Order Holon Modeling Method Based on Time Petri-nets and Its Solution with Particle Swarm Optimization

Fuqing Zhao, Qiuyu Zhang Lanzhou university of Technology

School of Computer and Communication Engineering

Lanzhou, 730050 Gansu ,P.R.China zhaofq@mail2.lut.cn

Aihong Zhu Lanzhou university of Technology

Software Engineering Research Laboratory Lanzhou, 730050 Gansu ,P.R.China

zhuah@ lut.cn

Abstract

The manufacturing system change from hierarchy

to parallel structure, from concentration to distribution based on notion of Holonic Manufacturing System. In this paper, the problem of how to demarcate the unit of the manufacturing system, management style of the unit, control structure and the corresponding control method are settled. The model on order settlement in system reconfiguration model based on time Petri-net is put forward, order intelligent operation series is guided by particle swarm optimization, Simulation results show that the proposed model and algorithm are effective to order evaluation and implementation . 1. Introduction

Advanced Manufacturing Technology (AMT) [1]is the one of the core foundation technology for thriving and prosperous of a country, it is also the important measure to create society wealth directly and the mostly technology support to the economy development for a country. Manufacturing technology will still play an important role in the development of country economy, it is the foundation of country economy, the development level express the integrated strength to a country to a great extent.

Aimed to the application and realization technology of advanced manufacturing technology and informationize, the research on enterprise alliance and its business reconfiguration to Holonic Manufacturing system is processed, by constructing the information platform to Holonic Manufacturing system, the enterprise alliance with dynamic reconfiguration and Holon feature is established, this system can realize the informationize within enterprise and among enterprise, then support the cooperation between enterprise.

2. State of arts of Holonic Manufacturing Systems (HMS)

Holonic Manufacturing Systems[2] is one of the Intelligent Manufacturing Systems (IMS) program's six major projects resulting from a feasibility study conducted in the beginning of the 1990’s. The objective of the work of the HMS consortium is to "attain in manufacturing the benefits that holonic organisation provides to living organisms and societies, e.g., stability in the face of disturbances, adaptability and flexibility in the face of change, and efficient use of available resources." [ 3]

The topology construction is showed as Fig.1, it has self-similar topology construction. The topology relationship and function model of Holon are determined by fixed rules, its concreted action is determined by flexible strategy. Every holon have tendency to integrate itself to Holon system and keep itself as independent and individuality, the former is cooperation character, the latter is self-discipline character, these are two basic attribute for holon or holon system. Self-discipline character is the dynamic expression of Holon which means holon itself having ability to finish task that system given , dynamic respond to environment change , self-repair and self study, etc. Collaboration attribute is the dynamic expression of holon autonomy which means autonomy attribute of Holon is relative, Holon take into effect within its constriction scope, accept command from top level system, fulfill the task with other holon by negotiation. So holon is autonomy unit having some independence, when met some unexpected accident, it can deal with itself while not need to ask for instructions for top level, which means it is a stable form not affected by disturbance.

2007 International Conference on Computational Intelligence and Security

0-7695-3072-9/07 $25.00 © 2007 IEEEDOI 10.1109/CIS.2007.161

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2007 International Conference on Computational Intelligence and Security

0-7695-3072-9/07 $25.00 © 2007 IEEEDOI 10.1109/CIS.2007.161

536

2007 International Conference on Computational Intelligence and Security

0-7695-3072-9/07 $25.00 © 2007 IEEEDOI 10.1109/CIS.2007.161

536

2007 International Conference on Computational Intelligence and Security

0-7695-3072-9/07 $25.00 © 2007 IEEEDOI 10.1109/CIS.2007.161

536

2007 International Conference on Computational Intelligence and Security

0-7695-3072-9/07 $25.00 © 2007 IEEEDOI 10.1109/CIS.2007.161

536

2007 International Conference on Computational Intelligence and Security

0-7695-3072-9/07 $25.00 © 2007 IEEEDOI 10.1109/CIS.2007.161

536

2007 International Conference on Computational Intelligence and Security

0-7695-3072-9/07 $25.00 © 2007 IEEEDOI 10.1109/CIS.2007.161

536

The basic communication mechanism for different Holons is illustrated in Fig.1.

Fig.1. communication mechanism for different Holons

3. Timed Petri-net(TPN)[4] Based order holon

Definition 1. sixth-tuple CN=(P, V, T; F, R, Wr) is

a C_net, the condition are: 1. φφφ =∩∧=∩∧≠∪∪ TPVPTVP

2.TVWr

RPTTPFTV

×⊆∧×∪×⊆∧=∩∧ ,φ

3.TWrRcodV

WrRdomTFFcodFdom

⊆∪∧=∪∧∪=∪∧

)(

)()()(

Where, P = {P1, P2, . . ., Pn} is a finite set of places; V={V1,V2,…,Vn} is a finite set of variables; T = {T1, T2, . . ., Tn} is a finite set of

transitions with φ≠∪TP and φ=∩TP

F, R, Wr are flow relation, read relation and write relation.

For duality relation 21 DDr ×⊆ , dom and

cod defined as

dom(r)= }),(:|{ 21221 rddDdd ∈∈∃

cod(r)= }),(:|{ 21112 rddDdd ∈∈∃

dom is the definition domain, cod is the value domain.

It is obvious that (P,T;F) is a directional net, (V,T;R ∪ Wr) is a nondirectional net, it is show as Fig.2.

x t z

y

Fig.2. nondirectional net Where

Vzyx ∈,, , Rtx ∈),( , Wrtz ∈),( ,

WrRty ∩∈),( .

Definition 2: Let PpTtVx ∈∈∈ ,,

1. ... ,,, pptt⋅ are the former aggregation and latter

aggregation. 2. }),(|{)( Rtxtxr ∈= is extension or read

aggregation of x. }),(|{)( Wrtxtxw ∈= is write aggregation of

x. 3. }),(|{)( Rtxxtr ∈= is read aggregation of t.

}),(|{)( Wrtxxxw ∈= is write aggregation of

t. 4. we use tp(x) denote the kind of variable x, if

permitted, also can use tp(x) denote value domain of x.

5. Type= )(xtpVx∈∪ is the kind aggregation of CN.

Definition 3. 1. },,2,1{: nPK L→ is the capacity funcition

of CN. 2. }1,,1,0{: −→ nPMp L is the flow mark of

CN, if )()(: pKPMPp p ≤∈∀

TypeVM v →: is the value mark of CN, if

)()(: vtpvMVv v ∈∈∀

vp MMM += is the ID of CN.

3. },2,1{: L→FW is the weigh function of CN.

4. status: }1,0{→T is the status function of CN.

guard: →T Boolean expression is the guard function of CN, if )())((: trtguardVarTt ⊆∈∀ ,

and for ,))(( VtguardVarx −∈ x can present itself

on guard(t) by the form of x=a, where a is a constant. Var(guard(t)) is the variable aggregation of guard(t), where the variable that does not belong to V is the assistant variable, x=a is to give x initial value.

body: →T evaluate sentence is the body function, if ,Tt ∈∀ body(t) only evaluate to the variable of

)(tw and the assistant variable of t. the evaluate

sentence only use assistant variable and variable of t.

bodyguardstatusMT ++= is the transition

identifier of CN. In an Order Holon, there are n (where n > 1) orders to be produced using m (where m > 1) processing units. For each order, the sequence by which the processing units will be visited is pre-specified and is referred to as the order (or job) routing or processing

recipes. Normally, the processing time ijτ for an order

(or job) ),,2,1( nii L= in unit ),,2,1( mjj L=

is given.

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4. Order form selection model based on PSO algorithm

According to TPN order form processing model presented in former section, assume one task Holon can process n order form, each order form can be finished in unit time, for order form i, there having

consignation date constriction 0>iD , if and only if

the order form can be finished before date constriction, then there are profit that Fun>0. one solution to the question is a subset J of n order form, all the order form in J can be finished before consignation date constriction. So the profit of feasible solution is the

sum of J, that is ∑∈ ji

jFun . The feasible solution

having maximum profit is the optimization solution. The above question can be solved by basic PSO algorithm, the process is listed following.

(1) establish question space

For an order form array )1(21 nkiii k ≤≤= Lσ

provided, the pioneer date to finish order form

)1( kji j ≤≤ is j , so if each order form satisfied

jdji ≥ , the array σ is a permitted scheduling

sequence, then J is a feasible solution. On the contrary,

if there is an order form having jdji < , then array

σ is not a permitted scheduling sequence, because at

least order form ji can not be finished before

consignment constriction, so other array form should be tested in J. In fact, one special array can be used to test feasibility of J, the array is a random array ranked by non degrade order of consignment constriction, if

there is a sequence nxxx L21 having length n, where

}1,0{∈ix ， 1=ix imply order i is selected, 0=ix

imply order i is not selected, judge a sequence is whether a feasible solution, the corresponding array

kiii L21 should satisfied following constriction(1)

jdji ≥ （1）

the concrete parameters index are selected during the process of encode sort to enhance the compute efficiency of algorithm and avoid all the candidate participant in calculation for objective function value.

(2) establish fitness function On the basis of above section, a fitness function is provided.

∑=

−=n

ieiin fxFunxxxf

121 max),,( L （2）

⎪⎩

⎪⎨⎧

≥

<==∑

jd

jdandxifFunf

j

jjj

i

jiii

e0

1α （3）

Where α is a punish factor. To the optimization

problem, an array kiii L21 should be found to

guarantee the fitness function )( 21 kiiif L got

maximum value. (3) algorithm flow To order form scheduling problem having

consignment constriction, a colony with n individual can be randomly selected in solution space, if some

individual x corresponding array kiii L21 satisfied

jdji ≥ , then x is a feasible solution to the problem, if

there are no x satisfied constriction in n swarm having −∞=)(xf , the best individual should be kept in

selection mechanism by the change of position and velocity of particle in PSO to make certain to get optimization result, this is in accordance with experiment result. Step 1: input profit value array

),,2,1(][ niiFun L= and consignment constriction

value array ),,2,1(][ niid L= in n order form.

Step 2: generate n initialization individual, compute

fitness function ),,,( 21 nxxxf L .

Step 3: put position and velocity update mechanism of PSO algorithm to swarm, adopt to keep optimization individual strategy to generate new position for next iteration. Step 4: calculate new generation fitness by (2), if swarm have satisfied solution, the program terminate, otherwise the program go to step 3.

The elaborate procedure of update mechanism of PSO[5][6] is described as follows.

The main compute procedure of PSO algorithm: 1) initialization, Assume accelerated constant c1

and c2, the maximum evolution generation Tmax, set current evolution generation t＝1, generate m particle

mxxx L,, 21 in designed space nR to establish

initiation population X(t), generate initialization vector

movement Svvv ,,, 21 L randomly to form vector

change array

11 12 1N

21 22 2N

M1 M1 MN

v v v

v v vV

v v v

⎡ ⎤⎢ ⎥⎢ ⎥=⎢ ⎥⎢ ⎥⎣ ⎦

L

L

M

L

538538538538538538538

(2) evaluate population

11 12 1N

21 22 2N

M1 M1 MN

x x x

x x xX

x x x

⎡ ⎤⎢ ⎥⎢ ⎥=⎢ ⎥⎢ ⎥⎣ ⎦

L

L

M

L,

compute each dimension fitness function for every particle.

(3) compare fitness function with pbest itself, if current fitness optimizer than pbest, set pbest as current data and current position in n dimension space.

(4) compare pbest with gbest swarm searched, if current pBest optimizer than gbest, set gbest as current data and current position in n dimension space.

(5) update vector direction and step for each particle to generate new population X(t + 1).

(6) check end condition, if satisfied then finish searching optimum; else set t＝t+l and go to step 2). The terminated condition is the maximum evolution generation get to Tmax , or the fitness is less than set precise ε .

5. simulation result

Assume there are 20 order form at time t in DHVE system To test performance of PSO, the compute result with different size got by PSO, GA[7], enumerations are provided in table 1. where “size” is problem solution space, “CPU time” is time cost of CPU in pursing optimum, “-＂express that the computation can not get solution in accept time, “Best rate” is the result got by 100 running random. There are other performance index such as“Best＂ ,“Mean＂ ,“ Minimum＂ and “ Best rate ＂ etc. “Best＂ ,“Mean＂,“Minimum＂ represent optimum, average and worst value respectively in 100 random running. The algorithm is tested by different parameter and different random with 100 run, so to other solution, the tested objective function have higher reliability,show as in Table 2.

TABLE I COMPARISONS OF DIFFERENT ALGORITHM

6. conclusion

Holonic Manufacturing System (HMS) is a new concept for enterprise reconfiguration, order form selection and evaluation are very important problem in task allocation and carry out. The problem of how to

TABLE II COMPARISON COMPUTATION RESULT BY DIFFERENT PROBLEM SIZE

model the unit of the manufacturing system, management style of the unit, control structure and the corresponding control method are presented in this paper. The model on order settlement in system reconfiguration model based on time Petri-net is put forward, order intelligent operation series is guided by particle swarm optimization, Simulation results show that the proposed model and algorithm are effective to order evaluation and implementation .

Acknowledgements This research is partially supported by Natural Science Foundation of GANSU province (Grant No. 3ZS062-B25-033)

References [1] Aravindan, P., Punniyamoorthy, M. “Justification of advanced

manufacturing technologies (AMT)”.International Journal of Advanced Manufacturing Technology,19(2):151-156,2002.

[2] Valckenaers, P.,Van Brussel, H. “Holonic manufacturing execution systems”.CIRP Annals - Manufacturing Technology,54(1):427-432,2005.

[3] http://homepages.ucalgary.ca/~rbrennan/hms.html [4] Kim, Young Woo, Suzuki, Tatsuya,Narikiyo, Tatsuo. “FMS

scheduling based on timed Petri Net model and reactive graph search”.Applied Mathematical Modelling,31(6):955-970,2007.

[5] Liu, Bo, Wang, Ling,Jin, Yi-Hui. “An effective PSO-based memetic algorithm for flow shop scheduling” .IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics,37(1):18-27,2007.

[6] Allahverdi, Ali, Al-Anzi, Fawaz S. “A PSO and a Tabu search heuristics for the assembly scheduling problem of the two-stage distributed database application”.Computers and Operations Research,33(4):1056-1080,2006.

[7] Saini, Ashish,Chaturvedi, Devendra K.,Saxena, A.K. “Optimal power flow solution: A GA-fuzzy system approach” .International Journal of Emerging Electric Power Systems,5(2):1-23,2006.

Best rate(100%) PSO GA Enumeration

Best 512 503 496 Mean 499 491 488

Maximum 510 497 491 CPU time 6.13” 16.10” 81.02”

PSO GA Tasks Time Fitness Time Fitness

10 3.15” 321 4.04” 307 20 6.13” 512 7.56” 501 30 9.35” 603 12.35” 594 40 11.43” 821 14.22” 790 50 16.26” 1017 19.18” 986 60 28.03” 1412 31.06” 1261 70 33.96” 1875 37.44” 1786 80 50.01” 2310 57.21” 2053 90 73.20” 2964 79.12” 2756

100 97.49” 3745 103.06” 3588 Total 329.01” 15580 365.24” 14622

Fitness function enhanced (%) : 6.22 Computation time degraded: 11.01%

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