Optimization of a high-speed placement machine using tabu search algorithms

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<ul><li><p>Annals of Operations Research 96 (2000) 125147 125</p><p>Optimization of a high-speed placement machine usingtabu search algorithms</p><p>Peter Csaszar a,, Thomas M. Tirpak a and Peter C. Nelson ba Motorola Advanced Technology Center, Motorola, Inc., Schaumburg, IL 60196-1078, USA</p><p>E-mail: apc067@email.mot.comb Artificial Intelligence Laboratory, Department of Electrical Engineering and Computer Science</p><p>(M/C 154), University of Illinois at Chicago, 851 South Morgan Street, Chicago, IL 60607-7053, USA</p><p>Combinatorial optimization represents a wide range of real-life manufacturing optimiza-tion problems. Due to the high computational complexity, and the usually high number ofvariables, the solution of these problems imposes considerable challenges.</p><p>This paper presents a tabu search approach to a combinatorial optimization problem, inwhich the objective is to maximize the production throughput of a high-speed automatedplacement machine. Tabu search is a modern heuristic technique widely employed to copewith large search spaces, for which classical search methods would not provide satisfactorysolutions in a reasonable amount of time. The developed TS strategies are tailored to addressthe different issues caused by the modular structure of the machine.Keywords: combinatorial optimization, tabu search, manufacturing optimization, placementmachines</p><p>1. Introduction</p><p>Electronics manufacturing companies face a highly competitive market, in whichadopting new technologies to cut production costs, while still maintaining high quality,becomes a crucial aspect in determining profitability. The majority of electronics prod-ucts involves printed wiring board (PWB) assembly, in which electronic componentsare placed onto circuit boards in an assembly line. The older through-hole method-ology has been essentially replaced by surface mount technology (SMT). Because ofthe reduced size of the electronic components or parts, increased assembly precisionbecame necessary. Studies conducted on SMT assembly lines [26] have shown that,considering the complete SMT production process, the bottleneck occurs most oftenin the placement phase. These facts explain why small parts placement has becomethe primary area for automation. Optimizing the operation of automated placementmachines is, therefore, a key issue in increasing the throughput and cost-effectivenessof the entire SMT production line.</p><p>This paper focuses on developing an optimization method for the family of mod-ular high-speed automated SMT placement machines. The formulated optimization Corresponding author.</p><p> J.C. Baltzer AG, Science Publishers</p></li><li><p>126 P. Csaszar et al. / Optimization of a high-speed placement machine</p><p>problem can be shown to be NP-complete; therefore, a modern heuristic algorithm,namely tabu search (TS) was selected, with special strategies to address the particularstructure of the placement machines.</p><p>Section 2 gives an introduction to the optimization of chip shooters, and a reviewof related literature. Section 3 describes the particular model of placement machinefor our study, while section 4 presents the formulated optimization problem and itspartitioning into two subproblems. The search problem based on the optimizationproblem is established is section 5. Section 6 describes the TS optimizer, explainingthe development and mechanism of the proposed tabu strategies. The experimentalresults are provided in section 7. Finally, section 8 gives a brief conclusion, anddiscusses opportunities for improvement and future applications.</p><p>2. Problem statement</p><p>This section first gives an introduction to the structure of placement machines,then discusses how their productivity can be increased. This is followed by a summaryof publications in the field of manufacturing optimization, with special emphasis onchip shooters.</p><p>Many different models of automated placement machines have been developedfor the electronics industry to perform a variety of assembly operations that differ interms of board size, part geometry, production quantity/throughput requirements, etc.All machines, however, share a common structure with the following three major com-ponents. (For an exhaustive and detailed classification of contemporary chip shooterssee [19].)</p><p> A feeder array, which may be divided into separate feeder banks. The feeder arraymay be movable or fixed, and is equipped with different types of feeder devices(feeders for short). Each feeder holds a large number of identical electronic parts. A placing component, which contains a nozzle or a group of nozzles, capable of</p><p>picking a part from the feeder, and placing it on the PWB. The nozzles may beassembled on a rotating turret, or a positionable head. The characteristics of thehead also vary in terms of the number of installed nozzles (one or more), thepossibility of run-time nozzle changeover (supported or not), and the positioningmachinery (gantry, robotic arm, etc.). A vision system, which determines the picked parts orientation and exact position</p><p>on the nozzle. The inherent imprecision of the picking process can then be correctedwhen the part is placed. A board support mechanism, on which the boards are affixed during part place-</p><p>ment. This can be a worktable (fixed board), a conveyor (one-dimensional boardmovement) or an X-Y table (two-dimensional board movement).</p></li><li><p>P. Csaszar et al. / Optimization of a high-speed placement machine 127</p><p>Machines can have multiple instances of the components listed above, providinga degree of parallelism to improve the production throughput. The precise structureof the machines in our study is detailed in section 3.</p><p>The primary goal of optimization for every machine is to minimize the cycletime, the time elapsed between two consecutive board completions. This can beachieved in the following ways:</p><p> Minimizing the time of each placement cycle, i.e., the time for picking a part fromthe feeder and placing it on the board. Minimizing the time required by board transport, fiducial mark checking and other</p><p>off-cycle activities. Minimizing the occurrence of occasional non-productive events taking a relatively</p><p>long time, such as feeder replenishment, nozzle changeover (if applicable), etc. Maximizing the machines parallel operation (if applicable).</p><p>A great amount of work has been done with simulation and optimization forautomated placement machines. The framework of the problem is well stated in thepapers by McGinnis et al. [18] and Ammons et al. [1]. In their classical paper, Balland Magazine [2] developed an algorithm for optimizing the auto-insertion processof a single pick-up head placement machine with a stationary board and feeder. Theproblem they formulated to model the insertion operations is equivalent to the directedpostman problem. A plethora of different optimization approaches for different ma-chines has been developed. Leipala and Nevalainen [16] investigated a single headsequential placement machine with a moving feeder carriage and an X-Y table. Theyfound that the problem can be broken into two subproblems: an asymmetric travel-ing salesman problem (TSP) representing the insertion sequence optimization, and aquadratic assignment problem (QAP) regarding the feeder allocation. The heuristicapproach applied does not guarantee optimality, but fairly good suboptimal solutions.Crama et al. [4] worked on an entire line of placement machines operating concurrently,and found a hierarchical approach to the solution by dividing the whole problem intosimpler subproblems, which are solved separately. The machine in Grotzingers paper[14] is a system with dual heads on a fixed length arm and two component deliverycarriers on either side of the worktable. Here the dual delivery system causes diffi-culties resulting in several nonlinearities in the formulation. The method presented inthe paper begins with linearization, after which the result is solved as a mixed integerprogramming problem.</p><p>Foulds and Hamacher [8] identified the optimal bin locations in order to determinethe best parts insertion sequence for the machine of their study. The bin locationassignment was formulated as a single-facility location problem. Different distancenorms, such as the Chebyshev distance, were used for the solution. After the feederassignment is identified, the insertion sequence is achieved by solving the formulatedTSP. In their work, Mauckner et al. [17] tackle the placement sequence generationwith an algorithm called clock heuristic, and provide its comprehensive analysis for</p></li><li><p>128 P. Csaszar et al. / Optimization of a high-speed placement machine</p><p>three different distance metrics above. Sohn and Park [24] examined a multi-headturret placement machine. Their method first determined the locations of componentreels in the rack, followed by the placement sequence of components, such that aminimized total assembly time is achieved. Shih et al. [23] designed an expert systemfor finding the optimal placement sequence, feeder-, tooling- and nozzle-setup for agantry type machine. Their knowledge base contained information on the placementprocesses, machine specifications and components, the inference engine implementedforward chaining as the search strategy.</p><p>Contemporary general heuristic techniques have also been applied to attack theplacement machine optimization problem. Su and Shribari [25] dealt with a verysimilar machine to that of Shih et al. mentioned above, and produced an optimizercombining expert systems with artificial neural networks (ANNs). The ANNs wereinvolved in order to address the unstructured and ill-defined nature of the problem.An integer programming (IP) relaxation approach is presented by Kumar and Li [15].Relaxing the problem to linear programming (LP), and solving the LP with a com-mercially available software tool provides a near-optimal solution to the feeder slotassignment and component placement sequence. Dikos et al. [7] applied genetic algo-rithms (GA) a generic method to solve combinatorial optimization problems basedon the principles of natural selection to solve the feeder slot assignment problem fora high-speed turret machine in high-mix environment. Rubinovitz and Volovich [22]used GA to optimize task sequence and layout design of a robotic assembly cell con-currently an effort also present in our optimization approach.</p><p>3. Description of the placement machine</p><p>The placement machine, which is the subject of this study, belongs to the familyof modular multi-station walking beam, very high-speed chip mounters, specializingin placing small-size surface mount devices. Figure 1 shows a rough sketch of themachine structure.</p><p>Before the problem formulation can be given, we discuss how the relevant struc-tural components, introduced in the previous section, have been implemented on thisparticular type of machine.</p><p>The placement of parts is done by sixteen adjacently positioned identical, concur-rently operating placement modules (stations). Each station consists of the followingelements:</p><p> A fixed feeder bank, which is divided into twelve logical feeder slots. The widthof feeder devices, expressed by the number of occupied feeder slots, vary. Thewidth and type of feeders impose different constraints on the feeder slot location,at which a given feeder can be installed. These constraints have to be satisfiedby a feeder setup, otherwise it is not considered feasible. (Note that in the rest ofthis article, we will refer to feeder slots instead of the feeders themselves. A wide</p></li><li><p>P. Csaszar et al. / Optimization of a high-speed placement machine 129</p><p>Figure 1. The structure of the placement machine.</p><p>feeder, which occupies more than one feeder slot, is represented by one filled andone or more empty, but occupied feeder slots.) A vision system based on a charge coupled device (CCD) camera, which determines</p><p>the orientation and alignment of the part on the nozzle. The position of the camerais also fixed. A placement head mounted on a robotic arm, equipped with four nozzles, which</p><p>each can pick a part appropriate for the given nozzle diameter and, after visioninspection, place it on the board. The nozzles have to be installed prior to operation,i.e., no runtime changeover is supported.</p><p>The board support mechanism is a pallet circulating system (conveyor), whichreceives the incoming boards, affixes them on a pallet, transfers them through thestations, releases them at the end of the machine, and returns the pallets to receivenew boards. The conveyor can make arbitrarily long high-precision steps in incrementsof one inch. Up to six steps can be programmed for the assembly of one board, afterwhich the positioning of the boards under the stations must be the same as before thefirst step. (Note, however, that for all products in our study, the board layout underthe different stations is identical in any moment.)</p><p>During board assembly, the robotic arms of the stations are working au-tonomously. In a head cycle a head picks up to four part from the feeders, movesabove the vision camera for part inspection, and places the parts on the circuit board.Each station completes the placements that are assigned to the given station in thegiven conveyor position. This interval of operation is called the conveyor step cycle.The individual head cycles on the stations need not be synchronized. This is not trueabout the conveyor step cycles because of the continuous conveyor, whose movement</p></li><li><p>130 P. Csaszar et al. / Optimization of a high-speed placement machine</p><p>affects the operation of all stations. Having completed the placements assigned to aconveyor step, the conveyor is moved; after the last conveyor step, the board appearingat the end of the machine is finished, and will be removed from the pallet. (A moredetailed description of the placement machine, and the object-oriented simulation toolcapturing its physical model can be studied in [6].)</p><p>4. Optimization of the placement machine</p><p>This section presents the optimization problem in its entirety, then introducesa partitioning approach, which separates the problem to an augmented feeder setupoptimization (also referred to as feeder slot assignment problem), and a placementsequence generation heuristic.</p><p>4.1. The complete optimization problem</p><p>Based on the machine properties detailed in the previous section, the optimizationproblem is the following:</p><p>Given the list of placements, for each station, assign parts to the feeder slots,and define a placement sequence, such that the setup is feasible, and the cycle timefor production (the elapsed time between the completion of two consecutive boards) isminimized.</p><p>First the atomic unit of feeder setup optimization, the unique part set (UQP-setfor short) has to be defined. A unique part set is formed out of all placements usinga certain feeder slot. The size of the unique part set is the number of placements itcontains. Since a feeder device is not only expensive, but also increases the overallprobability of failure, the number of feeders used (i.e., feeder slots occupied) by asetup s...</p></li></ul>


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