A comparison of machine-learning algorithms for dynamic scheduling of flexible manufacturing systems

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<ul><li><p>Engineering Applications of Articial Int</p><p>afa</p><p>nt</p><p>ersi</p><p>rm</p><p>14</p><p>Dispatching rules are frequently used to schedule jobs in exible manufacturing systems (FMSs) dynamically. A drawback, however,</p><p>to using dispatching rules is that their performance is dependent on the state of the system, but no single rule exists that is superior to all</p><p>the others for all the possible states the system might be in. This drawback would be eliminated if the best rule for each particular</p><p>of exible manufacturing system (FMS) scheduling can be</p><p>NP-complete type (Garey and Johnson, 1979), so heuristicand off-line type algorithms are usually used (Cho and</p><p>for reasonably large-scale problems.</p><p>systems using simulation, concluding that performancedepends on several factors, such as the due date tightness</p><p>ARTICLE IN PRESS(Baker, 1984), the systems conguration, the workload,and so on (Cho and Wysk, 1993). FMSs led to manystudies evaluating the performance of dispatching rules in</p><p>0952-1976/$ - see front matter r 2005 Elsevier Ltd. All rights reserved.</p><p>doi:10.1016/j.engappai.2005.09.009</p><p>Corresponding author. Tel.: +0034985182107; fax: +0034985182010.E-mail address: priore@epsig.uniovi.es (P. Priore).divided into the following categories: the analytical, theheuristic, the simulation-based and the articial intelli-gence-based approaches. The analytical approach consid-ers an FMS scheduling problem as an optimisation modelwith an objective function and explicit constraints. Anappropriate algorithm resolves the model (see for example,Stecke, 1983; Kimemia and Gershwin, 1985; Shanker andTzen, 1985; Lashkari et al., 1987; Han et al., 1989;Hutchison et al., 1989; Shanker and Rajamarthandan,1989; Wilson, 1989). In general, these problems are of a</p><p>These difculties led to research into many heuristicapproaches, which are usually dispatching rules. Theseheuristics employ different priority schemes to order thediverse jobs competing for the use of a machine. A priorityindex is assigned to each job and the one with the lowestindex is selected rst. Many researchers (see for example,Panwalkar and Iskander, 1977; Blackstone et al., 1982;Baker, 1984; Russel et al., 1987; Vepsalainen and Morton,1987; Ramasesh, 1990; Kim, 1990) have assessed theperformance of these dispatching rules on manufacturingand by analysing the earlier performance of the system, scheduling knowledge is obtained whereby the right dispatching rule at each</p><p>particular moment can be determined. Three different types of machine-learning algorithms will be used and compared in the paper to</p><p>obtain scheduling knowledge: inductive learning, backpropagation neural networks, and case-based reasoning (CBR). A module that</p><p>generates new control attributes allowing better identication of the manufacturing systems state at any particular moment in time is</p><p>also designed in order to improve the scheduling knowledge that is obtained. Simulation results indicate that the proposed approach</p><p>produces signicant performance improvements over existing dispatching rules.</p><p>r 2005 Elsevier Ltd. All rights reserved.</p><p>Keywords: Knowledge-based systems; Scheduling; FMS</p><p>1. Introduction</p><p>The different approaches available to solve the problem</p><p>Wysk, 1993; Chen and Yih, 1996). The problem is thatthese analytical models include simplications that are notalways valid in practice. Moreover, they are not efcientsituation could be used. To do this, this paper presents a scheduling approach that employs machine learning. Using this latter technique,A comparison of machine-learningof exible manu</p><p>Paolo Priore, David de la Fue</p><p>Escuela Tecnica Superior de Ingenieros Industriales, Univ</p><p>Received 3 November 2004; received in revised fo</p><p>Available online</p><p>Abstractelligence 19 (2006) 247255</p><p>lgorithms for dynamic schedulingcturing systems</p><p>e, Javier Puente, Jose Parreno</p><p>dad de Oviedo, Campus de Viesques, 33203, Gijon, Spain</p><p>16 September 2005; accepted 26 September 2005</p><p>November 2005</p><p>www.elsevier.com/locate/engappai</p></li><li><p>2. Machine learning</p><p>According to Quinlan (1993), machine-learning algo-rithms can be classied into the following categories: CBR,neural networks and inductive learning. A brief descriptionof the machine-learning algorithms applied in this workwill be provided next. The most commonly used CBRalgorithm is the nearest neighbour algorithm (Aha, 1992).The formulation of this algorithm, called NN, or k-NN inthe more sophisticated version, is very simple. The startingpoint is a metric, d, amongst examples, and a set of trainingexamples, E. When a new case x occurs, its solution or classis determined as follows:</p><p>ARTICLE IN PRESSof Artificial Intelligence 19 (2006) 247255these systems (see for example, Stecke and Solberg, 1981;Egbelu and Tanchoco, 1984; Denzler and Boe, 1987; Choiand Malstrom, 1988; Henneke and Choi, 1990; Montazeriand Wassenhove, 1990; Tang et al., 1993).Given the variable performance of dispatching rules, it</p><p>would be interesting to change these rules dynamically andat the right moment according to the systems conditions.Basically, there are two approaches to modifying dispatch-ing rules dynamically in the literature. Firstly, the rule ischosen at the right moment by simulating a set of pre-established dispatching rules and selecting the one thatgives the best performance (see for example, Wu and Wysk,1989; Ishii and Talavage, 1991; Kim and Kim, 1994; Jeongand Kim, 1998). The second approach, from the eld ofarticial intelligence, employs a set of earlier systemsimulations (training examples) to determine what the bestrule is for each possible system state. These training casesare used to train a machine-learning algorithm (Michalskiet al., 1983) to acquire knowledge about the manufacturingsystem. Intelligent decisions are then made in real time,based on this knowledge (see for example, Nakasuka andYoshida, 1992; Shaw et al., 1992; Kim et al., 1998; Min etal., 1998). A set of control attributes need to be establishedwhich identify the manufacturing systems state at eachparticular moment in time in order to generate trainingexamples. Aytug et al. (1994) and Priore et al. (2001)provide a review in which machine learning is applied tosolving scheduling problems. Finally, it has to be notedthat many works take benet from a combination of two ormore approaches (see for example, Glover et al., 1999;Flanagan and Walsh, 2003).Machine learning solves problems by using knowledge</p><p>acquired while solving earlier problems in the past similarin nature to the problem at hand. The main algorithmtypes in the eld of machine learning are case-basedreasoning (CBR), neural networks and inductive learning.The right training examples and machine-learning algo-rithm must be selected if this scheduling approach based onmachine learning is to work properly. However, there arehardly any studies in the literature dealing with thisproblem. This paper thus aims to compare three of theabove-mentioned machine-learning algorithms. In anattempt to improve the manufacturing systems perfor-mance, a new approach is also proposed whereby newcontrol attributes that are arithmetical combinations of theoriginal attributes can be determined.The rest of this paper is organised as follows. Machine-</p><p>learning algorithms used in this paper are rst described.An approach to scheduling jobs that employs machinelearning is then presented. The experimental study describ-ing a new approach to determining new control attributesfrom the original ones now follows, along with acomparison of the machine-learning algorithms. Theproposed scheduling approach is then compared with thealternative of using a combination of dispatching rules</p><p>P. Priore et al. / Engineering Applications248constantly. A summary of the results obtained rounds thepaper off.Classx classnn;where nn (nearest neighbour) satises:</p><p>dx; nn Minimumfdx; e : e 2 Eg.This means that the cases class coincides with that of the</p><p>nearest example or neighbour. This initial scheme can bene tuned by including an integer value, k (kX1), whichdetermines the k nearest neighbours in E for x. The class ofx is therefore a function of the class of the majority of the kneighbours.As regards neural networks, those that will be used in</p><p>this work are backpropagation neural networks (BPNs),or multilayer perceptron (Rumelhart et al., 1986). Theseare one of the most well-known and widely used as patternclassiers and function approximators (Lippman, 1987;Freeman and Skapura, 1991). Fig. 1 gives an overview of aneural network of this type. As can be seen, there is a singlehidden layer and there are no connections between neuronsin the same layer in this particular case.The backpropagation training algorithm is the one that</p><p>is used in this type of neural networks. There are severalversions of this algorithm, and the standard one (Rumel-hart et al., 1986; Freeman and Skapura, 1991) will next becommented on. We will assume a network with an inputlayer of n1 neurons, a hidden layer of n2 neurons, and anoutput layer of n3 neurons. The outputs of the input,hidden and output layers are called xi, yj and zk,respectively. The weights of the connections that connect</p><p>wjkwij</p><p>uk</p><p>uj</p><p>Input layer Hidden layer</p><p>Output layer</p><p>xi yj zk ok TargetFig. 1. An overview of a backpropagation neural network.</p></li><li><p>1. The training set is a sub-set of all possible cases.However, situations in which the scheduling system doesnot work properly can always be added as trainingexamples.</p><p>2. The systems performance depends on the number andrange of control attributes used in the design of thetraining examples.</p><p>3. A rule may perform well in a simulation over a long timeperiod for a set of given attributes, but will performpoorly when applied dynamically.</p><p>4. The system can be prone to inadequate generalisationsin extremely imprecise situations.</p><p>4. Experimental study</p><p>4.1. The proposed FMS</p><p>The selected FMS consists of a loading station, anunloading station, four machines and a material-handlingsystem. It is assumed that material-handling system has a</p><p>ARTICLE IN PRESSofthe rst two layers and the thresholds of the second layerneurons are called wij and uj, respectively. Similarly, w</p><p>0jk</p><p>and u0k are the weights of the connections between the twolatter layers and the thresholds of the third layer neurons.The training algorithm is iterative, and employs the</p><p>gradient algorithm to minimise a function that measuresthe difference between the network output (zmk) and thedesired one (omk). This algorithm has two phases, oneforward and the other backward. The former calculatesthe difference between the network output and the desiredone:</p><p>Ewij ; uj ; w0jk; u0k</p><p> 12</p><p>Xpm1</p><p>Xn3k1</p><p>omk f</p><p>Xn2j1</p><p>w0jk ymj u0k !" #2</p><p>,</p><p>where</p><p>ymj f</p><p>Xn1i1</p><p>wij xmi uj !</p><p>p is the number of training examples.This functioncalled the cost, target, error or energy</p><p>functionmeasures how appropriate the weights of theconnections are, and approaches zero when the networkoutput approximates to the desired output. Once thisfunction has been calculated, the backward phase follows.In this phase, by applying the gradient algorithm, theweights and thresholds are modied so that error isreduced. This process is iterated until the error is reducedto the desired amount.Finally, inductive learning algorithms generate a deci-</p><p>sion tree from a set of training examples. The original ideasprung from the works of Hoveland and Hunt at the end ofthe 1950s, culminating in the following decade in conceptlearning systems (Hunt et al., 1966). The idea is torecursively divide the initial set of training examples intosubsets composed of single-class collections of examples.Other researchers discovered the same or similar methodsindependently, and Friedman (1977) established thefundamentals of the CART system, which shared someelements with ID3 (Quinlan, 1979, 1983, 1986), PLS(Rendell, 1983) and ASSISTANT 86 (Cestnik et al.,1987). The C4.5 algorithm (Quinlan, 1993) is the mostwidely used of the inductive learning algorithms. Besidesthe decision tree that is generated, this algorithm alsoproduces a set of decision rules out of the decision tree,whereby the class of new cases can be determined.</p><p>3. Scheduling using machine learning</p><p>An overview of a scheduling system that employsmachine learning is shown in Fig. 2. A simulation modelis used by the example generator to create differentmanufacturing system states and choose the best dispatch-</p><p>P. Priore et al. / Engineering Applicationsing rule for each particular state. The machine-learningalgorithm acquires the knowledge that is necessary to makefuture scheduling decisions from the training examples.The real time control system using the scheduling knowl-edge, the manufacturing systems state and performance,determines the best dispatching rule for job scheduling. Theknowledge may need to be rened, depending on themanufacturing systems performance, by generating furthertraining examples.Finally, it must be remembered that there may be at least</p><p>four reasons why a machine learning-based approachmight perform worse than the best rules used individually:glotimFig. 2. General overview of a knowledge-based scheduling system.ManufacturingsystemSystem state and performance</p><p>Real time control system </p><p>Job schedulingSystemperformance</p><p>Control Attribute Combination </p><p>Machine learning algorithm</p><p>Training and test example generator </p><p>Training and test examples </p><p>Scheduling knowledge </p><p>KnowledgerefinementSimulation model </p><p>Artificial Intelligence 19 (2006) 247255 249bal maximal capacity of 30 parts and the transportationes between two machines are negligible. Two types of</p></li><li><p>evet</p><p>6.</p><p>7.</p><p>8.</p><p>the</p><p>ARTICLE IN PRESSof4.2. Generating training and test exampleswoingtraare</p><p>1.</p><p>2.</p><p>3.4.5.6.</p><p>7.The dispatching rules employed for the second type ofent in this FMS are (OKeefe and Kasirajan, 1992; Kimal., 1998; Min et al., 1998): SPT, shortest queue (NINQ),rk in queue (WINQ), and lowest utilised station (LUS).al.1. Each time a machine ends an operation, a schedulingdecision must be taken about the choice of the next partto process in the queue of parts that have been assignedto this machine.</p><p>2. Each time a machine ends an operation on a part/job, adispatching decision must be taken about the choice ofthe machine (and of the queue where to wait for it) thatwill realise the next operation for this part/job.</p><p>For the rst type of event, the following dispatchingrules are used: shortest processing time (SPT), earliest duedate (EDD), modied job due date (MDD), and shortestremaining processing time (SRPT). These rules wereselected because of their ne performance in earlier studies(see for example, Shaw et al., 1992; Kim et al., 1998; Min et, 1998).events that trigger a decision of the FMS control systemare studied for the FMS proposed (see Fig. 3):</p><p>Fig. 3. Flexible manufacturing system conguration.Machine 1 Machine 2 Machine 3 Machine 4 Material handling system stationstation</p><p>UnloadingLoading250 P. Priore et al. / Engineering ApplicationsThe control attributes used to describe the manufactur-system state must rst be dened in order to generateining and test examples. In...</p></li></ul>

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