119875119889 (23)






119909119895119894 (0) = 119887119900119906119899119889119904 (i 1) + 00002 lowast 119903119886119899119889 (0 1) (25)











EPSDEMDECODE


4

45

5

55

sens

ing

time (

s)






2 3 4 5 6 7 8 9 1010

02

04

06

08

1

12


EPSDEMDECODE


sens

ing

time (

s)




6 Conclusion


Data Availability




Acknowledgments



References























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Perceivedtime

Data transfer time

t T-t

Perceived time

Data transfer time

t T-t








119877 (120591) = 1198770 (120576 120591) + R1 (120576 120591) (21)





max 119877 (120591) = 1198770 (120576 120591)119904119905 119875119889 (120576 120591) ge 119875119889 (23)






119909119895119894 (0) = 119887119900119906119899119889119904 (i 1) + 00002 lowast 119903119886119899119889 (0 1) (25)











EPSDEMDECODE


4

45

5

55

sens

ing

time (

s)






2 3 4 5 6 7 8 9 1010

02

04

06

08

1

12


EPSDEMDECODE


sens

ing

time (

s)




6 Conclusion


Data Availability




Acknowledgments



References























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia












EPSDEMDECODE


4

45

5

55

sens

ing

time (

s)






2 3 4 5 6 7 8 9 1010

02

04

06

08

1

12


EPSDEMDECODE


sens

ing

time (

s)




6 Conclusion


Data Availability




Acknowledgments



References























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



2 3 4 5 6 7 8 9 1010

02

04

06

08

1

12


EPSDEMDECODE


sens

ing

time (

s)




6 Conclusion


Data Availability




Acknowledgments



References























RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia









RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


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