Enhancing optimal feeder assignment of the multi-head surface mounting machine using genetic algorit

Enhancing optimal feeder assignment of the multi-headsurface mounting machine using genetic algorithmsShaoyuan Li*,Chaofang Hu,Fuhou TianInstitute of Automation,Shanghai Jiao Tong University,800Dongchuan Road,Shanghai200240,ChinaReceived28November2005;received in revised form26January2007;accepted1February2007Available online4April2007AbstractThe problem of minimizing the time required to populate a printed circuit board using a multi-head surface mounting machine is considered in this paper.The multi-head surface mounting machine is becoming increasingly popular due to its merit of picking or placing multiple components simultaneously in one pick-and-place operation,which reduces much portion of the assembly time.The complexity of the optimization problem of minimizing the assembly time results in that acquiring its desired solution is difficult.The total assembly time depends on two optimization problems:feeder assignment problem and pick-and-place sequencing problem.Although these two problems are interrelated,they are solved, respectively.Feeder assignment problem is one crucial problem of affecting surface mounting machine’s productivity directly.Optimal feeder assignment can decrease sum of time of moving along slots,moving from slot to PCB and moving from PCB to slot for placement heads griping components after predetermining pick-and-place sequence.For it is of a combinatorial nature and NP-hard,there is no exact algorithm for it.As an efficient and useful procedure for solving the combinatorial optimization problems,the genetic algorithm with specific crossover and mutation operators is proposed in this paper.The running results show that the proposed method performs better than the conventional methods.#2007Elsevier B.V.All rights reserved.Keywords:Printed circuit board(PCB);Multi-head surface mounting machine;Feeder assignment problem;Genetic algorithms1.IntroductionAutomated manufacturing in the electronics industry is becoming more popular as product varieties increase,product volumes decrease and product life cycles shorten.Printed circuit boards(PCB)are the brains’of electronic products,and their cost plays a major role in determining the competitiveness of an electronicsfirm.With the recent development of the component manufacturing technology,surface mount technol-ogy(SMT)has replaced pin-through-hole technology.Because SMT permits a large number of components to be mounted on a single PCB,assembly time is the most significant factor in PCB production cost.The problem of minimizing the PCB assembly time with surface mounting machine is considered in this paper.For surface mounting machine,the total PCB assembly time depends on two optimization problems:feeder assignment problem and pick-and-place sequencing problem.Although these two problems are interrelated,they are solved,respectively.As suggested in most papers,the feeder assign-ment problem is treated as a Quadratic Assignment Problem (QAP)[1,2]and Minimum Weight Matching Problem (MWMP)[3],the pick-and-place sequencing problem can often be modeled as a Traveling Salesman Problem(TSP)[2–5].Being the combinatorial nature and NP-hard of these two problems,the best solution is not acquired so that they can usually be solved by many heuristic algorithms[6,7].In addition,other methods such as tabu[8],simulated annealing [9]and so on,are also presented in the literatures.In view of their characteristic such as near optimization,high speed and easy realization,genetic algorithms(GAs)as a search strategy have received much attention and been successfully applied in the combinatorial optimizationfields [10–12],especially production environment problems[13–16] such as FMS[17]and VLSI[18],and location problem[19] over the last decade.Moreover,GAs were also used as tool for PCB assembly optimization.Lee et al.focused on the systematic GA for a multi-head surface mounting machine [20].The assignment of feeders to heads and construction of feeder-groups were,respectively,optimized by their GA. Finally,the whole multi-head problem was identical to the/locate/asocApplied Soft Computing8(2008)522–529*Corresponding author.E-mail address:syli@(S.Li).1568-4946/$–see front matter#2007Elsevier B.V.All rights reserved.doi:10.1016/j.asoc.2007.02.012single-head problem.Khoo and Loh designed a prototype GA enhanced planning system for surface mounting machine with a rotary turret,a moving feeder carriage and a moving board[21]. In addition,some other researchers studied the productivity of SMT assembly line.Dikos et al.concentrated their research on optimizing the portion of the SMT manufacturing process with the similar machine to that of Khoo and Loh in high-mix environments[22].The GA was employed tofind the near optimal assignment of the feeder.Further,they extended the algorithm to the SMT with multi-station placement machines [23].Multiple setup PCB assembly planning using GA was considered by Deo et al.[24].Which setup each component is assigned to is added to the original optimization problems for surface mounting machine.In this paper,the feeder assignment problem is studied.For the advantages of GAs over the other conventional methodssuch as towards the global optimization instead of local minima,this paper proposes a GA to solve this problem for the SONY SE-1000surface mounting machine after the pick-and-place sequencing problem has been taken as TSP and solved by Nearest Neighbor.The GA presented here is used with specific integer coding,uniform order crossover and exchanging mutation operators.The rest of this paper is organized as follows.In Section2, the structure and principle of this multi-head surface mounting machine is described.Assumptions,and mathematical descrip-tion of PCB assembly time for feeder assignment problem are given,too.In Section3,the implementation details of the proposed GA is provided.The efficiency of the optimization strategy based on GA developed in this paper is verified through experiments in comparison with the conventional methods in wide industry use in Section4.Section5concludes this paper.2.Problem descriptions2.1.Machine introductionThe multi-head surface mounting machine is becoming increasingly popular due to its strong point that it can mount more components than the single head machine simultaneously. The machine concerned in this paper is SONY SE-1000surface mounting machine as in Fig.1.It uses a placement mechanism mounted on a rotating turret,with multiple heads,that can pick-and-place more components every time.The introduction of this machine are described in the following:Feeders:Arefixed and lie in the slots of the both sides of the machine,which have40slots on every side.Each feeder that only owns the same components must be assigned to exactly one slot.Rotating turret:Has12heads which can move in X,Y and Z simultaneously.Heads and nozzles:Are located on the rotating turret.Each head has a nozzle that grips and holds a component until it is placed on the PCB.Nozzles of different diameters are used depending on the size of the component to be retrieved.Thenozzles cannot be automatically changed during assembly.Therefore,they can only be altered at the beginning of the production.PCB:Cannot move during assembly.Before production,the feeders must be assigned to the corresponding slots according to the optimization results of the programmed optimization software,and the required nozzles should also be installed.After preparation,the PCB is transferred into the machine by a conveyor belt andfixed at a predetermined position for assembly.In one mounting cycle, the rotating turret moves along the slots,and picks as many components as possible.Then it moves back to the corresponding position of PCB and mount these components.2.2.Assumptions and statementAssumptions are given in terms of practices in real setting and operation of SONY SE-1000surface mounting machine.(1)The turret will rotate a certain angle after picking or placingone component.It moves and rotates concurrently except for gripping more same type of components from one slot.And the speed of rotating is much higher than that of moving.Therefore,only the moving time is considered during assembly.Since the mounting sequence is given,the rotating time for the picking more components from the same feeder can be regarded as constant and ignored during computation.The routine of the turret along the slots in every cycle is identical from right to left in Fig.1. (2)As for every component is concerned,the action of pickingor placing is always same and short.Therefore,the total action time is constant in any assembly sequence so that it can be neglected when computing assembly time.(3)In real production,the moving patterns are differentaccording to the type of the components.For example,if the quality of the component is different,the speeds of picking and placing are different,too.When the turret moves from one position to another,the alternation of its speed is complex,including accelerating,uniform and decreasing.These factors make the accurate computation difficult.So Fig.1.SONY SE-1000surface mounting machine.S.Li et al./Applied Soft Computing8(2008)522–529523the average speed is used in this paper for convenience.The moving speed is considered as constant.Then the assembly time is proportional to the moving distance of the turret.(4)Although the feeders can be assigned to the both sides of themachine,the concern in this paper is usually about assembly on one side.The total type number of the components is limited less than or equal to40.Based on the assumptions of the real assembly above,the following notations are used in the development:n:The number of the components to be mounted.m:The number of the component types,it satisfies 1m40for SONY SE-1000surface mounting machine.i,j:The order number of the components to be mounted, with1i,j n.s,s0:The order number of the slots,with1s,s040.t(i):The assembly cycle that the component i mounted belongs to.s l tðiÞ;s rtðiÞ:The farthest left and right slot in the same cycle t(i).d i(i+1):The assembly distance computed including pickingand placing between the component i and i+1.d pp(i,j):The Tchebycheff distance between the component iand j on PCB.d pf(i,s):The Tchebycheff distance between the component ion PCB and the slot s.d ff(s,s0):The Tchebycheff distance between the slot s and s0.d fp(s,j):The Tchebycheff distance between the slot s and thecomponent j on PCB.Then,the optimization objective of the whole assembly problem is formulated as follows:minX nÀ1i¼1d iðiþ1Þ(1) whereThe objective function in(1)describes the travel distance of the turret during assembly.It consists of four terms expressed in the constraints(2),i.e.the distance between the components on the PCB,the distance along the slots,the distance from slot to PCB and the distance from PCB to slot during one cycle.It must satisfy the system constraint that only one feeder can be assigned to one slot.Feeder assignment problem and pick-and-place sequencing problem determine the total assembly time. Feeder assignment problem is one crucial problem of affecting surface mounting machine’s productivity directly.The better feeder assignment problem is solved,the less sum of time of moving along slots,moving from slot to PCB and moving from PCB to slot for placement heads griping components is obtained.This paper focuses on the feeder assignment problem after predetermining pick-and-place sequence.The assumption that the pick-and-place sequence is given beforehand means the term d pp(i,i+1)in(2)is constant and can be ignored when t(i)=t(i+1).So the optimization objective of feeder assign-ment problem is reformulated in the following expression: minX nÀ1i¼1f d pfði;s r tðiþ1ÞÞþd ffðs r tðiþ1Þ;s l tðiþ1ÞÞþd fpðs l tðiþ1Þ;iþ1Þg(3) 3.Optimal solution by genetic algorithmsThis section will provide an overview and application of GAs,including the real genetic operators.3.1.OverviewSince this optimization problem is NP-hard and combina-torial nature,the traditional optimization techniques are unsuitable.According to their extensive applications in assembly sequence planningfield[25–27],GAs,which are a sort of population-oriented stochastic search techniques and adaptive methods to solve optimization problems,can be used to acquire the satisfactory solution of feeder assignment problem.Based on the mechanics of genetics and of nature selection,GAs differ from other optimization methods and search procedures.GAs are mainly composed of three basic operators: reproduction,crossover mutation.When solving a problem using GAs,first a proper representation andfitness measurement must be designed.Many representations are possible,and will work.Some are better than the others. Devising the termination criterion should be the next step. The termination criterion usually allows at most some predefined number of iterations and verifies whether an acceptable solution has been found.New population will becreated by genetic operators without satisfying the criterion, and iteration will continue.3.2.CodingTraditionally,chromosomes are simple binary vector.The simple representation is not convenient for the complex feeder assignment problem.A better method is needed to change the chromosome syntax tofit the problem.Referring to the coding examples of representing search nodes for multiprocessor scheduling in reference[28],expressing assembly sequence of product structure in reference[26]and allocating rectangular pieces onto a strip in reference[29],a special coding is used to represent the chromosome instead of the conventional0–1d iðiþ1Þ¼d ppði;iþ1ÞtðiÞ¼tðiþ1Þd pfði;s r tðiþ1ÞÞþd ffðs r tðiþ1Þ;s l tðiþ1ÞÞþd fpðs l tðiþ1Þ;iþ1ÞtðiÞ<tðiþ1Þ(2)S.Li et al./Applied Soft Computing8(2008)522–529524coding in this paper.Each gene of the chromosome denotes a slot. This representation is similar to those in references[20–24].For references[20,21,24],the chromosome is made up of two parts: one represents the feeder assignment and the other represents the pick-and-place sequence.In this paper,however,only the former problem is solved such that the genes of the chromosome just denote the feeder assignment.As for SONY SE-1000surface mounting machine with40slots presented in this paper,the chromosome includes40genes.With the notations in Section2, some definitions are given.Let V and W are integer sets,i.e. V={1,2,...,40}and W={mÀ40,mÀ39,...À1,1,...,m}. Let the chromosome is defined as¯g¼½gð1Þ;gð2Þ;...;gð40Þ , where g is a function representing the mapping g:V!W,and g(s)¼g(s0)if s¼s0.The integer number in set W corresponding to every gene in the chromosome stands for whether one slot own one type of components or not.For the position s of the chromosome,g(s)>0expresses that the type g(s)of components have been assigned to the corresponding slot s.Inversely, g(s)<0describes that there is not components in the slot s.The negative integer numbers from big to small are the deputies of the empty slots from left to right in the chromosome.This coding method fully satisfies the system constraint in Section2.For example,there is a PCB including11types of components shown in Table1.The component type3is assigned to slot5with g(5)=3and the component7in slot11 with g(11)=7,and so on.Because there is no special large component occupying more slots and requiring empty slots in this paper,this chromosome coding is different from that of [22,23].3.3.Creation of initial populationThe individual number of the population is100.Variable a is the iterative number of individuals in initial population with a100and b is the iterative number of component types with b m.The procedure creating the initial population is as follows:Step1:a=1.Step2:b=1.Step3:A slot number s which is greater than0and less than or equal to40is randomly generated.If there is none in the gene s of the chromosome a,the value of this gene,i.e.g(s), is considered as b and go to step4.It means that if there is no component in the slot s,the component type b can be assigned to the slot.Otherwise repeat step3.Step4:b=b+1,if b>m,the negative integer numbers in set W fromÀ1are degressively assigned to the empty positions of the chromosome from left to right,then repeat step4till each element of¯g has definite value,and go to step5.Otherwise go back to step3.Step5:a=a+1,if a>100,the initial population has been created,and program stops.Otherwise go back to step2.During the above steps,every component type is randomlyassigned among the40slots,which means that the initial population is created stochastically.However,the random search maybe increase the generations of evolution and computation in spite of satisfactory results.So some better chromosomes can be selected as the individuals of the initial population.This paper predetermines a reasonable range of slots according to the size of the PCB and the number of the component types.For example, exclude the slots far away from the PCB,and require the components chosen in the reasonable range.But it may be result in the premature despite the good initial individuals.3.4.Fitness functionThe paper’s purpose is to get the satisfactory solution of feeder assignment problem,which minimizes the production time as much as possible.Thefitness function can be acquired based on the objective function(3).Since GAs could have better chances for the surviving individuals with relatively higherfitness but the aim of(3)is minimum,the paper obtains thefitness function by transforming(3).Thefitness function is expressed byfitness.Letfitness¼MÀv(4) where v is the objective function(3),i.e.v¼X nÀ1i¼1f d pfði;s r tðiþ1ÞÞþd ffðs r tðiþ1Þ;s l tðiþ1ÞÞþd fpðs l tðiþ1Þ;iþ1Þg(5) and M is the biggest objective value of(5)among all indivi-duals.From the chromosome coding¯g,the positions of com-ponents assigned in each assembly cycle are got by decoding sothat the coordinates of variables s ltðiÞ,s rtðiÞcan be known.The distances along slots,between the slots and components on PCB can be computed,too.3.5.ReproductionThe selection tactics is roulette wheel selection in this paper. Different from the methods in references[20–24],itsfitness function must be modified when the individual with the biggest objective function value is not selected based on(4).If the fitness function value of individual a is equal to0,and only less than that of individual a0,then assumefitnessðaÞ¼12fitnessða0Þ(6)Table1Chromosome codingSlot(s)(1)...(5)...(11)(12)(13)(14)...(18)(19)(20)(26)(27)(28)...(32)(33)(34)(35)(36) (40)g(s)À131À10924À14À1511À21810À25576À29S.Li et al./Applied Soft Computing8(2008)522–529525so that every individual will probably be selected.In this paper,about 15%of all individuals will be replaced during reproduc-tion.3.6.CrossoverThere are many new types of crossover operators [30,31]to be adopted in order to get the better solution of assembly planning problem.In this paper,uniform order crossover with less iteration developed by Davis [32]is required to satisfactory solution for the feeder assignment problem as [22,23].Firstly,the selection strategy of the parents is roulette wheel selection in order to make the individual with high fitness evolve.The crossover probability is 50%in this paper.Secondly,for simplicity the chromosome with nine genes expressed by integer is considered as an example according to the coding of feeder assignment problem including four types of components in nine slots.Uniform order crossover is shown in Fig.2.The procedure of uniform order crossover above is as follows:Step 1:A binary string having the same number of bits with the above individuals is randomly generated.Step 2:The genes in the positions of parent A,in which the bits are equal to 1in binary string,are copied to the same position of offspring A,so do parent B and offspring B.Step 3:Check up every gene of parent B orderly,and insert the genes not existing in offspring A into its empty positions from left to right,the same to parent A and offspring B.The crossover stops.3.7.MutationThe individuals are randomly selected with mutation probability 5%.Because of the special coding in this paper,the result of chromosomes will contain two copies of the same integer,and thus result in an infeasible solution if simple mutation operator is used.Therefore,the mutationoperator used here is exchanging mutation.An example of the chromosome with nine genes is taken as the same as that in Section 3.6.The exchanging mutation is shown in Fig.3.The procedure of exchanging mutation above is as follows:Step 1:Two genes are stochastically chosen in the same chromosome.Step 2:These two genes are exchanged in this chromosome.4.Software and experiments 4.1.Software introductionThe optimization software is programmed by Visual C++6.0language in light of the requirement of SONY SE-1000surface mounting machine.The data of PCB including the number of components,the number of component types,position of each component,the number of nozzles required,are regarded as inputs.Its outputs are the feeder assignment result and the final assembly time that can be acquired after running the optimization software.The demo of this software shows the assembly structure and assembly procedure using the assign-ment result as in Fig.4.Referring to Fig.4,the functions of the software are expressed as follows:Button ‘‘configuration’’:Inputs the component data of PCB and sets optimization parameters.Button ‘‘sequence’’:Begins the optimization procedure and obtain the satisfactory result of feeder assignment problem.Button ‘‘play’’:Is pressed down,and the assembly simulation procedure will be shown.Blocks on the up and down sides :Express the slots,the red ones express the slots owning feeders,the blue ones are the empty slots.Dots :Denote all the components on PCB,the red and white ones stand for those mounted and unmounted components,respectively.Little window ‘‘nozzles illustration’’:Is located on the left and up corner,shows the pick-and-place sequence of placement heads.Illustrations such as picking or placing time of the component being mounted,total assembly time,current assembly action and type of component being gripped,can be seen on it.The specific pick-and-place action can be shown through pressing down the buttons on it step bystep.Fig.2.Uniform ordercrossover.Fig.3.Exchanging mutation.S.Li et al./Applied Soft Computing 8(2008)522–5295264.2.ExperimentsIn this software,the optimization method is treated as a module so that various optimization strategies can be studied and compared.To evaluate the optimization method for feeder assignment with GA proposed in this paper,the total assembly time is compared with that of the typical industry tactic such as a greedy assignment algorithm,which is commonly used to solve the problem of assigning feeders under the condition of the same pick-and-place sequence acquired by Nearest Neighbor TSP algorithm.The pick-and-place time is con-sidered as given constant as in Section2.Then the total assembly time being computed is the sum of(3)and this constant.In GA presented here,the number of generation is 1000,the size of population is100,the number of each chromosome’s genes is40and the crossover probability and mutation probability are,respectively,50%and5%.The GA module is programmed through Visual C++6.0according to the proposed algorithm with uniform order crossover and exchan-ging mutation.The data of six different PCBs from real production are given in Table2,which includes the number of components, that of component types and of nozzles types required.For example,the data of a little PCB with a few components among these six PCBs are listed in Table3.Table4shows the optimization results of these PCBs using the two methods.For each board,the second column gives the result of the traditional industry algorithm.The results of GA are expressed from the third tofifth column,i.e.the average initial results,average satisfactory results and the most satisfactory result for running10times.The sixth and seventh columns give comparison results between the two algorithms. The comparisons of average saved cost of six PCBs are given in thefinal row.The optimization results in Table4indicate that all over the range of tested boards in Table2,the method proposed in this paper,respectively,results in10.4%the best savings,5.0%the worst savings and7.2%the average savings of most satisfaction over the conventional industry method in total assembly time. Moreover,the best savings,the worst savings,and the average savings of average satisfaction are10.4%,3.5%and6.2%,Fig.4.Assembly optimization software.Table2Data of6PCBsPCB DataNumber of components Number ofcomponent typesNumber of nozzletypes requiredPCB138122PCB2238322PCB3301253PCB4448393PCB51562PCB694173S.Li et al./Applied Soft Computing8(2008)522–529527respectively.Therefore,the optimization method with GA presented in this paper is superior to the conventional industry strategy.5.ConclusionIn this paper,the optimization for the feeder assignment problem by a GA with specific genetic operators is presented,given that the order of pick-and-place is known.The genetic model is formulated,and the satisfactory solution is obtained.The above experimental results prove the optimization method with GA is efficient.The optimization software runs in computer with Pentium III 450MHz CPU,which costs less than 1min for the data of any PCB of the experiments.This indicates that the proposed GA is significant to increase the productivity in real production for a number of different PCBs.This GA can be improved further.Some parameters,e.g.the number of population,the crossover probability and the mutation probability can be changed according to the convergence.In addition to the optimization for feeder assignment problem,the pick-and-place sequencing problem is also optimized after assigning the feeders.Then better results can be acquired by iteration.AcknowledgementsThis work was supported by the National Natural Science Foundation of China under Grant 60474051,the Specialized Research Fund for the Doctoral Program of Higher Education of China under Grant 20060248001and partly by the program for New Century Excellent Talents in University of China (NCET).The authors are grateful to the anonymous reviewers for their helpful comments and constructive suggestions with regard to this paper.References[1]T.Leipa¨la ¨,O.Nevalainen,Optimization of the movements of component placement machines,Eur.J.Operational Res.88(1989)167–177.[2]I.Or,E.Demirkol,Optimization issues in automated production of printedcircuit boards:operations sequencing and feeder configuration problems,in:Proceedings of 1995INRIA/IEEE Symposium on Emerging Technol-ogies and Factory Automation,1995,pp.479–487.[3]S.H.Lee,B.H.Lee,T.H.Park,A hierarchical method to improve theproductivity of a multi-head surface mounting machine,in:Proceedings of the 1999IEEE International Conference on Robotics and Automation,1999,pp.2110–2115.[4]R.Kumar,H.Li,Integer programming approach to printed circuit boardassembly time optimization,IEEE ponents Packaging Manuf.Technol.Part B 18(4)(1995)720–727.Table 3Example of PCB’data Component typeData X -coordinateY -coordinate Component code Nozzle type 10K-0603À1.213R11No.410K-0603À18.15 5.3R21No.410m F/16V À15.812.35C11No.510m F/6.3V À1.26C12No.510m F/6.3V À1810C22No.52N4401À4 3.35Q11No.52N4401À8 3.35Q12No.52N4401À14.813.8Q21No.52N4401À11.1514.8Q22No.5510V -0603À6.913.2R13No.4510V -0603À11.1510.2R23No.462V -0603À4.27.3R12No.462V -0603À4.212.05R15No.462V -0603À9.457.35R22No.462V -0603À9.454.5R25No.4Table 4Comparison between optimization method using GA and conventional industry algorithm PCBConventional industry algorithmGASaved cost (%)Average initial solution Average satisfactory solution Most satisfactory solution Average satisfaction Mostsatisfaction PCB 1694.53940.76622.53622.5310.410.4PCB 22168.613281.962062.612060.62 4.9 5.0PCB 35662.487691.385333.255300.70 5.8 6.4PCB 417107.2622620.8216218.3215925.88 5.2 6.9PCB 515388.3322243.6514848.5114539.95 3.5 5.5PCB 634611.5140436.7332035.7831565.037.48.8Average save cost of six PCBs6.27.2S.Li et al./Applied Soft Computing 8(2008)522–529528。