optimization of high-speed multistation smt placement machines using evolutionary algorithms

IEEE TRANSACTIONS ON ELECTRONICS PACKAGING MANUFACTURING, VOL. 22, NO. 2, APRIL 1999 137

Optimization of High-Speed MultistationSMT Placement Machines Using

Evolutionary AlgorithmsWeihsin Wang, Peter C. Nelson, and Thomas M. Tirpak,Member, IEEE

Abstract—Surface mount technology (SMT) is a robust method-ology that has been widely used in the past decade to producecircuit boards. Analyses of the SMT assembly line have shownthat the automated placement machine is often the bottleneck,regardless of the arrangement of these machines (parallel orsequential) in the assembly line. Improving and automating theplacement machine is a key issue for increasing SMT productionline throughput.

This paper presents experimental results using genetic algo-rithms to optimize the feeder slot assignment problem for ahigh-speed parallel, multistation SMT placement machine. Fourcrossover operators, four selection methods, and two probabilitysettings are used in our experiments. A penalty function isused to handle constraints. A comparison of genetic algorithmswith several other optimization methods (human experts, vendorsupplied software, expert systems, and local search) is presented,which supports the use of genetic algorithms for this problem.

Index Terms—Electronics manufacturing, genetic algorithms,optimization, surface mount technology.

I. INTRODUCTION

ONE important process in electronics manufacturing todayis printed wiring board (PWB) assembly, by which

electronic components are placed onto circuit boards. Thistechnology has changed dramatically over the past severalyears, motivated by a desire for increased machine utilization,and the need for reliability in smaller products. Assemblyhas also changed from manual production to automated pro-duction, since it is virtually impossible for humans to placecomponents reliably in modern electronic devices by hand. Asthe processes become more complex and fully automated inoperation, it is vital that assembly process planning also beautomated. The motivation for this comes from the abundanceand complexity of information that needs to be manipulated.Furthermore, automated assembly provides consistent qualityand can increase the rate of production.

Surface mount technology (SMT) is a robust methodologythat has been widely used in the past decade to producecircuit boards. In this technology, a surface pad is used as

Manuscript received February 12, 1999; revised April 29, 1999. This workwas supported in part by Motorola’s Advanced Technology Center and theManufacturing Research Center.

W. Wang and P. C. Nelson are with the Artificial Intelligence Laboratory,Department of Electric Engineering and Computer Science, University ofIllinois at Chicago, Chicago, IL 60607-7053 USA.

T. M. Tirpak is with the Motorola Advanced Technology Center, Motorola,Schaumburg, IL 60196-0178 USA.

Publisher Item Identifier S 1521-334X(99)05842-5.

the connection point, and the components are held by locallyapplied glue, tacky solder paste, or other means until solderreflow takes place. SMT has for the most part replacedthe older through-hole technology and provided a way toreduce PWB area. The densities of components per boardare dramatically increased since interconnection space on theprinted wiring board is decreased.

The SMT methodology involves the following processsteps: screen printing of solder, glue dot application (forlarge components), automated placement of large and smallcomponents, robotic and/or manual placement of parts (forodd-shaped parts), and solder reflow. Often different quantitiesof various card designs are produced by a single assemblysetup. The automated placement of small components on aparticular board design may be performed by one or moremachines. Distinct boards will utilize different types and quan-tities of components as well as distinct component placementlocations on the circuit board.

The whole SMT process line requires a hierarchy of com-plex decisions for grouping board types, staging components atassembly machines, arranging feeders, and sequencing place-ment operations. Computer-aided process planning systems[1], [2] for PWB assembly have been developed to help theindustrial planner construct a process plan. Optimization of thejob sequence on the PWB assembly line is required to operatethe assembly line efficiently. This problem is usually solved asa flow shop problem [3]–[5]. Analyses of the SMT assemblyline [6]–[8] have shown that the automated placement machineis often the bottleneck, regardless of the arrangement ofthese machines (parallel or sequential) in the assembly line.Improving and automating the placement machine is the keyissue for increasing SMT production line throughput.

This paper focuses on the optimization of a complex, state-of-the-art automated placement machine, the Fuji QP-122, ahigh-speed parallel, multistation SMT placement machine.

II. OVERVIEW OF SMT PLACEMENT MACHINES

The component placement machine, also called a “chipshooter,” is a key element of the electronic assembly line. Agreat variety of component assembly machines have been de-veloped for the varied requirements of the electronics industry.Despite the differences between each implementation, threemajor structures are shared by all machines, namely the feedercarrier, the placement head, and the board supporting system.

1521–334X/99$10.00 1999 IEEE

138 IEEE TRANSACTIONS ON ELECTRONICS PACKAGING MANUFACTURING, VOL. 22, NO. 2, APRIL 1999

Fig. 1. SMT assembly machine.

These three parts can be either fixed or movable depending onthe specification of the machine. The essential elements of anSMT assembly machine are shown in Fig. 1.

The feeder carrier, which in some cases is divided intoseparate feeder banks, consists of a number of feeder slots.The feeder reels, which are tapes holding the components,are positioned in these feeder slots according to a feederassignment. A reel containing wider parts, (e.g., 24 mm)typically occupies more than one feeder slot. The placementhead is responsible for picking the components from a feederslot and placing them on the board. There are different forms ofplacement heads, such as a rotating turret head, or a positioningarm head. One or more vacuum nozzles are installed on theplacement head. The purpose of the board supporting systemis to position the board for placement and hold the board whilethe placement proceeds. It could be a stationary worktable, aconveyor system, or an - motion table. Some machineshave multiple stations, where each station contains the threeunits described above.

The processing time of the chip shooter can be divided intotwo categories. One is the pick-and-place time, and the otheris the tool change and feeder replenish time. Pick-and-placetime is determined by two factors: the time that the nozzletakes to move to the successive component after a placementis complete, and the time it takes for the nozzle to movefrom the carrier to the placement position on the board. Whenvarious products requiring different parts are produced at thesame time, changing the reel setup is necessary. Replacing thecurrent setup with a new one is typically a time-consumingprocess since it requires the removal and/or addition of feedercarriage mechanisms by human operators. A multisetup strat-egy for several different products using one setup is preferredsince fewer changes will be needed.

To maximize the throughput of the chip shooter, both thepick-and-place time and the replenish time need to be reduced.As mentioned above, the replenish time can be reduced bydecreasing the frequency of the reel setup changes. Loadingthe feeder carrier with all the components needed to produceall the products simultaneously may seem like an answer toreduce the setup changeover frequency, but as the number ofparts in the feeder slots increases, so does the delay time ofacquiring the next part. Thus, it is necessary to minimize the

pick-and-place time simultaneously. The pick-and-place timecan be reduced if the nozzle moving time for both acquiringthe part and placing the part is reduced. The part placing timecan be reduced through optimizing the placement sequence.To reduce the part acquisition time, the feeder setup needsto be optimized such that the feeder slot positions of twoconsecutive placement operations are close to each other. Sincethe component type transitions are accomplished by eithersliding the feeder to the desired position or moving the nozzleto the desired slot, a good feeder assignment should minimizethis transition time.

Working with our electronics manufacturing partner, wehave concentrated our research on optimizing a set of PWBassembly machines for their large, state-of-the-art factories.Cycle time, the time needed to complete the assembly of onePWB, usually serves as a measurement unit for the efficiencyof the placement machine. Since current high speed automatedplacement machines are capable of inserting 300–2000 partsper minute, even a slight improvement in cycle time canresult in a significant increase in the machine’s throughput.In a high-volume production environment, questions arisewith respect to the effective utilization of the machine. Ourresearch focuses on the assignment of components to thefeeder slots of high-speed parallel, multistation machines ina single product environment. This research demonstrateshow genetic algorithms can be used to find a near optimalsolution for the feeder assignment problem. We also show thatthe capability of genetic algorithms can be expanded usingconstraint relaxation techniques.

III. L ITERATURE REVIEW

Efforts to increase the productivity of an electronic assemblymachine were started in the 1980’s. Ball and Magazine [9]developed a heuristic algorithm for the insertion (placing)process on a PWB for a single pick-up head placementmachine with a stationary board and feeder. Later efforts usedmixed integer linear programming to develop mathematicalmodels for optimizing electronics assembly problems [10],[11]. Ahmadi et al. [12] also presented an analytical modelfor a dual head placement machine. Grotzinger [13] extendedthe work with noninterference and space constraints.

The assembly problem is usually approached by optimiz-ing two subproblems, the feeder assignment and placementsequence. The feeder assignment problem is usually solvedas a quadratic assignment problem, and the placement se-quence problem is solved as a traveling salesman problem(TSP). Different heuristics have been developed for solvingthis problem using this decomposition [14]–[16]. Other typesof approaches have also been proposed. Sadiqet al. [17]developed an intelligent slot-assignment algorithm to sequencea group of printed wiring board assemblies on a high-speedplacement machine with a single, stationary placement headusing two sizes of parts in the assembly job. Moyer andGupta [18] proposed two types of heuristic algorithms tosolve the feeder slot assignment problem with predeterminedcomponent placement paths for a turret head machine. Carmonet al. [19] proposed a group setup (GSU) model to reduce the

WANG et al.: OPTIMIZATION OF HIGH-SPEED MULTISTATION SMT PLACEMENT MACHINES 139

overall setup time and increase production throughput in theprinted wiring board assembly process in a high-mix, low-volume production environment. Knowledge-based systemsare another technique that has been applied to the SMTassembly problem [20]–[22].

Heuristic algorithms usually generate a good solution effi-ciently. The drawback is that the development effort must becompletely redone for each specific type of machine. Grouptechnology is a generic method, but it only considers one ofthe many scenarios in the problem.

Genetic algorithms are a generic method to solve com-binatorial optimization problems based on natural selection.Earlier efforts have successfully used genetic algorithms foroptimizing machines other than the one studied in this paper.Leu et al. [23] used genetic algorithms to solve the insertionsequence and feeder setup problems with a single size of partsfor three types of machines: fixed-head with a moving board,single-head pick-and-place, and turret head machines. Dikoset al. [24] applied genetic algorithms to solve the feeder slotassignment problem on a high speed placement machine witha turret-type head in a high-mix environment. Sch¨afer [25]applied genetic algorithms to solve the feeder setup problemfor a revolver head placement machine.

IV. GENETIC ALGORITHMS

Various types of SMT assembly machines have been usedon the assembly line. Each of them has different characteristicsand restrictions. A generic optimizing technique is desirable toaddress the different physical constraints. Genetic algorithms(GA’s) are a general-purpose stochastic optimization tech-nique. GA’s emulate biological evolution to improve an initialset of feasible solutions through an iterative process. Theseartificial evolution processes were introduced by Holland [26]in 1975. During these processes, initial populations evolvebased on the principles of natural selection and “survival ofthe fittest.” Each iteration is called ageneration, and eachindividual in the population is called agenoor achromosome.

Conventional genetic algorithms contain four major prepara-tory steps. First, a chromosome must be constructed to describethe aspects of the given problem. Second, an evaluationfunction must be formulated to measure the performance ofthe chromosome. Third, the population size and the prob-ability values of reproduction, crossover and mutation mustbe determined. Finally, the termination criteria of the geneticalgorithm must be decided.

A. Representation Schema

In optimizing feeder carriage allocation using genetic al-gorithms, the principal task is finding a schema to representthe problem. Different sizes of components are used in theprinted wiring board assembly line. Difficulties occur in ap-plying genetic operators when working with wider parts, e.g.,24 mm. One such complication occurs during the movementof a part to a new location in the chromosome. In somecases, this movement causes a redistribution of empty slotsin the chromosome. For example consider Fig. 2, where anexchange occurs between parts 1 and 2 in the initial string.

Fig. 2. Difficulties exchanging wide parts.

In the final string, a simple exchange of parts has resultedin the reallocation of empty slots. Complications also occurbecause of the numerous exchanges in each genetic operation.Fragmentation algorithms had to be developed to redistributethe empty slots in the feeder carriage. These fragmentationalgorithms are computationally expensive. Because of this,genetic operations are performed on alogical string—a stringcontaining only integers which are mapped to distinct parts.Logical strings are then converted back tophysical stringsevery time a chromosome is evaluated. This is the samelogical-physical stringrepresentation scheme as in Dikosetal. [24].

B. Fitness Scaling Technique

Premature convergence must be avoided to keep the searchfrom falling into a local optimum. This is accomplished byusing a fitness scaling technique calledsigma truncationbecause of the use of population standard deviationinformation [27]. The rescaled fitness value can be representedas

where is the average fitness of the population. In thisequation, the constant is chosen as a reasonable multipleof the population’s standard deviation (between 1 and 3), andnegative results are arbitrarily set to 0. The value of

used in our experiments is 2.

C. Selection Scheme

Selection determines the parents of the next generation.Therefore, the quality of the next generation is decided bythe selection technique. A good selection scheme should finda good solution with a reasonable convergence speed andwithout sacrificing further exploration of the search space.Our experiments include results for four different selectionmethods, roulette wheel, elitist, stochastic tournament, andergodic.

Roulette wheel selection, which some articles call stochasticsampling with replacement [28], is the fundamental selectionscheme of genetic algorithms. This selection method picks anindividual based on the probability where is equal to thefitness value of the individual, divided by the sum of the fitnessvalue of each individual in the population.

140 IEEE TRANSACTIONS ON ELECTRONICS PACKAGING MANUFACTURING, VOL. 22, NO. 2, APRIL 1999

Fig. 3. Valid crossover operator.

De Jong [29] proposed anelitist modelwhich augments anyselection model by preserving the best individual in the parentgeneration. If the best individual of the parent generation isnot contained in the children’s generation, it is added to thechildren’s generation. For our experiments we use his elitistscheme in combination with roulette wheel selection.

Stochastic tournament selection [30] picks successive pairsof individuals using roulette wheel selection. After picking apair of chromosomes, the one with the better fitness value isselected. This process is repeated until the whole populationis filled.

Ergodic matching selection method [31] is similar to tour-nament selection. The geno with a better evaluation functionvalue is selected from a pair of individuals. The pair of genos ispicked using the following method. Assume that the populationsize is A prime number is arbitrarily selected. The thelement will be paired with the ( ) modulo element(geno) in the population. The selection process starts with thefirst pair (i.e., setting 0). The element with the betterfitness value in this pair will be selected as a parent for thenext generation. Then, the selection method continues withthe second pair by incrementing by one. This process willrepeat until the whole population for the next generation iscreated.

D. Crossover Operators

The crossover operator exchanges chosen genes betweentwo selected individuals. The fact that our problem involves anordered representation restricts the type of crossover operatorsthat can be used. We tested four operators: valid crossover,PMX, cycle, and ordered crossover. Each is briefly discussedbelow.

The valid crossover was proposed by Dikoset. al. [24]. Acutting point is selected randomly. Then, the components fromthe start of the chromosome to the cutting point are copiedto the offspring. Missing components are then copied from asecond chromosome in the order in which they are found. Anexample is shown in Fig. 3.

Partially matched crossover (PMX) was proposed by Gold-berg and Lingle [32]. In this crossover operation, two chro-mosomes are aligned, and two positions are randomly chosenalong the length of the chromosome. These two positionsdefine thematchingsection along the two chromosomes whichwill be used to effect a cross-through position-by-position ex-change operation. Consider Fig. 4 whereParent#2is mappedto Parent#1.The 4 and 1, the 5 and 2, the 6 and 3, and the7 and 10 are exchanged position-wise. InChild#1 when the 1replaces the 4, a new 4 is placed in 1’s old position, and so on

Fig. 4. PMX operator.

Fig. 5. Cycle crossover.

Fig. 6. Order crossover.

until all exchanges are completed.Child#2 is obtained usingthe same methods, usingParent#2instead ofParent#1.

The cycle crossover operator [33] can be explained usingthe example shown in Fig. 5.Parent#1andParent#2produceoffspring by taking the first element from each parent. In ourexample, the first element ofParent#1is 9. The correspondingelement in Parent#2 is 1. Next, the element ofParent#2corresponding to the position where 1 is located inParent#1is 4. Repeat this rule until acycle is formed, e.g., 9-1-4-6 in our example. The remaining empty positions are filledfrom Parent#2. The same procedure is used to generate asecond child using the first element ofParent#2as a startingpoint.

The order crossover operator [34] starts in a manner similarto PMX. An example of this genetic operator is depictedin Fig. 6. Given Parent#1 and Parent#2 the procedure forgeneratingChild#1 is as follows.

1) Randomly generate a bit mask that has the same lengthas the parents.

2) Fill a portion of the positions onChild#1 by copyingthem fromParent#1wherever the bit mask contains a 1.

3) Create a list of the components fromParent#1associatedwith 0 in the bit mask.

4) Order the list of missing components from step 3 asthey appear inParent#2, using this ordered list to fillthe gaps inChild#1.

WANG et al.: OPTIMIZATION OF HIGH-SPEED MULTISTATION SMT PLACEMENT MACHINES 141

Fig. 7. Single-purpose multistation machine.

E. Mutation Operators

A simple mutation operator flips the value of a single bit ina geno when using a binary representation schema. For integerrepresentations, several versions of mutation have been devel-oped [35]. The version we have used in our experiments isto interchange the position of two arbitrarily selected integersin the geno.

V. MACHINE DESCRIPTION

The Fuji QP-122, is a high-speed multistation machinedesigned for placing small-sized surface-mount componentsonto a printed wiring board (See Fig. 7). The machine consistsof two major subsystems: a pallet circulating system (conveyorsystem) that transfers and indexes printed wiring boards toeach placing station and a placing station that is responsible forplacing the chips onto the printed wiring board. Each placingstation is composed of several devices: a vision system tohandle the component alignment, a fixed multifeeder unit toload the initial feeder configuration, and a placement headwith a single nozzle to pick up the chips from the feederlocation and place it on the board. In the conveyor system,each board is transferred and indexed, not directly, but carriedby pallet. The conveyor system can move any arbitrary lengthin increments of one inch. The user can customize a movingstep sequence with different moving lengths for each step.The whole system is coordinated by a central control system.This controls the vision processing system, the pallet transfersystem, and the placing stations, and manages a collection ofproduction information.

The placing procedure works as follows: after a new printedwiring board has been put onto the pallet, a Charged CoupledDevice (CCD) camera reads the fiducial marks on the board,calculates the exact position of the printed wiring board usingthese readings, and transmits this information to the placingstations. The pallet circulating system transfers the board intothe desired position, usually the center of the placing area.When a pallet with a printed wiring board is positioned ata placing station, a sensor on that station detects the IDcarrier data to identify the programs stored in the controllerand downloads the relevant program data for placement. Theplacing station starts the placement sequence. The nozzle picksup a component, moves the component to the CCD camera for

alignment, and mounts it onto the PC board. This procedurerepeats until the whole placement sequence for the currentplacing station is done. Then, the conveyor moves the palletto the next station. All the stations operate concurrently.

VI. A SSUMPTIONS

Before giving the mathematical formulation, some assump-tions are made in order to simplify the model.

1) The number of different board designs and the quantityof each board to be produced is given before theassembly starts.

2) Board design specifications include the number and sizesof particular chips, their - coordinates on the board,and rotational angles.

3) All boards of a given type will be produced consecu-tively.

4) The quantity of chips on each reel is sufficient to producethe required quantities of all the boards.

5) The components on each board can be placed in anygiven order.

6) Checking the fiducial marks in the pallet initializationstation does not become a bottleneck that limits thethroughput of the machine.

7) Repeating components of the same type on the feedercarriage is not allowed. If in fact it is necessary, therepeated component is regarded as a different type ofpart.

VII. M ATHEMATICAL FORMULATION

Our goal is to minimize the total assembly time of theentire machine for the given product. Since each station worksconcurrently, the total assembly time will be the maximumplacement time of all the stations. The placement time ofeach station is the summation of the placement time for eachcomponent placed by that particular station. Letbe the placement time of station Then, the total assemblytime can be represented as

(1)

where is the total number of stations.Each can be represented using

(2)

where is the placement time of placement is 1if placement is placed at machine otherwise it is 0.The quantity denotes the total number of components(placements) in the placement sequence.

Let be the total number of unique types of parts. Theplacement matrix, is defined as a dimensional binaryvalue matrix where will be 1 if and onlyif placement uses a component of type The assignmentmatrix, is defined as an dimensional binary valuematrix where is 1 if and only if componenttype is located at the station Then, can be written as

(3)

142 IEEE TRANSACTIONS ON ELECTRONICS PACKAGING MANUFACTURING, VOL. 22, NO. 2, APRIL 1999

The placement movement of the multistation machine can bedivided into two steps. The first step is picking the componentfrom the feeder slot, carrying it to the station’s fixed positionvision camera, and checking its orientation with the visionsystem. The second step is moving the component fromthe vision camera to the placement position on the board.Therefore, can be represented as

(4)

The difference in the traveling time from any two feederslots to the vision system is relatively small. Therefore,

can be assumed to be constant. Thehas no relationship with the feeder assign-

ment, and it can also be calculated without the knowledge offeeder slot assignment. Thus, can be known prior to thebeginning of the optimization. Therefore, the total assemblytime can be represented as

(5)

The objective of our research is to minimize the assemblytime, which can be written as

(6)

Since and are given, the problem is to identify theassignment for each station such that the total assemblytime is minimized. Although the exact feeder slot assignmentwithin a particular station has a negligible impact, as comparedto the station to which a component is assigned, we stillsolve the problem based on feeder assignments. This can bedone because a unique feeder location for a component willdetermine the station to which the component is assigned.By computing feeder assignments we are also able to checkseveral physical constraints.

The total number of occupied slots can not exceed thetotal number of the feeder slots in each station. Currently,the capacity of each station is 24 slots. Letdenote a sizematrix which is a 1 dimensional matrix. Each element inthe matrix, represents the size of the component typeWe can formulate this constraint as

(7)

where is the feeder capacity.Since components of the same type can not be repeated on

the feeder carriage, each row in can have exactly one 1.This constraint can be represented by the following equation:

for all (8)

VIII. E VALUATION FUNCTION

In formulating the evaluation function for the high-speedmultistation placement machine, our goal is to minimize thetotal placement time. Therefore, total placement time will beused to evaluate the fitness of ourgeno. The total placementtime is the maximum of the total placement time on eachstation. Thus, the evaluation formula can be represented as

(9)

where is the total number of stations in the machine andis the total placement time of the stationThere-

fore, individuals in the population with smaller evaluationfunction values have a higher probability to be selected.

IX. I NFEASIBLE SOLUTIONS

The solutions, which violate the physical constraints of theproblem, will be regarded as infeasible solutions. Genetic al-gorithms were originally designed to deal with nonconstrainedproblems. Therefore, solutions may become infeasible evenwhen every individual in the previous population is feasible.

Several physical constraints result in infeasible solutionsfor this application. Station information is not contained inthe geno representation. Thus, a wider part, occupying morethan one slot, might “occupy” two consecutive stations whenthe components in the chromosome change positions. The reel(component) has to be located in the feeder carriage of exactlyone station. Hence, an infeasible solution will be generated inthese circumstances.

Another infeasible solution occurs when applying bulk partconstraints. Bulk parts take up two slots in the feeder carriage.Furthermore, bulk parts cannot be placed next to regular parts;they can only be adjacent to bulk parts or empty spaces. Ifone of thegenosetups has a bulk part next to a regular part,it is an illegal setup. Yet another constraint that may lead toinfeasible solutions is that a 12 mm part has to occupy fourslots and can only be placed at slot number 2, 6, 10, 14, 18,or 22. Since there is no feeder slot number information inthe genorepresentation, a 12 mm part allocated to infeasiblefeeder slot positions is possible.

The penalty function is perhaps the most common tech-nique used in genetic algorithms for constrained optimizationproblems. It transforms the constrained problem into a non-constrained problem and can be represented as

(10)

where is the objective function of problem, andis the penalty term. Penalty functions are used to guide thegenetic search in handling the three constraints in this problem.Our penalty function is calculated using

(11)

where is the evaluation function, and theis the number of constraint violations.

WANG et al.: OPTIMIZATION OF HIGH-SPEED MULTISTATION SMT PLACEMENT MACHINES 143

Fig. 8. Performance range forPr = 40%,Pc = 55%, andPm = 5%.

X. EXPERIMENTAL RESULTS

The experimental results presented in this section for thevarious operators and selection schemes use industrial dataprovided by our manufacturing partner. The goal was to finda combination of genetic operators, selection methods, andprobabilities that are applicable within the domain of the feederallocation problem for the high-speed multistation machine.

The four crossover operators and four selection methodswere tested using a production scenario that contains more thanone hundred unique types of components. Given the stochasticnature of GA’s, each experiment for a specific operator andselection scheme was repeated thirty times. The graphs in thissection represent the performance averaged over the thirtytrials.

Two sets of experiments with different operator probabilitieswere conducted. The first set used a population of 50 chromo-somes with the probability of reproduction () set to 40%,the probability of mutation ( ) at 5%, and the probabilityof crossover ( ) at 55%. The second set used a populationof 50 chromosomes with the probability of reproduction ()set to 40%, the probability of mutation ( ) at 40%, and theprobability of crossover ( ) at 20%. The population size wasset to 50 given run-time constraints imposed by our industrialpartner. Using a population size of 50 with a 1000 iterations(generations), our GA optimizer requires approximately twohours on a SUN Ultra-1 workstation. The experiments weredesigned to determine the best combination(s) of selectionmethods, crossover operators, and probability settings. Theperformance is measured using an “improvement ratio” whichis calculated by dividing the best individual of the randomlygenerated initial population by the final solution (i.e., the bestgeno in the last generation).

For the first set of experiments usingand the best combination was the PMX crossoveroperator using the elitist selection method, whose performanceis shown in Fig. 8. This combination yielded an averageimprovement ratio value of 1.99 over the thirty trials. Oneof the poorer performing combinations, the ordered crossoveroperator using the roulette wheel selection method is alsographed in Fig. 8 to depict the range of performance of the

TABLE IRESULT OF THE CROSSOVEROPERATORS WITH DIFFERENT SELECTION

METHODS USING Pr = 40%; Pc = 55%; AND Pm = 5%

four selection methods and four crossover operators using thisprobability setting.

Table I shows the average results for the sixteen differentcombinations using the four selection methods and the fourcrossover operators using the first probability setting of40%, 55%, and 5%. The results are averagesover the thirty trials for the best geno (solution) in the initialpopulation, the best final solution in the ending population, theimprovement ratio, and the standard deviation of the improve-ment ratio. The results in Table I show that the PMX crossoveroperator using the elitist and ergodic selection methods hasthe strongest performance, with average improvement ratiosof 1.99 and 1.95, respectively. The elitist selection method hasreasonably strong performance with all four operators, whilethe ergodic selection method performs well with every oper-ator except the ordered crossover operator. The tournamentselection method has more modest performance with averageimprovement ratios between 1.76 and 1.83. The roulette wheelselection method has the poorest performance with averageimprovement ratios between 1.61 and 1.66.

For the second set of experiments usingand the best combination was again the

PMX crossover operator using the elitist selection method,whose performance is shown in Fig. 9. This combinationproduced the same average improvement ratio of 1.99 that thefirst probability setting yielded. The cycle crossover operatorusing elitist selection matched the performance of PMX withelitist selection producing an identical improvement ratio of1.99. One of the poorer performing combinations, the orderedcrossover operator with the ergodic selection method is alsographed in Fig. 9 to depict the range of performance of thefour selection methods and four crossover operators using thisprobability setting.

144 IEEE TRANSACTIONS ON ELECTRONICS PACKAGING MANUFACTURING, VOL. 22, NO. 2, APRIL 1999

Fig. 9. Performance range forPr = 40%; Pc = 20%; andPm = 40%:

TABLE IIRESULT OF THE CROSSOVEROPERATORS WITHDIFFERENT SELECTION

METHODS USING Pr = 40%; Pc = 20%; AND Pm = 40%

Table II shows the average results for the sixteen differentcombinations using the four selection methods and the fourcrossover operators with the second probability setting of

and This probabilityratio generally outperforms the previous probability ratio sum-marized in Table I. More specifically, the second setting hasbetter improvement ratios in ten of the sixteen combinations.Of the remaining six, three are equal and three are worse usingthe second setting. Six of the combinations shown in Table IIhave average final solutions under 81, while none of the resultsin Table I are under 83. The second setting, with its highermutation rate, strengthens the performance of all the crossoveroperators using the tournament and elitist selection methods.The results are mixed for the roulette wheel and ergodicselection method. Our overall conclusion from Tables I andII is that the higher mutation rate (i.e.,

TABLE IIIPRODUCTION TIME (SEC)

and is preferred and should be used with the elitistselection method combined with a PMX or cycle crossoveroperator. Alternatively, tournament selection combined with avalid or ordered crossover using and

also performs quite well for this problem.One interesting phenomenon observed is that the ordered

crossover operator “vibrates” heavily (see Figs. 8 and 9) andgenerates poor results for the roulette wheel and ergodicselection methods. The ordered crossover operator is tryingto preserve the order of a set of elements. Consider the natureof the problem. The set of unique parts in the same stationwill affect our result rather than the ordering of the uniqueparts in each station or the whole machine. The orderedcrossover operator causes a large set of unique parts in eachstation to totally rearrange. Thus, the value of the evaluationfunction jumps significantly. The elitist and tournament se-lection methods apply higher selective pressure compared tothe roulette wheel and ergodic selection methods, and tendto suppress the vibrating effect. In the probability settingof and the vibratingeffect is on average smaller than with the probability ratio of

and although this cannotbe seen from Figs. 8 and 9 which only show a few cases. Thereason for this situation is primarily that the crossover operatorhas a smaller effect on the solution when the mutation rate isincreased.

XI. COMPARING GAS WITH OTHER OPTIMIZATION METHODS

Several other techniques have also been applied to solveour problem, as a benchmark for our GA optimization results.The first method is the optimization software provided by themachine vendor. The second method is a human expert, anengineer familiar with the machine and the optimization offeeder setups. The third method is a rule-based system [36]which consists of a complex set of rules to handle the setup ofthe multistation machine. The fourth method is a local searchmethod callediterated descent[37], [38].

Table III shows the best result and the average result afterthirty trials generated by genetic algorithms, as well as thefinal results produced by the other techniques. For the GA, aprobability ratio of and wasused with the elitist selection method and the PMX crossoveroperator. Each of the methods was tested on three differentproduction files provided by our manufacturing partner. Thenumber of feeder reels used for the final setup generated byeach technique is shown in Table IV.

WANG et al.: OPTIMIZATION OF HIGH-SPEED MULTISTATION SMT PLACEMENT MACHINES 145

TABLE IVFEEDER REELS NEEDED FOR THE SETUP

The GA’s had approximately the same performance withrespect to production time and feeder reels as our humanexpert. However for reasons mentioned earlier in the paper,hand optimization is not really a viable option in a productionenvironment.

Comparing our genetic algorithm to the solutions providedby the vendor software, we find that the GA generates lowerproduction times and uses fewer feeder reels for each ofthe test cases. The vendor software produced setups withproduction times that on average were 7.2% higher than theGA setups.

With regards to the expert system, the GA solutions usethe same number of feeder reels. For the first two cases theproduction times are very similar. However, for the third casethe expert system generates a production time which is morethan 10% longer than the average GA solution.

Ten, thirty, and three hundred starting points were testedfor local search. The results recorded for local search arethe average final solutions of ten trials. In each case, GA’soutperform the local search technique using ten and thirtystarting points. GA’s generate better solutions than the localsearch method in two of the testing cases using 300 startingpoints. The only case where local search performed better with300 starting points has fewer feeders, and is therefore a smallersearch space. Our implementation of local search using 300starting points is approximately 20 times slower than our GA.

XII. CONCLUSION

A study of the optimization of feeder setups for a high-speedparallel, multistation machine was conducted. A mathematicalmodel was developed. The experimental results using ge-netic algorithms to solve the feeder assignment problem werepresented. Two probability settings, four selection methods,and four crossover operators were used in our experiments.A penalty function was used to incorporate the physicalconstraints of our problem. Each experimental setting wastested thirty times. Their average solutions and improvementratios were recorded. The performance of each setting wascompared and discussed.

No single crossover operator completely dominated all ofthe eight experiment settings. However, the PMX crossoveroperator has equal or superior performance compared to theother crossover operators. The solution quality of our problemrelies on grouping a set of unique parts in the same station,rather than the order of the parts. Since the PMX crossoveroperator preserves the information of a group of elements, itis not surprising that its performance is good.

With the probability setting andthe elitist selection method generates the best

improvement ratio among the four selection methods regard-less of the crossover operator used. When the probabilityratio is set to and thetournament or elitist selection methods are both good choicesfor this probability setting. Probability settings with a highermutation probability ratio generated better results in general.There were only three combinations that did not generate abetter improvement ratio with the higher mutation probabilityratio.

A penalty technique was employed to deal with variousconstraints. This technique converts a problem into a regularnonconstrained operations research problem. Additionally, thistechnique generalizes the optimization software for differenttypes of machines. The penalty technique can eliminate thenecessity of a complicated representation scheme. Unfortu-nately, there are no general guidelines for the design of penaltyfunctions. Our simple penalty function easily managed theconstraints in the high-speed parallel, multistation machine.As the ratio of maximum component size and feeder bank sizeincreases, the efficiency of this penalty function decreases. Amore complicated penalty function using the distance betweenthe current evaluation function value and the expected eval-uation value should be tested in the future. For example, theaverage value of feasible solutions at the current generationcould be used as an expected value for a penalty function.Then a penalty function value can be calculated by subtractingthe expected value from the evaluation function value.

A thorough study of solving these problems using GA’swith a wide range of crossover operators and selection methodswas achieved. A comparison of genetic algorithms with severalother alternative optimization methods (human experts, vendorsoftware, expert systems, and local search) was presented,which supports the use of genetic algorithms for this prob-lem. Our results also provide insight for designing genericoptimization software for the feeder setup problem for SMTassembly machines.

ACKNOWLEDGMENT

The authors would like to thank Dr. S. Kasif for hissuggestion of using local search as a benchmark.

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Weihsin Wang received the M.S. degree in mechan-ical engineering and the M.S. and Ph.D. degrees incomputer science from the University of Illinois atChicago.

He is Senior Software Engineer with OpenpathInc., Taiwan, R.O.C. From 1992 to 1998, he wasa Research Assistant with the Artificial IntelligenceLaboratory, University of Illinois at Chicago.

Peter C. Nelsonreceived the B.A. degree in com-puter science and mathematics from North ParkCollege, Chicago, IL, in 1984, and the M.S. andPh.D. degrees in computer science from Northwest-ern University, Evanston, IL, in 1986 and 1988,respectively.

He is Director of the Artificial Intelligence Lab-oratory, Department of Electrical and ComputerScience, University of Illinois at Chicago, where heis also an Associate Professor. His current researchinterests include both pure and applied techniques

of heuristic search. Basic research has focused on general techniques forimproving search efficiency, e.g., developing agenda data structures, reducingcycles during depth-first searches on graphs, and developing a new searchmethod, perimeter search. Applied research has focused on developing usefulAI techniques for intelligent transportation systems, manufacturing, andmolecular biology. His research has been funded by the National Institutes ofHealth, National Research Council, Federal Highway Administration, IllinoisDepartment of Transportation, Manufacturing Research Center, and Motorola.

Thomas M. Tirpak (M’91) received the B.S. andM.S. degrees in general engineering robotics and thePh.D. degree in electrical and computer engineeringfrom the University of Illinois, Urbana-Champaign.

He is a Principal Staff Engineer with the MotorolaAdvanced Technology Center, Schaumburg, IL, andmanages the Process Optimization Software Group.Since joining Motorola in 1991, he has workedon methods for improving the cycle time, quality,and cost of electronics manufacturing and productdesign operations. In cooperation with Motorola

University, he developed the “SMT Manufacturing Optimization” class andtaught it for over 200 Motorolans world-wide. He was a Visiting Lecturerwith the University of Metallurgy and Mining, Krakow, Poland. His cur-rent research interests include assembly process modeling and optimization,enterprise decision support systems, and Web-based tools for manufacturingmanagement.

Dr. Tirpak is a member of the Institute for Operations Research andManagement Science and Tau Beta Pi.