research article radial basis function neural...

Research ArticleRadial Basis Function Neural Network with ParticleSwarm Optimization Algorithms for Regional LogisticsDemand Prediction

Zhineng Hu Yixin Zhang and Liming Yao

Uncertainty Decision-Making Laboratory Sichuan University Chengdu 610064 China

Correspondence should be addressed to Liming Yao lmyaoscueducn

Received 26 June 2014 Revised 8 September 2014 Accepted 4 November 2014 Published 26 November 2014

Academic Editor Zhigang Jiang

Copyright copy 2014 Zhineng Hu 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

Regional logistics prediction is the key step in regional logistics planning and logistics resources rationalization Since regionaleconomy is the inherent and determinative factor of regional logistics demand it is feasible to forecast regional logistics demandby investigating economic indicators which can accelerate the harmonious development of regional logistics industry and regionaleconomy In this paper the PSO-RBFNN model a radial basis function neural network (RBFNN) combined with particle swarmoptimization (PSO) algorithm is studied The PSO-RBFNN model is trained by indicators data in a region to predict the regionallogistics demand And the corresponding results indicate the modelrsquos applicability and potential advantages

1 Introduction

With the rapid economic development and the continuousadvancement of information and technology modern logis-tics industry is developing fast on a global scale Thereforelogistics industry is considered to be the foundation as well asthe basic industry of national economic development Mean-while its level of development becomes an essential symbolof measuring a countryrsquos modernization and comprehensiveeconomic strength

Regional logistics demand prediction system is a cru-cial part of regional logistics system planning and logisticsrational allocation process of resources This is because theregional logistics demand prediction system provides thenecessary basis for decisionmaking of the government It alsoprovides support for the construction of logistics infrastruc-ture Scholars at home and around theworld establishedmorepredictive models for macrologistics needs for examplethe space-time multinomial probity model of forecastingfreight transportation [1] nonlinear air services demandmodel based on time series [2] stepwise linear regressionmethod for cargo forecasting [3] logistics demand analysismodel combining input-output and spatial price [4] routecomparison model and gravity model [5] grey prediction

model fuzzy forecast and neural network prediction modeland so forth [6ndash8] Yet few scholars combined regional eco-nomic development with regional logistics demand forecastsclosely togetherThe vast majority of the literature focused onusing historical data of logistics needs for logistics demandforecasting rather than utilizing economic data to forecastdemand for logistics

Many domestic and foreign scholars have conductedresearches on the prediction of regional logistics demand Itis basically divided into two categories time series predictionmethod and causality predictionmethod Time series predic-tion method is a kind of approach based on the evolutionrules of the predicted object which are found out from thehistorical data of the time series Commonly used modelsinclude moving average exponential smoothing and greymodel Causality predictionmethod is to infer the developingtrend of things by establishing the appropriate causality fore-casting model based on the relationship between variablesof prediction object and variables of its related things foundout from historical data and using the causal relationship ofthings development Commonly used models include elasticcoefficient method linear regression model and artificialneural network model Commonly used prediction methodsand the applicable situation are shown in Table 1

Hindawi Publishing CorporationDiscrete Dynamics in Nature and SocietyVolume 2014 Article ID 414058 13 pageshttpdxdoiorg1011552014414058

2 Discrete Dynamics in Nature and Society

Table 1 Common forecasting methods

Forecasting methods The applicable situationMoving average [24] Suitable for spot predictionExponentialsmoothing [25]

Repeated prediction with or without achange in seasons

Grey model [6] Development of time series showingexponential trend

Elastic coefficientmethod [26]

Two factors between119883 and 119884 have anexponential relationship

Linear regressionmodel [3]

A linear relationship betweenindependent variables and dependentvariables

Artificial neuralnetwork model [7]

Being able to make prediction ofnonlinear corresponding relationship

Time series forecasting method does not consider theinfluence of other economic development indicators It dis-regards that the regional logistics demand is of derivationHence there are often serious prediction errors On the otherhand compared with the macrologistics regional logisticsdemand prediction has its own characteristics there existsa high degree of nonlinearity between logistics demand andthe impact of logistics demand indicators as well as greatervolatility than macrologistics Due to these features the tra-ditional time series forecastingmethods (such as greymodel)and linear prediction methods (such as linear regressionmodel) do notwork effectively Consequently artificial neuralnetwork (ANN) model is more suitable Furthermore it isexactly the complexity and nonlinearity of regional logisticsdemand system that make a single predictionmodel functionnot well [9ndash12] Therefore it is necessary to use a combinedmodel

In this paper a regional logistics demandprediction indexsystem with economic indicators and logistics indicatorsand a regional logistics demand prediction model based onradial basis function neural network (RBFNN) combinedwith particle swarm optimization (PSO) algorithm will bebuilt The PSO-RBFNNmodel will be trained with processeddata from Sichuan province and will be applied to predictthe regional logistics demand in the very area as well Theprediction result will be evaluated and compared with abackpropagation (BP) neural network and regular RBFNNEventually the results and conclusions drawn from the PSO-RBFNNpredictionmodel will be discussed and summarized

2 Problem Description

21 Problem Background In order to enhance the investmentenvironment to increase the attraction of foreign invest-ment to solve the employment pressure and to improvethe comprehensive competitiveness of urban areas multipleregions in China have adopted a variety of planning policiesto encourage the development of logistics and construction oflogistics infrastructure Nonetheless Chinarsquos logistics startedlate and the related policies strategies and planning arenot mature Plannersrsquo understanding of the development ofmodern logistics concept and mode of operation is still not

unified especially in the field of logistics demand and soon When formulating logistics development policies andstudying the feasibility of logistics infrastructure scholarsascertain that the lack of quantitative data about logisticsdemand results in numerous problems in the planningprocess for instance the imbalance between actual supplycapacity of logistics and logistics demand repeated construc-tion and sedimentation of money caused by tremendouswaste of resources and false prosperity of logistics industryOverall predicting regional logistics demand is critical for thesustainable development of regional logistics industry

Therefore the quantitative prediction of the scale anddevelopment trends of logistics demand is essential To beginwith this kind of predictions can purposefully guide socialinvestment into the field of logistics Various types of logisticsinfrastructure can be rationally planned and constructedlogistics supply system and network layout can be improvedMoreover the predictions continuously provide the basis forthe supply to meet the demand so as to maintain a relativebalance between supply and demand for logistics services andto make the regional logistics maintain high efficiency

22 Related Concepts of Regional Logistics Demand Cur-rently there is no uniform view for the definition of regionallogistics Dong [13] holds that regional logistics is a systemaiming at optimizing the socioeconomic strategies throughthe planning and construction of a certain region Mean-while it also refers to activities associated with logistics oper-ation and control In accordance with the systems definedby systems engineering the regional logistics system canbe defined as follows in a certain economic geographicarea it is an organic whole with specific operating lawand function formed by interrelated interdependent andinteracting elements of all logistics at different spatial scalesThe regional logistics system is illustrated in Figure 1

Compared with the national logistics systems and enter-prise logistics system the regional logistics system is anorganic integrated logistics system within the range of theeconomic region The basic structural unit of the regionallogistics system is a microenterprise supply sales logisticsand so on Meanwhile it is a vital part of the nationallogistics international logistics and other macrologisticssystems The regional logistics system which is mesolevelbecomes the convergence of the microscopic and macro-scopic logistics systems Its purpose is to apply the logisticschain management solutions to address a variety of logisticalproblems beyond a single enterprise so as to achieve logisticsrationalization in a region or in a wider range of areas [14ndash16]as is indicated in Figure 2

Logistics demand prediction is based on the relation-ship between past and current logistics market demandinformation and factors affecting the changes in the logis-tics market demand It uses sound judgment experiencetechnical methods and predictive models on the basis ofhistorical data and statistical information to derive someregularity trends and intrinsic link trends among the factorswhich predicts indicators reflecting market demand trendsLogistics demand prediction is preestimates and predictions

Discrete Dynamics in Nature and Society 3

TargetKeep balance

Dem

and

Dem

and

Primary industry

Secondary industry

Tertiary industry

Logistics infrastructure

Logistics park

Logistics enterprises

Figure 1 The regional logistics system

Urbandistribution

centers

Manufacturers

Distributors

Consumer

Warehousing

Machining

Package

Handling

Regionallogisticscenter

Airport

Port

Railway freightstation t

RTS highway t

The international

City

Region

The domestic

Figure 2 Internal structure of regional logistics system

of the cargo traffic source flow velocity and other goodsconstituting in the area which have not occurred or is not yetclear so as to meet the scale of regional logistics demand andhierarchy of needs Finally it provides decision-making basisfor the regional logistics planning

3 Methodologies

Beforemodeling we select suitable regional logistics demandprediction indicators thereby keeping accuracy and reliabil-ity of regional logistics demand prediction


31 Selecting the Regional Logistics Demand Indicators Theregional logistics demand scale indicator is the most impor-tant indicator in regional logistics demand indicators Itreflects the development of the logistics industry and thesupply of logistics services in the region namely the sizeand level of total demand for logistics It is also the mostsignificant data the government and corporate decision-makers should first master Generally scale indicators ofregional logistics demand can be set from several differentangles as demonstrated in Table 2

According to the logistic current situation and the prin-ciple of regional logistic prediction indicators we select totalfreight traffic (TFT 119910

1 10 000 tons) and freight turnover (FT

1199102 100 million ton-km) as the prediction targetsRegional economic indicators are the economic indica-

tors utilized in the prediction and have tremendous impactson regional logistics demand The total regional economyregional economic structure and distribution are majoreconomic factors impacting regional logistics demand Inaddition intraregional trade regional income per capita andconsumption level are also important influencing factorsHence when setting regional economic indicators we selectas many related indicators as we can tomake predictionmoreeffectiveMeanwhile we have to consider that indicatorsrsquo datashould be relatively easy to obtain from the regional statisticalyearbook Regional economic indicators are set using themeasures illustrated in Table 3

32 Building Regional Logistics Demand Prediction IndexSystem Combined with the previous analysis and takinginto account the availability of statistical data limits in thisresearch we select total freight traffic (TFT 119910

1 10 000 tons)

and freight turnover (FT 1199102 100 million ton-km) to measure

the scale of regional logistics demand Likewise we selectgross domestic product (GDP 119909

1 billion yuan) primary

industry output value (PIO 1199092 billion yuan) secondary

industry output value (SIO1199093 billion yuan) tertiary industry

output value (TIO 1199094 billion yuan) regional retail sales

(RRS 1199095 million yuan) total import and export (TIE 119909

6

million dollar) and per capita consumption (PCC 1199097 yuan

per person) as economic indicators to predict the regionallogistics demand These indicators of input and output willbe utilized to train the PSO-RBFNN and predict the regionallogistics demandThe index system predicting regional logis-tics demand is exhibited in Figure 3

33The Radial Basis FunctionNeural Network (RBFNN) Theartificial neural network (ANN) is a nonlinear informationprocessing system which imitates human brain structure andfunction According to the potential law ANN is able toextrapolate new output by using new input Hence ANNhas the ability to adapt to the changing environment andto achieve real value mapping of any complex functionsANN is widely utilized to resolve problems such as patternrecognition forecasting andprediction optimization controland intelligent decision-making The feedforward neuralnetworks are one of the most widely used ANNs Backprop-agation (BP) network radial basis function neural network

Table 2 Regional logistics demand indicators

Indicatorspecies

Classificationstandards Setting indicators

Indicators oflogisticsdemand scale

Freight scale Volume of freight trafficand freight turnover

Logistics costsTotal logistics costs and theproportion of logistics costsin GDP

Investment infixed assets

Total investment inlogistics fixed assets

Industrypersonnel

The proportion of thenumber of employees intotal employment or totalpopulation

Table 3 Logistics demand forecast economic indicators

Indicator species Setting indicators

Indicators of economic scale Gross domestic product (GDP)and GDP per capita

Indicators of industrialstructure

Primary industry output valuesecondary industry output valueand tertiary industry outputvalue

Indicators of trade Regional retail sales and totalvolume of regional foreign trade

Indicators of householdconsumption level

Consumption level per capitaand income per capita

(RBFNN) and group method of data handling (GMDH)network are the typical feedforward neural networks

The radial basis function neural network (RBFNN) wasproposed by Moody and Darken [17] It is a commonlyused FNN with only one hidden layer A RBFNN consistsof three layers the input layer the hidden layer and theoutput layer The transformation from the input layer to thehidden layer is nonlinear The output layer is linear andgives a summation at the output units The architecture ofRBFNN is illustrated in Figure 4 where 119899 input units ℎhidden units and 119898 output units are in the RBFNN x =

[1199091 1199092 119909

119899]119879isin R119899 is the input vector W = Rℎtimes119898 is the

output weight matrix 1198871 119887

119898are the output units migra-

tion y = [1199101 1199102 119910

119898]119879 is the output vector Φ

119894(119909 minus 119888

119894)

is 119894th hidden unitrsquos activation function sum in the output unitindicates that the output layer neurons use linear activationfunction As a result the 119896th output can be represented as119910119896= sumℎ

119894=1119908119894Φ119894(119909 minus 119888

119894) where 119908

119894denotes the connection

weight with which decision makers endow the radial basisfunction

The essential feature of the RBFNN is that it utilizes thedistance (Euclidean distance) function as the basis functionand the radial basis function (such as Gaussian function)as activation functions The radial basis function is a radial


Regional economic indicators

Logistics scale indicators

Gross document product (GDP x1 billion yuan RMB)

Primary industry output (PIO x2 billion yuan RMB)

Secondary industry output (SIO x3 billion yuan RMB)

Tertiary industry output (TIO x4 billion yuan RMB)

Regional retail sales (RRS x5 billion yuan RMB)

Total import and export (TIE x6 billion yuan RMB)

Per capita consumption (PCC x7 billion yuan RMB)

Freight turnover (FTy2100million ton-km)

Total freight trac (TFTy2 100million ton-km)

Figure 3 Regional logistics demand prediction index system

Input layer Hidden layer Output layer

W isin Rhtimesm

x1

x2

xn

c1

c2

ch

Σ

Σ

b1

bm

y1

ym

120601(x minus c1)

120601(x minus ch)

Figure 4 The architecture of RBFNN

symmetry about a center point in 119873-dimension space Thefarther the input neurons are away from the center point thelower the level of the neuron activation is This characteristicof hidden units is called ldquolocal qualityrdquoTherefore each hiddenunit has a center point As is shown in Figure 4 119888

119894is the center

point value of the 119894th hidden unit 119909 minus 119888119894 is the Euclidean

norm which indicates the distance from 119909 to 119888119894 The radial

basis function Φ119894(sdot) has various forms which are commonly

used as follows where 120575119894is called the spread of the basis

function [18]

Φ119894(119905) = 119890

minus(11990521205752

119894) Gaussian function

Φ119894(119905) =

1

1 + 11989011990521205752 reflected sigmoid function

Φ119894(119905) =

1

(1199052 + 1205752

119894)120572 120572 gt 0

inverse multiquadric function

(1)

Like the human brainrsquos neural network RBFNNrsquos func-tions are obtained through continuous learning As theproperty of the neural network depends on network topologyand connection weights between nodes and the topologicalstructure is often chosen according to specific applicationsthe RBFNN learning problem is to adjust the connectionweights between nodes Weights can be determined by twomethods (a) determined when RBFNN is designed (b)determined by learning (or training) according to certainrules Overall the latter ismainly applied because the RBFNNobtained by learning has better adaptability RBFNNrsquos topol-ogy and basis function have some advantages

(1) RBFNN has a good capability to approximate anynonlinear mapping and processing systemrsquos inherentregularity which is difficult to express For noise-freedata RBFNN has better fitting capability and higherprediction accuracy For data with noise RBFNNrsquosfitting error and prediction error are smaller and the


convergence rate is faster than other neural networkssuch as BP neural network

(2) RBFNN topology can not only improve the learn-ing speed but also avoid the local minimum Inaddition RBFNNrsquos transfer function adopts radialbasis functions particularly the Gaussian functionAs the Gaussian function has a simple representationso even a multivariable input would not add muchcomplexity And it is easy to theoretically analyse

(3) RBFNN has a self-learning self-organizing self-adaptive capability and a fast learning speed RBFNNcan achieve a wide range of data fusion and dataparallel processing at high speed

34The Particle SwarmOptimization Algorithm Theparticleswarm optimization (PSO) algorithm is an evolutionarytechnique first proposed by Kennedy and Eberhart [19]and inspired by the natural flocking and swarming behav-ior of birds and insects [20] The PSO algorithm worksthrough initializing a swarm randomly in the search spaceattracting the particles to search for space positions of highfitness Each particle has an adaptive value determined bythe optimized function The velocity of each particle willdetermine its direction and distance and the particles willfollow the optimal particle searching in the searching space[21]

Evolutionary algorithm is varied Generalized evolution-ary algorithm includes genetic algorithms particle swarmoptimization and ant colony algorithm in which geneticalgorithm and particle swarm algorithm are most typicalIn comparison with other evolutionary algorithms such asgenetic algorithm PSO algorithm has the following advan-tages (a) the algorithm is simple and easy to implement(b) computation amount of the algorithm is small (c) thecomputational efficiency of the algorithm is high

341 The Principle of PSO Suppose in 119873-dimensionalsearching space a swarm consisting of 119898 particles is X =

(1199091 1199092 119909

119894 119909

119898) where the position of the 119894th particle

is 119909119894= (1199091198941 1199091198942 119909

119894119899)119879 the velocity of the 119894th particle is

V119894= (V1198941 V1198942 V

119894119899)119879 the best position of the 119894th particle

being searched is 119875119894

= (1198751198941 1198751198942 119875

119894119899)119879 and the best

position of the total particle swarm being searched is 119875119892=

(1198751198921 1198751198922 119875

119892119899)119879 Through some iterations each particle

updates its velocity and position based on the influence of itsbest position119875

119894as well as the best position of the total particle

swarm 119875119892 The iterative calculation is

V119896+1119894119889

= 120596V119896119894119889+ 1198881120585 (119901119896

119894119889minus 119909119896

119894119889) + 1198882120578 (119901119896

119892119889minus 119909119896

119892119889)

119909119896+1

119894119889= 119909119896

119894119889+ V119896+1119894119889

(2)

where 1198881 1198882are the learning factors acceleration coefficients

with positive values They control the maximum step sizethe particle can achieve 120596 is inertia weight 120585 and 120578 arerandom numbers between 0 and 1 120585 120578 isin U[minus1 1] Particlesize 119898 inertia weight 120596 and maximum iteration number 119870

are considered as important factors in PSO Inertia weight120596 describes the influence of particlersquos previous generationvelocity on the current generation Controlling the valueof 120596 can adjust the global and local searching capabilitiesof PSO algorithm The larger is 120596 the better is the globalsearching capability with a local searching capability beingweaker Contrarily the local searching capability can beenhanced while the global searching capability is weakened[22]

342The Process of PSOAlgorithm Standard PSO algorithmprocedures [23] are as follows

Step 1 Initialize the particles X = (1199091 1199092 119909

119894 119909

119898)

the best position of the 119894th pariticle being searched is119875119894

= (1198751198941 1198751198942 119875

119894119899)119879 and the particlesrsquo velocities V

119894=

(V1198941 V1198942 V

119894119899)119879 randomly Then set the acceleration coeffi-

cients 1198881and 1198882 themaximum iteration number119870 maximum

velocity and a maximum particle movement amplitude inorder to decrease the cost of evaluation and to achieve a goodconvergence rate

Step 2 Calculate the fitness value of each particle via thefitness function There are many options when choosing afitness function but finding a good one often requires trialand error

Step 3 Compare the particlersquos fitness value with the particlersquosbest position119875

119894 If the current value is better than the previous

best solution replace it and set the current solution as thelocal best position 119875

119894

Step 4 Compare the individual particlersquos fitness with thepopulationrsquos global best position 119875

119892 If the fitness of the

current solution is better than the global best fitness set thecurrent solution as the new global best position 119875

119892

Step 5 Update the particlesrsquo positions and velocities by (2)

Step 6 Repeat Step 2 to Step 4 until a stopping criterion issatisfied or the iterations number 119870 is completed

In this paper we use real code to make neural networkconnectionweights and threshold values expressed as particleparameters The specific encode mode is as follows let thenumber of input nodes be119898 let the number of hidden nodesbe 119899 and let the number of output nodes be 119904 with theindividual string length of particle swarm being 119871 = 119899 times 119898 +

119904 times 119899 + 119899 + 119904 Assume that the input layer and hidden layerconnection weight matrix is

IW =

[[[[

[

IW11

IW12

sdot sdot sdot IW1119898

IW21

IW22


d

IW1198991

IW1198992


]]]]

]

(3)


The threshold vector from the input layer to hidden layeris 1198611= [11988711 11988712 119887

1119899]119879 then assume that the hidden layer

and output layer connection weight matrix is

LW =

[[[[

[

LW11

LW12

sdot sdot sdot LW1119899

LW21

LW22


d

LW1199041

LW1199042


]]]]

]

(4)

The threshold vector from the hidden layer to output layeris 1198612= [11988721 11988722 119887

2119904]119879 So the particlersquos encoding is 119883 =

[IW11sdot sdot sdot IW

11989911989811988721 11988722 119887

2119904]

35The Combination of PSO and RBF As the PSO algorithmcan easily fall into local optimum it fails to achieve globaloptimum The PSO algorithm is not theoretically rigorousproof of convergence to any type of functionsrsquo global extremepoint hence it may be difficult to obtain satisfactory resultsof complex test functions When the PSO algorithm isrunning if the parameter design of the algorithm or theselection of particles is in error it will lead to a rapiddisappearance of the diversity of particles resulting in analgorithm ldquoprematurerdquo phenomenon further restricting thealgorithm from converging to the global extreme point

Meanwhile the PSO algorithmrsquos convergence speed isslow In practical problems it is necessary to reach theappropriate accuracy within a certain period of time and it isnot worth taking a long time to get feasible solutionThis slowconvergence speed is caused by the PSO using an individualoptimum and the global optimum at each iteration

Therefore combining ANN and PSO will overcome theirown shortcomings and achieve better prediction and opti-mization results ANN and PSO are two different methodsand have big difference in their information processingand the complementariness between them is high Thetwo principal ways to combine them are (a) using PSOalgorithmrsquos global searching capability to optimize ANNrsquostopology connection weights and learning rules improvingthe generalization capability and learning efficiency whichimprove the ANNrsquos global searching performance and (b)embedding ANN into the PSO algorithm and using ANNrsquosgood learning performance to enhance the performance ofPSO optimization In this study we adopt the PSO algorithmto optimize the RBFNNrsquos connection weights and thresholdsas revealed in Figure 5

The procedures are as follows

Step 1 Collect networking training specimens

Step 2 Build the topology structure of RBFNN that is todetermine the number of input output and hidden nodes

Step 3 Initialize population

Step 4 Calculate the fitness value of each particle



Economicindicators

Logisticsscale

W

PSO

y1

y2

x1

x2

c1

c2

cn

Figure 5 The physical model for the regional logistics demand


119894




119892



Step 9 Decode the populationrsquos global best position Theoptimized values are RBFNNrsquos connection weights andthreshold values Then train the RBFNN

The algorithm flowchart is shown in Figure 6

4 Case Study

41 Data Processing In this section the proposed PSO-RBFNN model will be applied to predict regional logisticsdemand in Sichuan province China The data are selectedfrom the Sichuan Province Statistical Yearbook from 1994 to2008 as exhibited in Table 4

Before using these indicators the correlation betweenregional economic indicators and logistics demand indicatorsshould be verifiedThe verification result of the correlation isindicated in Table 5

From Table 5 all the correlation coefficients are close to1 and correlation is significant at the 001 level (2-tailed)Accordingly the logistics scale indicators that is total freighttraffic (119910

1) freight turnover (119910

2) and regional economic

indicators namely gross domestic product (1199091) primary

industry output value (1199092) secondary industry output value

(1199093) tertiary industry output value (119909

4) regional retail sales

(1199095) total import and export (119909

6) and per capita consump-

tion (1199097) have high correlation These indicators are valid as

inputs and outputs of the PSO-RBFNN


Yes

No

Collect specimens

Build the topology structure of RBFNN

Initialize population

Calculate the fitness value of particles

Compare and update

Check the endconditionk = K

Decode the populationrsquos global best position

Determine the connection weights and threshold values

Train the RBFNN

Figure 6 The algorithm flowchart

As the selected indicators have different attributes anddimensions the input and output data should be prepro-cessed to accelerate the networkrsquos training speed and conver-gence and improve the prediction accuracy of PSO-RBFNNIn this paper we adopt normalization processing

119883119894=

119883 minus 119883min119883max minus 119883min

(5)

where 119883119894is the normalized data 119883 is the sample value and

119883max and 119883min are the maximum and minimum sample val-ues For the output of the network the reverse normalizationformula is119883 = 119883min + (119883max minus 119883min) times 119883

119894

After the normalization processing the input data isshown in Table 6 Each row has at least one 0 and one 1For the S-shaped curve the training effect will be worsetraining times will increase and it may not be able to reachthe expected target

To avoid the extreme data 0 and 1 disrupting predictionresult we set the maximum normalized value as 09999 andthe minimum normalized value as 00001

42 The PSO-RBFNN Training On the determination ofnodes in the hidden layer there is no uniform standardConsequently we use a trial-and-error method based onempirical principles let 119898 be the number of input nodes let119899 be the number of output nodes and let 119896 be the numberof hidden nodes therefore (a) 119896 = radic119898 + 119899 + 119886 where 119886

is a constant between 1 and 10 (b) 119896 = 119898 times (119899 + 1) (c)119896 = radic119898 times 119899 (d) 119896 = log

2119898 (e) 119896 = 2 times (119898 + 119899)3

and (f) 119896 = 2119899 + 1 The network training starts from

1

2

3

7

1

2

3

14

15

1

2


x1

x2

x3

x7

y1

y2

Figure 7 The PSO-RBFNNmodel structure

a smaller number of hidden nodes If the training is done toomany times or does not reach the specified training times orthe network does not converge to a predetermined accuracythe training process should be interrupted The number ofhidden nodes is gradually increased The model is retraineduntil a satisfactory training effect is achieved In this waythe number of hidden nodes is ultimately determined as 15According to the index system we built the numbers of inputand output nodes are determined as 7 and 2 Therefore thePSO-RBFNN node configuration form can be identified as 7-15-2 The topology is demonstrated in Figure 7

To determine the PSO-RBFNN learning factors we havea parametric test of the learning factors 119888

1and 1198882in this study

The results are demonstrated in Table 7 Additionally 1198881= 15

and 1198882= 02 are determined because of the lowest training

error 0001291In order to train the PSO-RBFNN we chose data from

the 1994sim2004 yearbooks as network training specimensThePSO parameters are determined 120596max = 09 120596min = 04119909min = minus10 119909max = 10 and Vmax = 8 Then we can determinethe connectionweights and thresholds train the RBFNN anduse it to predict the logistics demand of Sichuan province in2010sim2015

The transfer function of hidden layer utilizes S typetangent function 119891(119909) = (1 minus 119890

minus119909)(1 + 119890

minus119909) mapping

from domain (minusinfin +infin) to range (minus1 1) The output layertransfer function uses linear function 119891(119909) = 119909 The trainingspecimens and transfer function are shown in Figure 8

5 Analysis of Result

51 The Model Evaluation After training we test the PSO-RBFNNmodelrsquos fitness and prediction capability Fitness testuses the model to fit to historical data and to estimate thepreprediction error Extrapolation test utilizes postpredictionerror to estimate the preprediction error In the actualprediction historical data are divided into two groups withmost of the data being a sample to build the predictive model


Table 4 The logistics demand indicators and regional economic indicators statistical data

Year 1199091

1199092

1199093

1199094

1199095

1199096

1199097

1199101

1199102

1994 200141 59737 78277 62127 7247408 291645 136717 72336 4971995 244321 66246 98091 79984 9363651 235872 164627 67154 5651996 287165 77002 115601 94562 10914485 214883 18796 52004 5361997 324147 88028 126532 109587 12123699 179005 207774 56935 5491998 347409 91224 132401 123784 12985695 209328 224341 50759 5681999 364912 92603 134963 137346 13825869 247069 234753 50142 5742000 39282 94558 143311 154951 15237490 254517 255048 54943 5972001 42935 98168 157201 173981 16804041 309916 270715 54141 6482002 472501 104795 173338 194368 18500576 446919 291439 57297 7042003 533309 112861 20148 218968 20910543 446919 320336 57200 6992004 637963 137992 249317 250654 23839515 563862 36562 65580 8042005 738511 148114 306723 283674 29813734 687162 413008 70364 8982006 863781 160348 377519 323914 34216483 790476 450134 74200 8912007 1030530 203200 464130 383200 40155746 1102097 525922 79940 9792008 1260123 221615 582339 456169 48007638 1438461 607200 114513 15132009 1415136 223591 670774 520770 52783510 2422728 681742 102635 1913

Table 5 The correlation between indicators

1199091

1199092

1199093

1199094

1199095

1199096

1199097

1199101

0867lowastlowast

0826lowastlowast

0892lowastlowast

0838lowastlowast

0859lowastlowast

0921lowastlowast

0835lowastlowast

1199102

0951lowastlowast

0906lowastlowast

0961lowastlowast

0939lowastlowast

0939lowastlowast

0985lowastlowast

0938lowastlowast

lowastlowastCorrelation is significant at the 001 level (2-tailed)

Table 6 The normalized data

Year 1199091

1199092

1199093

1199094

1199095

1199096

1199097

1199101

1199102

1994 00001 00001 00001 00001 00001 00502 00001 04228 000011995 00364 00397 09154 00389 00404 00253 00512 03241 004801996 00716 01054 06798 00707 00747 00160 00940 00355 002751997 01021 01727 05911 01035 01014 00000 01304 01294 003671998 01212 01922 06308 01344 01205 00135 01608 00118 005011999 01356 02006 06761 01640 01390 00303 01799 00001 005442000 01586 02125 07462 02024 01702 00337 02171 00915 007062001 01887 02345 08043 02439 02049 00583 02459 00762 010662002 02242 02750 08152 02883 02423 01194 02839 01363 014622003 02742 03242 08458 03420 02956 01194 03369 01345 014272004 03603 04776 07545 04111 03603 01715 04200 02941 021682005 04431 05394 08215 04830 04924 02265 05069 03852 028322006 05462 06140 08896 05708 05897 02725 05751 04583 027822007 06835 08756 07806 07000 07209 04114 07141 05677 034042008 08724 09879 08831 08591 08945 09058 08632 08453 071752009 09999 09999 09999 09999 09999 09999 09999 09999 09999

and the other small parts of the data being used for theextrapolation test

The data collected from the 1994sim2004 yearbooks areselected as fitness test specimens The fitness error is under9 times 10

minus12 hence the PSO-RBFNN model fits well withhistorical data from 1994 to 2004The data during 2005sim2009are chosen as extrapolation test specimens In this paper

the extrapolation test utilizes mean absolute percent error(MAPE) as an error indicator The formula is

MAPE =1

119899

119899

sum

119894=1

(

1003816100381610038161003816119909119894 minus 119909119894

1003816100381610038161003816

119909119894

times 100) (6)



1198881

1198882

Trainingerror 119888

11198882

Trainingerror

4

07 0014683

17

07 000270505 0008015 05 000347404 0011149 04 000308702 0008810 02 0001945

3

07 0002918

15

07 000231005 003043 05 000322404 0019198 04 000301102 0003097 02 0001291

2

07 0002679

13

07 000324105 0002578 05 000205304 0003098 04 000270302 0002796 02 0003204

1 2 3 4 5 6 7 80

02040608

1Training vectors

Input vectors P

Targ

et v

ecto

rs T

minus8 minus6 minus4 minus2 0 2 4 6 8minus1

minus05

0

05

1 Transfer function

a

Figure 8 Training vectors and transfer function

Various predictionmodelsrsquo capability can bemeasured byMAPE and the range of MAPE The prediction accuracy isshown in Table 8 Referring to (6) we can calculate MAPE =

27 which is under 10 According to Table 8 this PSO-RBFNN has a good fitness capability and extensionality Thefitness error and prediction error are illustrated in Figure 9

To prove the PSO-RBFNNrsquos good prediction capabilitywe compare the prediction capability among PSO-RBFNN aregular BP (backpropagation) network and a regular RBFNNmodel All the inputs and outputs are the same in eachmodelThe prediction errors are shown in Figure 10 Compared withthe BP network and the regular RBFNN model the PSO-RBFNN has smaller errors as well as a better convergenceand convergence rate The training performance of the twodifferent RBFNNs is shown in Figure 11 The training perfor-mance of PSO-RBFNN is 000125095 less than the trainingperformance of the regular RBFNN 000147074 Accordinglythe PSO-RBFNN has a better prediction capability andconvergence

Table 8 The MAPE range and prediction evaluation

MAPE range Prediction evaluationMAPE le 10 Precision prediction10 le MAPE le 20 Good prediction20 le MAPE le 50 Feasible predictionMAPE gt 50 Error prediction

52 Prediction Result For the purpose of predicting theregional logistics demands in 2010sim2015 it is necessary toinput the economic indicators of Sichuan in 2010sim2015 In therecent years the economic development of Sichuan provincehas grown rapidly with the average GDP annual growthrate of 1393 from 1994 to 2009 Hence it is assumed thatthe average annual growth rate in the next few years willbe 1393 2011 was the first year of the ldquoTwelfth Five-YearProgramrdquo in China During the period of the ldquoTwelfth Five-Year Programrdquo the industrial structure in China will adjustfurther and it is expected that the tertiary industry annualgrowth rate in Sichuan province will increase by 1523as acceptable with the Delphi method In 1994sim2009 theaverage annual growth rate of the total consumer goodsretail sales was 1386 and the consumption growth rate was1153 Therefore in the same assumption the total retailsales of consumer goods and consumption will have the samegrowth trend from 2010 to 2015 The foreign trade averageannual growth rate from 1994 to 2007 in Sichuan provincewas 1516 hence we assume that foreign trade will maintainsuch a growth rate

The prediction outcomes for the Sichuan provinceregional economy are illustrated in Table 9 The predictionresults in Table 10 show that the total freight traffic and freightturnover are expected to grow faster

According to Tables 9 and 10 the economic indicatorsand the scale of logistics demand in Sichuan province reveala rapid growth trend in the next five years and also provethe inherent relevance between regional logistics demand andregional economy

In particular the ldquo512 Wenchuan Earthquakerdquo inflictedheavy loss on Sichuan province Hence after the recon-struction process is completed logistics demand is expectedto increase sharply with the result that the regional logis-tics industry will be highlighted in the growth of theregional economy Further as ldquoThe 12th Five-Year Programon National Economic and Social Developmentrdquo proposesindustrial optimizationwill beChinarsquos top priority To achievethis optimization China will need to speed up the develop-ment of the modern service industry in which the logisticsindustry is the principal development focus

6 Conclusion and Discussion

Logistics is a pioneer in the development of logistics demandDuring the process of conducting logistics development plan-ning regional plannersrsquo lack of correct understanding of thelogistics demand will result in the imbalance between supplyand demand Furthermore it will cause the phenomenon of


The prediction errorminus14

minus12

minus10

minus08

minus06

minus04

minus02

00

02

04

2 3 41

1 2 3 4 5 6 7 8 9 10 112

3

4

5

6

7

8

9

10

The fitting error

times10minus12

Figure 9 The fitting and predicting error

Table 9 2010sim2015 economic indicators prediction

Year GDP PIO SIO TIO RRS TIE PCC2010 1612237 244157 774057 600072 60098067 2789982 7588222011 1836791 266614 893241 691451 68426249 3212906 8446172012 2092621 291137 1030778 796745 77908523 3699940 9401122013 2384083 317916 1189491 918072 88704817 4260802 10464042014 2716140 347157 1372642 1057875 100997224 4906683 11647142015 3094447 379088 1583994 1218968 114993071 5650472 1296400

8060402000

minus20minus40minus60

BPPSO-RBFNNRBF

1 2 3 4

Figure 10 The prediction errors in different models

insufficient supply and overinvestment It will also hinderthe development of the logistics industryTherefore studyingthe forecast of regional logistics demand has vital practicalsignificance In this paper based on the theory of regionallogistics demand and its prediction the characteristics andthe main content of regional logistics demand predictionare analyzed the PSO-RBFNN prediction model is builtand an empirical research of logistics demand in Sichuan

province is conducted The principal conclusions are asfollows

(1) By feasibility analysis and empirical research it isproved that a PSO-RBFNN model which introduces a PSOalgorithm to optimizing the RBF neural network connectingweights and thresholds is scientific and practical Combin-ing RBFNN with PSO overcomes their own shortcomingsand achieves better prediction and optimization results (2)Through correlation analysis the strong correlation betweenthe regional economy and regional logistics demand isproven The rapid development of the regional economy willdrive the rapid development of regional logistics (3) In theempirical research we applied the PSO-RBFNN model topredict the regional logistics demand of Sichuan provincefrom 2010 to 2015 After inputting the regional logisticsdemand prediction indicators values into the PSO-RBFNNmodel valid results are calculated in Table 9 suggesting thatthe total freight traffic and freight turnover will increaseby 137 and 588 respectively The PSO-RBFNN modelis utilized to fit well the nonlinear relationship betweenthe regional economy and regional logistics demand (4)Through empirical research it is obvious that using logisticsdemand and regional economic indicators to predict regional


Perfo

rman

ce

100

10minus1

10minus2

10minus3

10minus4

Perfo

rman

ce

Stop training Stop training

100

10minus1

10minus2

10minus3

10minus4

1000 epochs1000 epochs0 100 200 300 400 500 600 700 800 900 10000 100 200 300 400 500 600 700 800 900 1000

Performance is 000125095 goal is 0001 Performance is 000147074 goal is 0001

Figure 11 The training errors in different RBFNNs

Table 10 Total freight traffic and freight turnover prediction results

Year 2010 2011 2012 2013 2014 2015TFT (10 000 tons) 104337 108129 110364 114438 115782 118621FT (billion ton-km) 2077 2320 2514 2796 3013 3298

logistics demand is a viable researchmethodMultiple factorsaffect the demand for logistics Studying the development oflogistics demand based on the trend of only one indicatoris unreasonable On the other hand compared with thetraditional forecasting methods the PSO-RBFNN modelpredicts regional logistics demand more accurately

Nevertheless our study should be improved in termsof the index system of regional logistics demand predic-tion It is not enough to establish indicators only basedon the perspective of economic indicators and freight vol-ume even though these indicators are easy to be col-lected Other indicators such as logistics cost GDP ratioshould also be studied Further we predict the scale ofregional logistics demand rather than the structure andquality of regional logistics demand In future research thestructure and quality of regional logistics demand will beinvestigated

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

This work is supported by the National Natural ScienceFoundation of China (Grant no 71301109) the Westernand Frontier Region Project of Humanity and Social Sci-ences Research Ministry of Education of China (Grant no

13XJC630018) and the Initial Funding for Young Teachers ofSichuan University (Grant no 2013SCU11014)

References

[1] R Godrigo and H Mahmassani ldquoForecasting freight trans-portation demand with the space-time multinomial probitmodelrdquo Transportation Research Part B Methodological vol 34no 5 pp 403ndash418 2000

[2] B Adrangi A Chatrath and K Raffiee ldquoThe demand for USair transport services a chaos and nonlinearity investigationrdquoTransportation Research Part E Logistics and TransportationReview vol 37 no 5 pp 337ndash353 2001

[3] J T Fite G D Taylor J S Usher J R English and J N RobertsldquoForecasting freight demand using economic indicesrdquo Interna-tional Journal of Physical Distribution amp Logistics Managementvol 32 no 4 pp 299ndash308 2002

[4] X Guo S Xie and B Hu ldquoRegional logistics demand analysismodel and solutionrdquo Journal of Southeast University (NaturalScience) vol 31 no 3 pp 1ndash5 2001

[5] R Wang C Chen and V Berkhard ldquoTheories and method-ology on long term projection of cargo flows in Tumen Rivereconomic developmen areardquo Human Geography vol 9 pp 21ndash25 1999

[6] Y Lai Q Zheng S Zhang and C Ji ldquoApplication of grayforecast model to transport volume in Jinsha Riverrdquo Journal ofWuhan University of Hydraulic and Electric Engineering vol 33no 1 pp 96ndash99 2000

[7] Y Zhang H Ye M Ren and C Ji ldquoApplication of gray forecastusing neural networkmodelrdquo Southeast Jiaotong University vol34 no 5 pp 602ndash605 1999


[8] H Niu and Y Yin ldquoFuzzy forecasting on freight demands inrailroad hubrdquo Journal of Lanzhou Railway University vol 17 no3 pp 89ndash94 1998

[9] R Garrido and H Mahmassani ldquoForecasting freight trans-portation demand with the space-time multinomial probitmodelrdquo Transportation Research Part B Methodological vol 34no 5 pp 403ndash418 2000

[10] Q Sun and H Ding ldquoTheory and model establishment forregional logistics demand predictionrdquo Theoretical Discussionno 10 pp 27ndash30 2004

[11] L Chu Z Tian and X Xie ldquoApplication of an combinationforecasting model in logistics demandrdquo Journal of DalianMaritime University vol 30 no 4 pp 43ndash46 2004

[12] J Sun and X Xiang ldquoLogistics demand prediction researchbased on the gray linear regression combination modelrdquo Indus-trial Technology amp Economy vol 26 no 10 pp 146ndash148 2007

[13] Q Dong ldquoRegional logistics information platform and resourceplanningrdquo Traffic and Transportation Engineering no 4 pp 56ndash58 2002

[14] J Xiao ldquoDevelopment of urban centers and modern logisticsindustryrdquo Commodity Storage and Conservation vol 5 pp 7ndash10 2002

[15] X Heng ldquoReflections on the development of logistics enter-prises in Chinardquo Containerization vol 5 pp 21ndash22 2003

[16] Q Zhang ldquoUnited States Japan logisticsrdquo Modern EnterpriseEducation no 4 pp 18ndash19 2003

[17] J Moody and C Darken ldquoFast learning in networks of locally-tuned processing unitsrdquo Neural Computation vol 1 no 2 pp281ndash294 1989

[18] S Haykin Neural Networks and Learning Machines PrenticeHall 2008

[19] J Kennedy and R Eberhart ldquoParticle swarm optimizationrdquoin Proceedings of the IEEE International Conference on NeuralNetworks pp 1942ndash1948 December 1995

[20] E Assareh M A Behrang M R Assari and A GhanbarzadehldquoApplication of PSO (particle swarm optimization) and GA(genetic algorithm) techniques on demand estimation of oil inIranrdquo Energy vol 35 no 12 pp 5223ndash5229 2010

[21] PWang Z-Y HuangM-Y Zhang and X-W Zhao ldquoMechani-cal property prediction of strip model based on PSO-BP neuralnetworkrdquo Journal of Iron and Steel Research International vol15 no 3 pp 87ndash91 2008

[22] Z Ji H Liao and Q Wu Particle Swarm Optimization and ItsApplication Science Press Beijing China 2009

[23] Y Shi and R Eberhart ldquoA modified particle swarm optimizerrdquoin Proceedings of the IEEE International Conference on Evolu-tionary Computation (ICEC rsquo98) pp 69ndash73 IEEE AnchorageAlaska USA May 1998

[24] R Yang H Zhang and Z Miao ldquoMoving average method inlogistics forecasting techniquesrdquo Journal ofWuhan University ofTechnology vol 25 no 3 pp 353ndash355 2001

[25] H Widiarta S Viswanathan and R Piplani ldquoOn the effec-tiveness of top-down strategy for forecasting autoregressivedemandsrdquo Naval Research Logistics vol 54 no 2 pp 176ndash1882007

[26] X Qiao M Dong andM Zhang ldquoPrediction of passenger andcargo traffic of National Highway based on elastic coefficientmethodrdquo East China Highway no 5 pp 87ndash90 2004

Submit your manuscripts athttpwwwhindawicom

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

MathematicsJournal of


Mathematical Problems in Engineering

Hindawi Publishing Corporationhttpwwwhindawicom

Differential EquationsInternational Journal of

Volume 2014

Applied MathematicsJournal of


Probability and StatisticsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Journal of


Mathematical PhysicsAdvances in

Complex AnalysisJournal of


OptimizationJournal of


CombinatoricsHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of


Operations ResearchAdvances in

Journal of


Function Spaces

Abstract and Applied AnalysisHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of Mathematics and Mathematical Sciences


The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014


Algebra

Discrete Dynamics in Nature and Society



Decision SciencesAdvances in

Discrete MathematicsJournal of


Volume 2014 Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Stochastic AnalysisInternational Journal of


Table 1 Common forecasting methods

Forecasting methods The applicable situationMoving average [24] Suitable for spot predictionExponentialsmoothing [25]

Repeated prediction with or without achange in seasons

Grey model [6] Development of time series showingexponential trend

Elastic coefficientmethod [26]

Two factors between119883 and 119884 have anexponential relationship

Linear regressionmodel [3]

A linear relationship betweenindependent variables and dependentvariables

Artificial neuralnetwork model [7]

Being able to make prediction ofnonlinear corresponding relationship

Time series forecasting method does not consider theinfluence of other economic development indicators It dis-regards that the regional logistics demand is of derivationHence there are often serious prediction errors On the otherhand compared with the macrologistics regional logisticsdemand prediction has its own characteristics there existsa high degree of nonlinearity between logistics demand andthe impact of logistics demand indicators as well as greatervolatility than macrologistics Due to these features the tra-ditional time series forecastingmethods (such as greymodel)and linear prediction methods (such as linear regressionmodel) do notwork effectively Consequently artificial neuralnetwork (ANN) model is more suitable Furthermore it isexactly the complexity and nonlinearity of regional logisticsdemand system that make a single predictionmodel functionnot well [9ndash12] Therefore it is necessary to use a combinedmodel

In this paper a regional logistics demandprediction indexsystem with economic indicators and logistics indicatorsand a regional logistics demand prediction model based onradial basis function neural network (RBFNN) combinedwith particle swarm optimization (PSO) algorithm will bebuilt The PSO-RBFNNmodel will be trained with processeddata from Sichuan province and will be applied to predictthe regional logistics demand in the very area as well Theprediction result will be evaluated and compared with abackpropagation (BP) neural network and regular RBFNNEventually the results and conclusions drawn from the PSO-RBFNNpredictionmodel will be discussed and summarized

2 Problem Description

21 Problem Background In order to enhance the investmentenvironment to increase the attraction of foreign invest-ment to solve the employment pressure and to improvethe comprehensive competitiveness of urban areas multipleregions in China have adopted a variety of planning policiesto encourage the development of logistics and construction oflogistics infrastructure Nonetheless Chinarsquos logistics startedlate and the related policies strategies and planning arenot mature Plannersrsquo understanding of the development ofmodern logistics concept and mode of operation is still not

unified especially in the field of logistics demand and soon When formulating logistics development policies andstudying the feasibility of logistics infrastructure scholarsascertain that the lack of quantitative data about logisticsdemand results in numerous problems in the planningprocess for instance the imbalance between actual supplycapacity of logistics and logistics demand repeated construc-tion and sedimentation of money caused by tremendouswaste of resources and false prosperity of logistics industryOverall predicting regional logistics demand is critical for thesustainable development of regional logistics industry

Therefore the quantitative prediction of the scale anddevelopment trends of logistics demand is essential To beginwith this kind of predictions can purposefully guide socialinvestment into the field of logistics Various types of logisticsinfrastructure can be rationally planned and constructedlogistics supply system and network layout can be improvedMoreover the predictions continuously provide the basis forthe supply to meet the demand so as to maintain a relativebalance between supply and demand for logistics services andto make the regional logistics maintain high efficiency

22 Related Concepts of Regional Logistics Demand Cur-rently there is no uniform view for the definition of regionallogistics Dong [13] holds that regional logistics is a systemaiming at optimizing the socioeconomic strategies throughthe planning and construction of a certain region Mean-while it also refers to activities associated with logistics oper-ation and control In accordance with the systems definedby systems engineering the regional logistics system canbe defined as follows in a certain economic geographicarea it is an organic whole with specific operating lawand function formed by interrelated interdependent andinteracting elements of all logistics at different spatial scalesThe regional logistics system is illustrated in Figure 1

Compared with the national logistics systems and enter-prise logistics system the regional logistics system is anorganic integrated logistics system within the range of theeconomic region The basic structural unit of the regionallogistics system is a microenterprise supply sales logisticsand so on Meanwhile it is a vital part of the nationallogistics international logistics and other macrologisticssystems The regional logistics system which is mesolevelbecomes the convergence of the microscopic and macro-scopic logistics systems Its purpose is to apply the logisticschain management solutions to address a variety of logisticalproblems beyond a single enterprise so as to achieve logisticsrationalization in a region or in a wider range of areas [14ndash16]as is indicated in Figure 2

Logistics demand prediction is based on the relation-ship between past and current logistics market demandinformation and factors affecting the changes in the logis-tics market demand It uses sound judgment experiencetechnical methods and predictive models on the basis ofhistorical data and statistical information to derive someregularity trends and intrinsic link trends among the factorswhich predicts indicators reflecting market demand trendsLogistics demand prediction is preestimates and predictions


TargetKeep balance

Dem

and

Dem

and

Primary industry

Secondary industry

Tertiary industry


Logistics park



Urbandistribution

centers

Manufacturers

Distributors

Consumer

Warehousing

Machining

Package

Handling


Airport

Port


RTS highway t

The international

City

Region

The domestic



3 Methodologies









1 10 000 tons)








6





Indicatorspecies







Industrypersonnel












[1199091 1199092 119909




tion y = [1199101 1199102 119910


119894(119909 minus 119888

119894)


119894=1119908119894Φ119894(119909 minus 119888

119894) where 119908


















W isin Rhtimesm

x1

x2

xn

c1

c2

ch

Σ

Σ

b1

bm

y1

ym

120601(x minus c1)

120601(x minus ch)



119894is the center





function [18]

Φ119894(119905) = 119890

minus(11990521205752


Φ119894(119905) =

1


Φ119894(119905) =

1

(1199052 + 1205752

119894)120572 120572 gt 0


(1)










(1199091 1199092 119909

119894 119909


is 119909119894= (1199091198941 1199091198942 119909


V119894= (V1198941 V1198942 V



= (1198751198941 1198751198942 119875

119894119899)119879 and the best


(1198751198921 1198751198922 119875





V119896+1119894119889

= 120596V119896119894119889+ 1198881120585 (119901119896

119894119889minus 119909119896

119894119889) + 1198882120578 (119901119896

119892119889minus 119909119896

119892119889)

119909119896+1

119894119889= 119909119896

119894119889+ V119896+1119894119889

(2)






119894 119909

119898)


= (1198751198941 1198751198942 119875


119894=

(V1198941 V1198942 V








119894




119892





IW =

[[[[

[

IW11

IW12


IW21

IW22


d

IW1198991

IW1198992


]]]]

]

(3)





LW =

[[[[

[

LW11

LW12


LW21

LW22


d

LW1199041

LW1199042


]]]]

]

(4)




11989911989811988721 11988722 119887

2119904]











Economicindicators

Logisticsscale

W

PSO

y1

y2

x1

x2

c1

c2

cn



119894




119892





4 Case Study















Yes

No

Collect specimens




Compare and update




Train the RBFNN



119883119894=


(5)



119894





2119898 (e) 119896 = 2 times (119898 + 119899)3


1

2

3

7

1

2

3

14

15

1

2


x1

x2

x3

x7

y1

y2










minus119909)(1 + 119890







Year 1199091

1199092

1199093

1199094

1199095

1199096

1199097

1199101

1199102

1994 200141 59737 78277 62127 7247408 291645 136717 72336 4971995 244321 66246 98091 79984 9363651 235872 164627 67154 5651996 287165 77002 115601 94562 10914485 214883 18796 52004 5361997 324147 88028 126532 109587 12123699 179005 207774 56935 5491998 347409 91224 132401 123784 12985695 209328 224341 50759 5681999 364912 92603 134963 137346 13825869 247069 234753 50142 5742000 39282 94558 143311 154951 15237490 254517 255048 54943 5972001 42935 98168 157201 173981 16804041 309916 270715 54141 6482002 472501 104795 173338 194368 18500576 446919 291439 57297 7042003 533309 112861 20148 218968 20910543 446919 320336 57200 6992004 637963 137992 249317 250654 23839515 563862 36562 65580 8042005 738511 148114 306723 283674 29813734 687162 413008 70364 8982006 863781 160348 377519 323914 34216483 790476 450134 74200 8912007 1030530 203200 464130 383200 40155746 1102097 525922 79940 9792008 1260123 221615 582339 456169 48007638 1438461 607200 114513 15132009 1415136 223591 670774 520770 52783510 2422728 681742 102635 1913


1199091

1199092

1199093

1199094

1199095

1199096

1199097

1199101

0867lowastlowast

0826lowastlowast

0892lowastlowast

0838lowastlowast

0859lowastlowast

0921lowastlowast

0835lowastlowast

1199102

0951lowastlowast

0906lowastlowast

0961lowastlowast

0939lowastlowast

0939lowastlowast

0985lowastlowast

0938lowastlowast



Year 1199091

1199092

1199093

1199094

1199095

1199096

1199097

1199101

1199102

1994 00001 00001 00001 00001 00001 00502 00001 04228 000011995 00364 00397 09154 00389 00404 00253 00512 03241 004801996 00716 01054 06798 00707 00747 00160 00940 00355 002751997 01021 01727 05911 01035 01014 00000 01304 01294 003671998 01212 01922 06308 01344 01205 00135 01608 00118 005011999 01356 02006 06761 01640 01390 00303 01799 00001 005442000 01586 02125 07462 02024 01702 00337 02171 00915 007062001 01887 02345 08043 02439 02049 00583 02459 00762 010662002 02242 02750 08152 02883 02423 01194 02839 01363 014622003 02742 03242 08458 03420 02956 01194 03369 01345 014272004 03603 04776 07545 04111 03603 01715 04200 02941 021682005 04431 05394 08215 04830 04924 02265 05069 03852 028322006 05462 06140 08896 05708 05897 02725 05751 04583 027822007 06835 08756 07806 07000 07209 04114 07141 05677 034042008 08724 09879 08831 08591 08945 09058 08632 08453 071752009 09999 09999 09999 09999 09999 09999 09999 09999 09999





MAPE =1

119899

119899

sum

119894=1

(

1003816100381610038161003816119909119894 minus 119909119894

1003816100381610038161003816

119909119894

times 100) (6)



1198881

1198882


11198882

Trainingerror

4

07 0014683

17

07 000270505 0008015 05 000347404 0011149 04 000308702 0008810 02 0001945

3

07 0002918

15

07 000231005 003043 05 000322404 0019198 04 000301102 0003097 02 0001291

2

07 0002679

13

07 000324105 0002578 05 000205304 0003098 04 000270302 0002796 02 0003204

1 2 3 4 5 6 7 80

02040608

1Training vectors

Input vectors P

Targ

et v

ecto

rs T


minus05

0

05

1 Transfer function

a















minus12

minus10

minus08

minus06

minus04

minus02

00

02

04

2 3 41

1 2 3 4 5 6 7 8 9 10 112

3

4

5

6

7

8

9

10

The fitting error

times10minus12




8060402000


BPPSO-RBFNNRBF

1 2 3 4






Perfo

rman

ce

100

10minus1

10minus2

10minus3

10minus4

Perfo

rman

ce


100

10minus1

10minus2

10minus3

10minus4

1000 epochs1000 epochs0 100 200 300 400 500 600 700 800 900 10000 100 200 300 400 500 600 700 800 900 1000









Acknowledgments



References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










TargetKeep balance

Dem

and

Dem

and

Primary industry

Secondary industry

Tertiary industry


Logistics park



Urbandistribution

centers

Manufacturers

Distributors

Consumer

Warehousing

Machining

Package

Handling


Airport

Port


RTS highway t

The international

City

Region

The domestic



3 Methodologies









1 10 000 tons)








6





Indicatorspecies







Industrypersonnel












[1199091 1199092 119909




tion y = [1199101 1199102 119910


119894(119909 minus 119888

119894)


119894=1119908119894Φ119894(119909 minus 119888

119894) where 119908


















W isin Rhtimesm

x1

x2

xn

c1

c2

ch

Σ

Σ

b1

bm

y1

ym

120601(x minus c1)

120601(x minus ch)



119894is the center





function [18]

Φ119894(119905) = 119890

minus(11990521205752


Φ119894(119905) =

1


Φ119894(119905) =

1

(1199052 + 1205752

119894)120572 120572 gt 0


(1)










(1199091 1199092 119909

119894 119909


is 119909119894= (1199091198941 1199091198942 119909


V119894= (V1198941 V1198942 V



= (1198751198941 1198751198942 119875

119894119899)119879 and the best


(1198751198921 1198751198922 119875





V119896+1119894119889

= 120596V119896119894119889+ 1198881120585 (119901119896

119894119889minus 119909119896

119894119889) + 1198882120578 (119901119896

119892119889minus 119909119896

119892119889)

119909119896+1

119894119889= 119909119896

119894119889+ V119896+1119894119889

(2)






119894 119909

119898)


= (1198751198941 1198751198942 119875


119894=

(V1198941 V1198942 V








119894




119892





IW =

[[[[

[

IW11

IW12


IW21

IW22


d

IW1198991

IW1198992


]]]]

]

(3)





LW =

[[[[

[

LW11

LW12


LW21

LW22


d

LW1199041

LW1199042


]]]]

]

(4)




11989911989811988721 11988722 119887

2119904]











Economicindicators

Logisticsscale

W

PSO

y1

y2

x1

x2

c1

c2

cn



119894




119892





4 Case Study















Yes

No

Collect specimens




Compare and update




Train the RBFNN



119883119894=


(5)



119894





2119898 (e) 119896 = 2 times (119898 + 119899)3


1

2

3

7

1

2

3

14

15

1

2


x1

x2

x3

x7

y1

y2










minus119909)(1 + 119890







Year 1199091

1199092

1199093

1199094

1199095

1199096

1199097

1199101

1199102

1994 200141 59737 78277 62127 7247408 291645 136717 72336 4971995 244321 66246 98091 79984 9363651 235872 164627 67154 5651996 287165 77002 115601 94562 10914485 214883 18796 52004 5361997 324147 88028 126532 109587 12123699 179005 207774 56935 5491998 347409 91224 132401 123784 12985695 209328 224341 50759 5681999 364912 92603 134963 137346 13825869 247069 234753 50142 5742000 39282 94558 143311 154951 15237490 254517 255048 54943 5972001 42935 98168 157201 173981 16804041 309916 270715 54141 6482002 472501 104795 173338 194368 18500576 446919 291439 57297 7042003 533309 112861 20148 218968 20910543 446919 320336 57200 6992004 637963 137992 249317 250654 23839515 563862 36562 65580 8042005 738511 148114 306723 283674 29813734 687162 413008 70364 8982006 863781 160348 377519 323914 34216483 790476 450134 74200 8912007 1030530 203200 464130 383200 40155746 1102097 525922 79940 9792008 1260123 221615 582339 456169 48007638 1438461 607200 114513 15132009 1415136 223591 670774 520770 52783510 2422728 681742 102635 1913


1199091

1199092

1199093

1199094

1199095

1199096

1199097

1199101

0867lowastlowast

0826lowastlowast

0892lowastlowast

0838lowastlowast

0859lowastlowast

0921lowastlowast

0835lowastlowast

1199102

0951lowastlowast

0906lowastlowast

0961lowastlowast

0939lowastlowast

0939lowastlowast

0985lowastlowast

0938lowastlowast



Year 1199091

1199092

1199093

1199094

1199095

1199096

1199097

1199101

1199102

1994 00001 00001 00001 00001 00001 00502 00001 04228 000011995 00364 00397 09154 00389 00404 00253 00512 03241 004801996 00716 01054 06798 00707 00747 00160 00940 00355 002751997 01021 01727 05911 01035 01014 00000 01304 01294 003671998 01212 01922 06308 01344 01205 00135 01608 00118 005011999 01356 02006 06761 01640 01390 00303 01799 00001 005442000 01586 02125 07462 02024 01702 00337 02171 00915 007062001 01887 02345 08043 02439 02049 00583 02459 00762 010662002 02242 02750 08152 02883 02423 01194 02839 01363 014622003 02742 03242 08458 03420 02956 01194 03369 01345 014272004 03603 04776 07545 04111 03603 01715 04200 02941 021682005 04431 05394 08215 04830 04924 02265 05069 03852 028322006 05462 06140 08896 05708 05897 02725 05751 04583 027822007 06835 08756 07806 07000 07209 04114 07141 05677 034042008 08724 09879 08831 08591 08945 09058 08632 08453 071752009 09999 09999 09999 09999 09999 09999 09999 09999 09999





MAPE =1

119899

119899

sum

119894=1

(

1003816100381610038161003816119909119894 minus 119909119894

1003816100381610038161003816

119909119894

times 100) (6)



1198881

1198882


11198882

Trainingerror

4

07 0014683

17

07 000270505 0008015 05 000347404 0011149 04 000308702 0008810 02 0001945

3

07 0002918

15

07 000231005 003043 05 000322404 0019198 04 000301102 0003097 02 0001291

2

07 0002679

13

07 000324105 0002578 05 000205304 0003098 04 000270302 0002796 02 0003204

1 2 3 4 5 6 7 80

02040608

1Training vectors

Input vectors P

Targ

et v

ecto

rs T


minus05

0

05

1 Transfer function

a















minus12

minus10

minus08

minus06

minus04

minus02

00

02

04

2 3 41

1 2 3 4 5 6 7 8 9 10 112

3

4

5

6

7

8

9

10

The fitting error

times10minus12




8060402000


BPPSO-RBFNNRBF

1 2 3 4






Perfo

rman

ce

100

10minus1

10minus2

10minus3

10minus4

Perfo

rman

ce


100

10minus1

10minus2

10minus3

10minus4

1000 epochs1000 epochs0 100 200 300 400 500 600 700 800 900 10000 100 200 300 400 500 600 700 800 900 1000









Acknowledgments



References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















1 10 000 tons)








6





Indicatorspecies







Industrypersonnel












[1199091 1199092 119909




tion y = [1199101 1199102 119910


119894(119909 minus 119888

119894)


119894=1119908119894Φ119894(119909 minus 119888

119894) where 119908


















W isin Rhtimesm

x1

x2

xn

c1

c2

ch

Σ

Σ

b1

bm

y1

ym

120601(x minus c1)

120601(x minus ch)



119894is the center





function [18]

Φ119894(119905) = 119890

minus(11990521205752


Φ119894(119905) =

1


Φ119894(119905) =

1

(1199052 + 1205752

119894)120572 120572 gt 0


(1)










(1199091 1199092 119909

119894 119909


is 119909119894= (1199091198941 1199091198942 119909


V119894= (V1198941 V1198942 V



= (1198751198941 1198751198942 119875

119894119899)119879 and the best


(1198751198921 1198751198922 119875





V119896+1119894119889

= 120596V119896119894119889+ 1198881120585 (119901119896

119894119889minus 119909119896

119894119889) + 1198882120578 (119901119896

119892119889minus 119909119896

119892119889)

119909119896+1

119894119889= 119909119896

119894119889+ V119896+1119894119889

(2)






119894 119909

119898)


= (1198751198941 1198751198942 119875


119894=

(V1198941 V1198942 V








119894




119892





IW =

[[[[

[

IW11

IW12


IW21

IW22


d

IW1198991

IW1198992


]]]]

]

(3)





LW =

[[[[

[

LW11

LW12


LW21

LW22


d

LW1199041

LW1199042


]]]]

]

(4)




11989911989811988721 11988722 119887

2119904]











Economicindicators

Logisticsscale

W

PSO

y1

y2

x1

x2

c1

c2

cn



119894




119892





4 Case Study















Yes

No

Collect specimens




Compare and update




Train the RBFNN



119883119894=


(5)



119894





2119898 (e) 119896 = 2 times (119898 + 119899)3


1

2

3

7

1

2

3

14

15

1

2


x1

x2

x3

x7

y1

y2










minus119909)(1 + 119890







Year 1199091

1199092

1199093

1199094

1199095

1199096

1199097

1199101

1199102

1994 200141 59737 78277 62127 7247408 291645 136717 72336 4971995 244321 66246 98091 79984 9363651 235872 164627 67154 5651996 287165 77002 115601 94562 10914485 214883 18796 52004 5361997 324147 88028 126532 109587 12123699 179005 207774 56935 5491998 347409 91224 132401 123784 12985695 209328 224341 50759 5681999 364912 92603 134963 137346 13825869 247069 234753 50142 5742000 39282 94558 143311 154951 15237490 254517 255048 54943 5972001 42935 98168 157201 173981 16804041 309916 270715 54141 6482002 472501 104795 173338 194368 18500576 446919 291439 57297 7042003 533309 112861 20148 218968 20910543 446919 320336 57200 6992004 637963 137992 249317 250654 23839515 563862 36562 65580 8042005 738511 148114 306723 283674 29813734 687162 413008 70364 8982006 863781 160348 377519 323914 34216483 790476 450134 74200 8912007 1030530 203200 464130 383200 40155746 1102097 525922 79940 9792008 1260123 221615 582339 456169 48007638 1438461 607200 114513 15132009 1415136 223591 670774 520770 52783510 2422728 681742 102635 1913


1199091

1199092

1199093

1199094

1199095

1199096

1199097

1199101

0867lowastlowast

0826lowastlowast

0892lowastlowast

0838lowastlowast

0859lowastlowast

0921lowastlowast

0835lowastlowast

1199102

0951lowastlowast

0906lowastlowast

0961lowastlowast

0939lowastlowast

0939lowastlowast

0985lowastlowast

0938lowastlowast



Year 1199091

1199092

1199093

1199094

1199095

1199096

1199097

1199101

1199102

1994 00001 00001 00001 00001 00001 00502 00001 04228 000011995 00364 00397 09154 00389 00404 00253 00512 03241 004801996 00716 01054 06798 00707 00747 00160 00940 00355 002751997 01021 01727 05911 01035 01014 00000 01304 01294 003671998 01212 01922 06308 01344 01205 00135 01608 00118 005011999 01356 02006 06761 01640 01390 00303 01799 00001 005442000 01586 02125 07462 02024 01702 00337 02171 00915 007062001 01887 02345 08043 02439 02049 00583 02459 00762 010662002 02242 02750 08152 02883 02423 01194 02839 01363 014622003 02742 03242 08458 03420 02956 01194 03369 01345 014272004 03603 04776 07545 04111 03603 01715 04200 02941 021682005 04431 05394 08215 04830 04924 02265 05069 03852 028322006 05462 06140 08896 05708 05897 02725 05751 04583 027822007 06835 08756 07806 07000 07209 04114 07141 05677 034042008 08724 09879 08831 08591 08945 09058 08632 08453 071752009 09999 09999 09999 09999 09999 09999 09999 09999 09999





MAPE =1

119899

119899

sum

119894=1

(

1003816100381610038161003816119909119894 minus 119909119894

1003816100381610038161003816

119909119894

times 100) (6)



1198881

1198882


11198882

Trainingerror

4

07 0014683

17

07 000270505 0008015 05 000347404 0011149 04 000308702 0008810 02 0001945

3

07 0002918

15

07 000231005 003043 05 000322404 0019198 04 000301102 0003097 02 0001291

2

07 0002679

13

07 000324105 0002578 05 000205304 0003098 04 000270302 0002796 02 0003204

1 2 3 4 5 6 7 80

02040608

1Training vectors

Input vectors P

Targ

et v

ecto

rs T


minus05

0

05

1 Transfer function

a















minus12

minus10

minus08

minus06

minus04

minus02

00

02

04

2 3 41

1 2 3 4 5 6 7 8 9 10 112

3

4

5

6

7

8

9

10

The fitting error

times10minus12




8060402000


BPPSO-RBFNNRBF

1 2 3 4






Perfo

rman

ce

100

10minus1

10minus2

10minus3

10minus4

Perfo

rman

ce


100

10minus1

10minus2

10minus3

10minus4

1000 epochs1000 epochs0 100 200 300 400 500 600 700 800 900 10000 100 200 300 400 500 600 700 800 900 1000









Acknowledgments



References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra























W isin Rhtimesm

x1

x2

xn

c1

c2

ch

Σ

Σ

b1

bm

y1

ym

120601(x minus c1)

120601(x minus ch)



119894is the center





function [18]

Φ119894(119905) = 119890

minus(11990521205752


Φ119894(119905) =

1


Φ119894(119905) =

1

(1199052 + 1205752

119894)120572 120572 gt 0


(1)










(1199091 1199092 119909

119894 119909


is 119909119894= (1199091198941 1199091198942 119909


V119894= (V1198941 V1198942 V



= (1198751198941 1198751198942 119875

119894119899)119879 and the best


(1198751198921 1198751198922 119875





V119896+1119894119889

= 120596V119896119894119889+ 1198881120585 (119901119896

119894119889minus 119909119896

119894119889) + 1198882120578 (119901119896

119892119889minus 119909119896

119892119889)

119909119896+1

119894119889= 119909119896

119894119889+ V119896+1119894119889

(2)






119894 119909

119898)


= (1198751198941 1198751198942 119875


119894=

(V1198941 V1198942 V








119894




119892





IW =

[[[[

[

IW11

IW12


IW21

IW22


d

IW1198991

IW1198992


]]]]

]

(3)





LW =

[[[[

[

LW11

LW12


LW21

LW22


d

LW1199041

LW1199042


]]]]

]

(4)




11989911989811988721 11988722 119887

2119904]











Economicindicators

Logisticsscale

W

PSO

y1

y2

x1

x2

c1

c2

cn



119894




119892





4 Case Study















Yes

No

Collect specimens




Compare and update




Train the RBFNN



119883119894=


(5)



119894





2119898 (e) 119896 = 2 times (119898 + 119899)3


1

2

3

7

1

2

3

14

15

1

2


x1

x2

x3

x7

y1

y2










minus119909)(1 + 119890







Year 1199091

1199092

1199093

1199094

1199095

1199096

1199097

1199101

1199102

1994 200141 59737 78277 62127 7247408 291645 136717 72336 4971995 244321 66246 98091 79984 9363651 235872 164627 67154 5651996 287165 77002 115601 94562 10914485 214883 18796 52004 5361997 324147 88028 126532 109587 12123699 179005 207774 56935 5491998 347409 91224 132401 123784 12985695 209328 224341 50759 5681999 364912 92603 134963 137346 13825869 247069 234753 50142 5742000 39282 94558 143311 154951 15237490 254517 255048 54943 5972001 42935 98168 157201 173981 16804041 309916 270715 54141 6482002 472501 104795 173338 194368 18500576 446919 291439 57297 7042003 533309 112861 20148 218968 20910543 446919 320336 57200 6992004 637963 137992 249317 250654 23839515 563862 36562 65580 8042005 738511 148114 306723 283674 29813734 687162 413008 70364 8982006 863781 160348 377519 323914 34216483 790476 450134 74200 8912007 1030530 203200 464130 383200 40155746 1102097 525922 79940 9792008 1260123 221615 582339 456169 48007638 1438461 607200 114513 15132009 1415136 223591 670774 520770 52783510 2422728 681742 102635 1913


1199091

1199092

1199093

1199094

1199095

1199096

1199097

1199101

0867lowastlowast

0826lowastlowast

0892lowastlowast

0838lowastlowast

0859lowastlowast

0921lowastlowast

0835lowastlowast

1199102

0951lowastlowast

0906lowastlowast

0961lowastlowast

0939lowastlowast

0939lowastlowast

0985lowastlowast

0938lowastlowast



Year 1199091

1199092

1199093

1199094

1199095

1199096

1199097

1199101

1199102

1994 00001 00001 00001 00001 00001 00502 00001 04228 000011995 00364 00397 09154 00389 00404 00253 00512 03241 004801996 00716 01054 06798 00707 00747 00160 00940 00355 002751997 01021 01727 05911 01035 01014 00000 01304 01294 003671998 01212 01922 06308 01344 01205 00135 01608 00118 005011999 01356 02006 06761 01640 01390 00303 01799 00001 005442000 01586 02125 07462 02024 01702 00337 02171 00915 007062001 01887 02345 08043 02439 02049 00583 02459 00762 010662002 02242 02750 08152 02883 02423 01194 02839 01363 014622003 02742 03242 08458 03420 02956 01194 03369 01345 014272004 03603 04776 07545 04111 03603 01715 04200 02941 021682005 04431 05394 08215 04830 04924 02265 05069 03852 028322006 05462 06140 08896 05708 05897 02725 05751 04583 027822007 06835 08756 07806 07000 07209 04114 07141 05677 034042008 08724 09879 08831 08591 08945 09058 08632 08453 071752009 09999 09999 09999 09999 09999 09999 09999 09999 09999





MAPE =1

119899

119899

sum

119894=1

(

1003816100381610038161003816119909119894 minus 119909119894

1003816100381610038161003816

119909119894

times 100) (6)



1198881

1198882


11198882

Trainingerror

4

07 0014683

17

07 000270505 0008015 05 000347404 0011149 04 000308702 0008810 02 0001945

3

07 0002918

15

07 000231005 003043 05 000322404 0019198 04 000301102 0003097 02 0001291

2

07 0002679

13

07 000324105 0002578 05 000205304 0003098 04 000270302 0002796 02 0003204

1 2 3 4 5 6 7 80

02040608

1Training vectors

Input vectors P

Targ

et v

ecto

rs T


minus05

0

05

1 Transfer function

a















minus12

minus10

minus08

minus06

minus04

minus02

00

02

04

2 3 41

1 2 3 4 5 6 7 8 9 10 112

3

4

5

6

7

8

9

10

The fitting error

times10minus12




8060402000


BPPSO-RBFNNRBF

1 2 3 4






Perfo

rman

ce

100

10minus1

10minus2

10minus3

10minus4

Perfo

rman

ce


100

10minus1

10minus2

10minus3

10minus4

1000 epochs1000 epochs0 100 200 300 400 500 600 700 800 900 10000 100 200 300 400 500 600 700 800 900 1000









Acknowledgments



References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra
















(1199091 1199092 119909

119894 119909


is 119909119894= (1199091198941 1199091198942 119909


V119894= (V1198941 V1198942 V



= (1198751198941 1198751198942 119875

119894119899)119879 and the best


(1198751198921 1198751198922 119875





V119896+1119894119889

= 120596V119896119894119889+ 1198881120585 (119901119896

119894119889minus 119909119896

119894119889) + 1198882120578 (119901119896

119892119889minus 119909119896

119892119889)

119909119896+1

119894119889= 119909119896

119894119889+ V119896+1119894119889

(2)






119894 119909

119898)


= (1198751198941 1198751198942 119875


119894=

(V1198941 V1198942 V








119894




119892





IW =

[[[[

[

IW11

IW12


IW21

IW22


d

IW1198991

IW1198992


]]]]

]

(3)





LW =

[[[[

[

LW11

LW12


LW21

LW22


d

LW1199041

LW1199042


]]]]

]

(4)




11989911989811988721 11988722 119887

2119904]











Economicindicators

Logisticsscale

W

PSO

y1

y2

x1

x2

c1

c2

cn



119894




119892





4 Case Study















Yes

No

Collect specimens




Compare and update




Train the RBFNN



119883119894=


(5)



119894





2119898 (e) 119896 = 2 times (119898 + 119899)3


1

2

3

7

1

2

3

14

15

1

2


x1

x2

x3

x7

y1

y2










minus119909)(1 + 119890







Year 1199091

1199092

1199093

1199094

1199095

1199096

1199097

1199101

1199102

1994 200141 59737 78277 62127 7247408 291645 136717 72336 4971995 244321 66246 98091 79984 9363651 235872 164627 67154 5651996 287165 77002 115601 94562 10914485 214883 18796 52004 5361997 324147 88028 126532 109587 12123699 179005 207774 56935 5491998 347409 91224 132401 123784 12985695 209328 224341 50759 5681999 364912 92603 134963 137346 13825869 247069 234753 50142 5742000 39282 94558 143311 154951 15237490 254517 255048 54943 5972001 42935 98168 157201 173981 16804041 309916 270715 54141 6482002 472501 104795 173338 194368 18500576 446919 291439 57297 7042003 533309 112861 20148 218968 20910543 446919 320336 57200 6992004 637963 137992 249317 250654 23839515 563862 36562 65580 8042005 738511 148114 306723 283674 29813734 687162 413008 70364 8982006 863781 160348 377519 323914 34216483 790476 450134 74200 8912007 1030530 203200 464130 383200 40155746 1102097 525922 79940 9792008 1260123 221615 582339 456169 48007638 1438461 607200 114513 15132009 1415136 223591 670774 520770 52783510 2422728 681742 102635 1913


1199091

1199092

1199093

1199094

1199095

1199096

1199097

1199101

0867lowastlowast

0826lowastlowast

0892lowastlowast

0838lowastlowast

0859lowastlowast

0921lowastlowast

0835lowastlowast

1199102

0951lowastlowast

0906lowastlowast

0961lowastlowast

0939lowastlowast

0939lowastlowast

0985lowastlowast

0938lowastlowast



Year 1199091

1199092

1199093

1199094

1199095

1199096

1199097

1199101

1199102

1994 00001 00001 00001 00001 00001 00502 00001 04228 000011995 00364 00397 09154 00389 00404 00253 00512 03241 004801996 00716 01054 06798 00707 00747 00160 00940 00355 002751997 01021 01727 05911 01035 01014 00000 01304 01294 003671998 01212 01922 06308 01344 01205 00135 01608 00118 005011999 01356 02006 06761 01640 01390 00303 01799 00001 005442000 01586 02125 07462 02024 01702 00337 02171 00915 007062001 01887 02345 08043 02439 02049 00583 02459 00762 010662002 02242 02750 08152 02883 02423 01194 02839 01363 014622003 02742 03242 08458 03420 02956 01194 03369 01345 014272004 03603 04776 07545 04111 03603 01715 04200 02941 021682005 04431 05394 08215 04830 04924 02265 05069 03852 028322006 05462 06140 08896 05708 05897 02725 05751 04583 027822007 06835 08756 07806 07000 07209 04114 07141 05677 034042008 08724 09879 08831 08591 08945 09058 08632 08453 071752009 09999 09999 09999 09999 09999 09999 09999 09999 09999





MAPE =1

119899

119899

sum

119894=1

(

1003816100381610038161003816119909119894 minus 119909119894

1003816100381610038161003816

119909119894

times 100) (6)



1198881

1198882


11198882

Trainingerror

4

07 0014683

17

07 000270505 0008015 05 000347404 0011149 04 000308702 0008810 02 0001945

3

07 0002918

15

07 000231005 003043 05 000322404 0019198 04 000301102 0003097 02 0001291

2

07 0002679

13

07 000324105 0002578 05 000205304 0003098 04 000270302 0002796 02 0003204

1 2 3 4 5 6 7 80

02040608

1Training vectors

Input vectors P

Targ

et v

ecto

rs T


minus05

0

05

1 Transfer function

a















minus12

minus10

minus08

minus06

minus04

minus02

00

02

04

2 3 41

1 2 3 4 5 6 7 8 9 10 112

3

4

5

6

7

8

9

10

The fitting error

times10minus12




8060402000


BPPSO-RBFNNRBF

1 2 3 4






Perfo

rman

ce

100

10minus1

10minus2

10minus3

10minus4

Perfo

rman

ce


100

10minus1

10minus2

10minus3

10minus4

1000 epochs1000 epochs0 100 200 300 400 500 600 700 800 900 10000 100 200 300 400 500 600 700 800 900 1000









Acknowledgments



References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra













LW =

[[[[

[

LW11

LW12


LW21

LW22


d

LW1199041

LW1199042


]]]]

]

(4)




11989911989811988721 11988722 119887

2119904]











Economicindicators

Logisticsscale

W

PSO

y1

y2

x1

x2

c1

c2

cn



119894




119892





4 Case Study















Yes

No

Collect specimens




Compare and update




Train the RBFNN



119883119894=


(5)



119894





2119898 (e) 119896 = 2 times (119898 + 119899)3


1

2

3

7

1

2

3

14

15

1

2


x1

x2

x3

x7

y1

y2










minus119909)(1 + 119890







Year 1199091

1199092

1199093

1199094

1199095

1199096

1199097

1199101

1199102

1994 200141 59737 78277 62127 7247408 291645 136717 72336 4971995 244321 66246 98091 79984 9363651 235872 164627 67154 5651996 287165 77002 115601 94562 10914485 214883 18796 52004 5361997 324147 88028 126532 109587 12123699 179005 207774 56935 5491998 347409 91224 132401 123784 12985695 209328 224341 50759 5681999 364912 92603 134963 137346 13825869 247069 234753 50142 5742000 39282 94558 143311 154951 15237490 254517 255048 54943 5972001 42935 98168 157201 173981 16804041 309916 270715 54141 6482002 472501 104795 173338 194368 18500576 446919 291439 57297 7042003 533309 112861 20148 218968 20910543 446919 320336 57200 6992004 637963 137992 249317 250654 23839515 563862 36562 65580 8042005 738511 148114 306723 283674 29813734 687162 413008 70364 8982006 863781 160348 377519 323914 34216483 790476 450134 74200 8912007 1030530 203200 464130 383200 40155746 1102097 525922 79940 9792008 1260123 221615 582339 456169 48007638 1438461 607200 114513 15132009 1415136 223591 670774 520770 52783510 2422728 681742 102635 1913


1199091

1199092

1199093

1199094

1199095

1199096

1199097

1199101

0867lowastlowast

0826lowastlowast

0892lowastlowast

0838lowastlowast

0859lowastlowast

0921lowastlowast

0835lowastlowast

1199102

0951lowastlowast

0906lowastlowast

0961lowastlowast

0939lowastlowast

0939lowastlowast

0985lowastlowast

0938lowastlowast



Year 1199091

1199092

1199093

1199094

1199095

1199096

1199097

1199101

1199102

1994 00001 00001 00001 00001 00001 00502 00001 04228 000011995 00364 00397 09154 00389 00404 00253 00512 03241 004801996 00716 01054 06798 00707 00747 00160 00940 00355 002751997 01021 01727 05911 01035 01014 00000 01304 01294 003671998 01212 01922 06308 01344 01205 00135 01608 00118 005011999 01356 02006 06761 01640 01390 00303 01799 00001 005442000 01586 02125 07462 02024 01702 00337 02171 00915 007062001 01887 02345 08043 02439 02049 00583 02459 00762 010662002 02242 02750 08152 02883 02423 01194 02839 01363 014622003 02742 03242 08458 03420 02956 01194 03369 01345 014272004 03603 04776 07545 04111 03603 01715 04200 02941 021682005 04431 05394 08215 04830 04924 02265 05069 03852 028322006 05462 06140 08896 05708 05897 02725 05751 04583 027822007 06835 08756 07806 07000 07209 04114 07141 05677 034042008 08724 09879 08831 08591 08945 09058 08632 08453 071752009 09999 09999 09999 09999 09999 09999 09999 09999 09999





MAPE =1

119899

119899

sum

119894=1

(

1003816100381610038161003816119909119894 minus 119909119894

1003816100381610038161003816

119909119894

times 100) (6)



1198881

1198882


11198882

Trainingerror

4

07 0014683

17

07 000270505 0008015 05 000347404 0011149 04 000308702 0008810 02 0001945

3

07 0002918

15

07 000231005 003043 05 000322404 0019198 04 000301102 0003097 02 0001291

2

07 0002679

13

07 000324105 0002578 05 000205304 0003098 04 000270302 0002796 02 0003204

1 2 3 4 5 6 7 80

02040608

1Training vectors

Input vectors P

Targ

et v

ecto

rs T


minus05

0

05

1 Transfer function

a















minus12

minus10

minus08

minus06

minus04

minus02

00

02

04

2 3 41

1 2 3 4 5 6 7 8 9 10 112

3

4

5

6

7

8

9

10

The fitting error

times10minus12




8060402000


BPPSO-RBFNNRBF

1 2 3 4






Perfo

rman

ce

100

10minus1

10minus2

10minus3

10minus4

Perfo

rman

ce


100

10minus1

10minus2

10minus3

10minus4

1000 epochs1000 epochs0 100 200 300 400 500 600 700 800 900 10000 100 200 300 400 500 600 700 800 900 1000









Acknowledgments



References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Yes

No

Collect specimens




Compare and update




Train the RBFNN



119883119894=


(5)



119894





2119898 (e) 119896 = 2 times (119898 + 119899)3


1

2

3

7

1

2

3

14

15

1

2


x1

x2

x3

x7

y1

y2










minus119909)(1 + 119890







Year 1199091

1199092

1199093

1199094

1199095

1199096

1199097

1199101

1199102

1994 200141 59737 78277 62127 7247408 291645 136717 72336 4971995 244321 66246 98091 79984 9363651 235872 164627 67154 5651996 287165 77002 115601 94562 10914485 214883 18796 52004 5361997 324147 88028 126532 109587 12123699 179005 207774 56935 5491998 347409 91224 132401 123784 12985695 209328 224341 50759 5681999 364912 92603 134963 137346 13825869 247069 234753 50142 5742000 39282 94558 143311 154951 15237490 254517 255048 54943 5972001 42935 98168 157201 173981 16804041 309916 270715 54141 6482002 472501 104795 173338 194368 18500576 446919 291439 57297 7042003 533309 112861 20148 218968 20910543 446919 320336 57200 6992004 637963 137992 249317 250654 23839515 563862 36562 65580 8042005 738511 148114 306723 283674 29813734 687162 413008 70364 8982006 863781 160348 377519 323914 34216483 790476 450134 74200 8912007 1030530 203200 464130 383200 40155746 1102097 525922 79940 9792008 1260123 221615 582339 456169 48007638 1438461 607200 114513 15132009 1415136 223591 670774 520770 52783510 2422728 681742 102635 1913


1199091

1199092

1199093

1199094

1199095

1199096

1199097

1199101

0867lowastlowast

0826lowastlowast

0892lowastlowast

0838lowastlowast

0859lowastlowast

0921lowastlowast

0835lowastlowast

1199102

0951lowastlowast

0906lowastlowast

0961lowastlowast

0939lowastlowast

0939lowastlowast

0985lowastlowast

0938lowastlowast



Year 1199091

1199092

1199093

1199094

1199095

1199096

1199097

1199101

1199102

1994 00001 00001 00001 00001 00001 00502 00001 04228 000011995 00364 00397 09154 00389 00404 00253 00512 03241 004801996 00716 01054 06798 00707 00747 00160 00940 00355 002751997 01021 01727 05911 01035 01014 00000 01304 01294 003671998 01212 01922 06308 01344 01205 00135 01608 00118 005011999 01356 02006 06761 01640 01390 00303 01799 00001 005442000 01586 02125 07462 02024 01702 00337 02171 00915 007062001 01887 02345 08043 02439 02049 00583 02459 00762 010662002 02242 02750 08152 02883 02423 01194 02839 01363 014622003 02742 03242 08458 03420 02956 01194 03369 01345 014272004 03603 04776 07545 04111 03603 01715 04200 02941 021682005 04431 05394 08215 04830 04924 02265 05069 03852 028322006 05462 06140 08896 05708 05897 02725 05751 04583 027822007 06835 08756 07806 07000 07209 04114 07141 05677 034042008 08724 09879 08831 08591 08945 09058 08632 08453 071752009 09999 09999 09999 09999 09999 09999 09999 09999 09999





MAPE =1

119899

119899

sum

119894=1

(

1003816100381610038161003816119909119894 minus 119909119894

1003816100381610038161003816

119909119894

times 100) (6)



1198881

1198882


11198882

Trainingerror

4

07 0014683

17

07 000270505 0008015 05 000347404 0011149 04 000308702 0008810 02 0001945

3

07 0002918

15

07 000231005 003043 05 000322404 0019198 04 000301102 0003097 02 0001291

2

07 0002679

13

07 000324105 0002578 05 000205304 0003098 04 000270302 0002796 02 0003204

1 2 3 4 5 6 7 80

02040608

1Training vectors

Input vectors P

Targ

et v

ecto

rs T


minus05

0

05

1 Transfer function

a















minus12

minus10

minus08

minus06

minus04

minus02

00

02

04

2 3 41

1 2 3 4 5 6 7 8 9 10 112

3

4

5

6

7

8

9

10

The fitting error

times10minus12




8060402000


BPPSO-RBFNNRBF

1 2 3 4






Perfo

rman

ce

100

10minus1

10minus2

10minus3

10minus4

Perfo

rman

ce


100

10minus1

10minus2

10minus3

10minus4

1000 epochs1000 epochs0 100 200 300 400 500 600 700 800 900 10000 100 200 300 400 500 600 700 800 900 1000









Acknowledgments



References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Year 1199091

1199092

1199093

1199094

1199095

1199096

1199097

1199101

1199102

1994 200141 59737 78277 62127 7247408 291645 136717 72336 4971995 244321 66246 98091 79984 9363651 235872 164627 67154 5651996 287165 77002 115601 94562 10914485 214883 18796 52004 5361997 324147 88028 126532 109587 12123699 179005 207774 56935 5491998 347409 91224 132401 123784 12985695 209328 224341 50759 5681999 364912 92603 134963 137346 13825869 247069 234753 50142 5742000 39282 94558 143311 154951 15237490 254517 255048 54943 5972001 42935 98168 157201 173981 16804041 309916 270715 54141 6482002 472501 104795 173338 194368 18500576 446919 291439 57297 7042003 533309 112861 20148 218968 20910543 446919 320336 57200 6992004 637963 137992 249317 250654 23839515 563862 36562 65580 8042005 738511 148114 306723 283674 29813734 687162 413008 70364 8982006 863781 160348 377519 323914 34216483 790476 450134 74200 8912007 1030530 203200 464130 383200 40155746 1102097 525922 79940 9792008 1260123 221615 582339 456169 48007638 1438461 607200 114513 15132009 1415136 223591 670774 520770 52783510 2422728 681742 102635 1913


1199091

1199092

1199093

1199094

1199095

1199096

1199097

1199101

0867lowastlowast

0826lowastlowast

0892lowastlowast

0838lowastlowast

0859lowastlowast

0921lowastlowast

0835lowastlowast

1199102

0951lowastlowast

0906lowastlowast

0961lowastlowast

0939lowastlowast

0939lowastlowast

0985lowastlowast

0938lowastlowast



Year 1199091

1199092

1199093

1199094

1199095

1199096

1199097

1199101

1199102

1994 00001 00001 00001 00001 00001 00502 00001 04228 000011995 00364 00397 09154 00389 00404 00253 00512 03241 004801996 00716 01054 06798 00707 00747 00160 00940 00355 002751997 01021 01727 05911 01035 01014 00000 01304 01294 003671998 01212 01922 06308 01344 01205 00135 01608 00118 005011999 01356 02006 06761 01640 01390 00303 01799 00001 005442000 01586 02125 07462 02024 01702 00337 02171 00915 007062001 01887 02345 08043 02439 02049 00583 02459 00762 010662002 02242 02750 08152 02883 02423 01194 02839 01363 014622003 02742 03242 08458 03420 02956 01194 03369 01345 014272004 03603 04776 07545 04111 03603 01715 04200 02941 021682005 04431 05394 08215 04830 04924 02265 05069 03852 028322006 05462 06140 08896 05708 05897 02725 05751 04583 027822007 06835 08756 07806 07000 07209 04114 07141 05677 034042008 08724 09879 08831 08591 08945 09058 08632 08453 071752009 09999 09999 09999 09999 09999 09999 09999 09999 09999





MAPE =1

119899

119899

sum

119894=1

(

1003816100381610038161003816119909119894 minus 119909119894

1003816100381610038161003816

119909119894

times 100) (6)



1198881

1198882


11198882

Trainingerror

4

07 0014683

17

07 000270505 0008015 05 000347404 0011149 04 000308702 0008810 02 0001945

3

07 0002918

15

07 000231005 003043 05 000322404 0019198 04 000301102 0003097 02 0001291

2

07 0002679

13

07 000324105 0002578 05 000205304 0003098 04 000270302 0002796 02 0003204

1 2 3 4 5 6 7 80

02040608

1Training vectors

Input vectors P

Targ

et v

ecto

rs T


minus05

0

05

1 Transfer function

a















minus12

minus10

minus08

minus06

minus04

minus02

00

02

04

2 3 41

1 2 3 4 5 6 7 8 9 10 112

3

4

5

6

7

8

9

10

The fitting error

times10minus12




8060402000


BPPSO-RBFNNRBF

1 2 3 4






Perfo

rman

ce

100

10minus1

10minus2

10minus3

10minus4

Perfo

rman

ce


100

10minus1

10minus2

10minus3

10minus4

1000 epochs1000 epochs0 100 200 300 400 500 600 700 800 900 10000 100 200 300 400 500 600 700 800 900 1000









Acknowledgments



References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











1198881

1198882


11198882

Trainingerror

4

07 0014683

17

07 000270505 0008015 05 000347404 0011149 04 000308702 0008810 02 0001945

3

07 0002918

15

07 000231005 003043 05 000322404 0019198 04 000301102 0003097 02 0001291

2

07 0002679

13

07 000324105 0002578 05 000205304 0003098 04 000270302 0002796 02 0003204

1 2 3 4 5 6 7 80

02040608

1Training vectors

Input vectors P

Targ

et v

ecto

rs T


minus05

0

05

1 Transfer function

a















minus12

minus10

minus08

minus06

minus04

minus02

00

02

04

2 3 41

1 2 3 4 5 6 7 8 9 10 112

3

4

5

6

7

8

9

10

The fitting error

times10minus12




8060402000


BPPSO-RBFNNRBF

1 2 3 4






Perfo

rman

ce

100

10minus1

10minus2

10minus3

10minus4

Perfo

rman

ce


100

10minus1

10minus2

10minus3

10minus4

1000 epochs1000 epochs0 100 200 300 400 500 600 700 800 900 10000 100 200 300 400 500 600 700 800 900 1000









Acknowledgments



References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











minus12

minus10

minus08

minus06

minus04

minus02

00

02

04

2 3 41

1 2 3 4 5 6 7 8 9 10 112

3

4

5

6

7

8

9

10

The fitting error

times10minus12




8060402000


BPPSO-RBFNNRBF

1 2 3 4






Perfo

rman

ce

100

10minus1

10minus2

10minus3

10minus4

Perfo

rman

ce


100

10minus1

10minus2

10minus3

10minus4

1000 epochs1000 epochs0 100 200 300 400 500 600 700 800 900 10000 100 200 300 400 500 600 700 800 900 1000









Acknowledgments



References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Perfo

rman

ce

100

10minus1

10minus2

10minus3

10minus4

Perfo

rman

ce


100

10minus1

10minus2

10minus3

10minus4

1000 epochs1000 epochs0 100 200 300 400 500 600 700 800 900 10000 100 200 300 400 500 600 700 800 900 1000









Acknowledgments



References



































Volume 2014




Journal of











Journal of


Function Spaces






Algebra




































Volume 2014




Journal of











Journal of


Function Spaces






Algebra









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