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

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Engineering Applications of Artificial Intelligence 19 (2006) 247–255

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

Paolo Priore�, David de la Fuente, Javier Puente, Jose Parreno

Escuela Tecnica Superior de Ingenieros Industriales, Universidad de Oviedo, Campus de Viesques, 33203, Gijon, Spain

Received 3 November 2004; received in revised form 16 September 2005; accepted 26 September 2005

Available online 14 November 2005

Abstract

Dispatching rules are frequently used to schedule jobs in flexible manufacturing systems (FMSs) dynamically. A drawback, however,

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

the others for all the possible states the system might be in. This drawback would be eliminated if the best rule for each particular

situation could be used. To do this, this paper presents a scheduling approach that employs machine learning. Using this latter technique,

and by analysing the earlier performance of the system, ‘scheduling knowledge’ is obtained whereby the right dispatching rule at each

particular moment can be determined. Three different types of machine-learning algorithms will be used and compared in the paper to

obtain ‘scheduling knowledge’: inductive learning, backpropagation neural networks, and case-based reasoning (CBR). A module that

generates new control attributes allowing better identification of the manufacturing system’s state at any particular moment in time is

also designed in order to improve the ‘scheduling knowledge’ that is obtained. Simulation results indicate that the proposed approach

produces significant performance improvements over existing dispatching rules.

r 2005 Elsevier Ltd. All rights reserved.

Keywords: Knowledge-based systems; Scheduling; FMS

1. Introduction

The different approaches available to solve the problemof flexible manufacturing system (FMS) scheduling can bedivided into the following categories: the analytical, theheuristic, the simulation-based and the artificial 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 aNP-complete type (Garey and Johnson, 1979), so heuristicand off-line type algorithms are usually used (Cho and

e front matter r 2005 Elsevier Ltd. All rights reserved.

gappai.2005.09.009

ing author. Tel.: +0034985182107; fax: +0034985182010.

ess: [email protected] (P. Priore).

Wysk, 1993; Chen and Yih, 1996). The problem is thatthese analytical models include simplifications that are notalways valid in practice. Moreover, they are not efficientfor reasonably large-scale problems.These difficulties led to research into many heuristic

approaches, 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 first. 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 manufacturingsystems using simulation, concluding that performancedepends on several factors, such as the due date tightness(Baker, 1984), the system’s configuration, the workload,and so on (Cho and Wysk, 1993). FMSs led to manystudies evaluating the performance of dispatching rules in

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w′jkwij

u′k

uj

Input layer Hidden layer

Output layer

xi yj zk ok Target

Fig. 1. An overview of a backpropagation neural network.

P. Priore et al. / Engineering Applications of Artificial Intelligence 19 (2006) 247–255248

these 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, itwould be interesting to change these rules dynamically andat the right moment according to the system’s 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 field ofartificial 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 system’s 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 benefit from a combination of two ormore approaches (see for example, Glover et al., 1999;Flanagan and Walsh, 2003).

Machine learning solves problems by using knowledgeacquired while solving earlier problems in the past similarin nature to the problem at hand. The main algorithmtypes in the field 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 system’s 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-learning algorithms used in this paper are first 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 rulesconstantly. A summary of the results obtained rounds thepaper off.

2. Machine learning

According to Quinlan (1993), machine-learning algo-rithms can be classified 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:

ClassðxÞ ¼ classðnnÞ;

where nn (nearest neighbour) satisfies:

dðx; nnÞ ¼Minimumfdðx; eÞ : e 2 Eg.

This means that the case’s class coincides with that of thenearest example or neighbour. This initial scheme can befine 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 k

neighbours.As regards neural networks, those that will be used in

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 patternclassifiers 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

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

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Systemperformance

Control Attribute Combination

Machine learning algorithm

System state and performance

Training and test example generator

Real time control system

Manufacturingsystem

Job scheduling

Training and test examples

Scheduling knowledge

KnowledgerefinementSimulation model

Fig. 2. General overview of a knowledge-based scheduling system.

P. Priore et al. / Engineering Applications of Artificial Intelligence 19 (2006) 247–255 249

the first two layers and the thresholds of the second layerneurons are called wij and uj, respectively. Similarly, w0jkand 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 thegradient algorithm to minimise a function that measuresthe difference between the network output (zmk) and thedesired one (omk). This algorithm has two phases, one‘forward’ and the other ‘backward’. The former calculatesthe difference between the network output and the desiredone:

Eðwij ; uj ;w0jk; u

0kÞ

¼1

2

Xp

m¼1

Xn3k¼1

omk � f

Xn2j¼1

w0jk � ymj � u0k

!" #2,

where

ymj ¼ f

Xn1i¼1

wij � xmi � uj

!

p is the number of training examples.This function—called the cost, target, error or energy

function—measures 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 modified so that error isreduced. This process is iterated until the error is reducedto the desired amount.

Finally, inductive learning algorithms generate a deci-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.

3. Scheduling using machine learning

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-ing rule for each particular state. The machine-learningalgorithm acquires the knowledge that is necessary to make

future scheduling decisions from the training examples.The real time control system using the ‘scheduling knowl-edge’, the manufacturing system’s state and performance,determines the best dispatching rule for job scheduling. Theknowledge may need to be refined, depending on themanufacturing system’s performance, by generating furthertraining examples.Finally, it must be remembered that there may be at least

four reasons why a machine learning-based approachmight perform worse than the best rules used individually:

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.
2.
The system’s performance depends on the number andrange of control attributes used in the design of thetraining examples.
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.
4.
The system can be prone to inadequate generalisationsin extremely imprecise situations.
4. Experimental study

4.1. The proposed FMS

The selected FMS consists of a loading station, anunloading station, four machines and a material-handlingsystem. It is assumed that material-handling system has aglobal maximal capacity of 30 parts and the transportationtimes between two machines are negligible. Two types of

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Unloadingstation

Machine 1 Machine 2 Machine 3 Machine 4

Material handling system

Loadingstation

Fig. 3. Flexible manufacturing system configuration.


events that trigger a decision of the FMS control systemare studied for the FMS proposed (see Fig. 3):

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.
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.
For the first type of event, the following dispatchingrules are used: shortest processing time (SPT), earliest duedate (EDD), modified job due date (MDD), and shortestremaining processing time (SRPT). These rules wereselected because of their fine performance in earlier studies(see for example, Shaw et al., 1992; Kim et al., 1998; Min etal., 1998).

The dispatching rules employed for the second type ofevent in this FMS are (O’Keefe and Kasirajan, 1992; Kimet al., 1998; Min et al., 1998): SPT, shortest queue (NINQ),work in queue (WINQ), and lowest utilised station (LUS).

4.2. Generating training and test examples

The control attributes used to describe the manufactur-ing system state must first be defined in order to generatetraining and test examples. In this particular FMS theseare:

1.
F: flow allowance factor which measures due datetightness (Baker, 1984).
2.
NAMO: mean number of alternative machines for anoperation.
3.
MU: mean utilisation of the manufacturing system. 4. Ui: utilisation of machine i. 5. WIP: mean number of parts in the system. 6. RBM: ratio of the utilisation of the bottleneck machine
to the mean utilisation of the manufacturing system.
7. RSDU: ratio of the standard deviation of individual
machine utilisations to mean utilisation.

latter two attributes:
The following expressions are employed to calculate the
RBM ¼maxðU1;U2;U3;U4Þ

MU,

RSDU ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiðU1 �MUÞ2 þ ðU2 �MUÞ2 þ ðU3 �MUÞ2 þ ðU4 �MUÞ2=4

qMU

.

The training and test examples needed for the learningstage are obtained by simulation using the WITNESSprogramme (Witness, 1996). The following suppositionswere made to do this:

1.
Jobs arrive at the system following a Poisson distribu-tion.
2.
Processing times for each operation are sampled from anexponential distribution with a mean of one.
3.
The actual number of operations of a job is a randomvariable, equally distributed among the integers fromone to four.
4.
The probability of assigning an operation to a machinedepends on the parameters percentage of operationsassigned to machine i (POi). These percentages (ran-domly generated) fluctuate between 10% and 40%. Tostudy the behaviour of the FMS in an unbalancedsituation, it is also assumed that the first two machineshave a greater workload.
5.
The number of alternative machines for an operationvaries between one and four.
6.
The precedence constraints between some pairs ofoperations are randomly generated for each job.
7.
The job arrival rate varies so that the overall use of thesystem ranges between 55% and 95%.
8.
The value of factor F fluctuates between one and ten.
As mean tardiness and mean flow time in the system arethe most widely used criteria to measure system perfor-mance in all manufacturing systems, they are alsoemployed in this study. In all, 1100 different controlattribute combinations were randomly generated; 100 ofthese were used as test examples, while the other 1000 wereused as training examples. For each combination ofattributes, mean tardiness and mean flow time valuesresulting from the use of each of the dispatching rules inisolation were calculated. Sixteen simulations were actuallyneeded to generate a training or test example, as there are16 combinations because each type of decision (choice ofthe next machine for an operation, choice of the nextoperation for a machine) has four rules. The number oftimes that each of the combinations of the dispatching rulesemployed is selected for the criteria of mean tardiness andmean flow time is shown in Table 1 as a percentage. Mostof the combinations are selected, to a greater or lesserextent, in each of the scenarios that are proposed, pointingto the need to modify the dispatching rules in real time as afunction of the state the manufacturing system is in at eachparticular moment.

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Table 1

Comparison of combinations of the dispatching rules in the examples

generated

Combination of the dispatching

rules employed

Mean tardiness

(%)

Mean flow time

(%)

SPT+SPT 23.27 50

SPT+NINQ 4.64 22.45

SPT+WINQ 6.09 25

SPT+LUS 0.36 0

EDD+SPT 1.09 0

EDD+NINQ 8.73 0

EDD+WINQ 4.73 0

EDD+LUS 9.09 0

MDD+SPT 25.64 0

MDD+NINQ 11.27 0

MDD+WINQ 3.82 0.64

MDD+LUS 1.27 0

SRPT+SPT 0 0

SRPT+NINQ 0 0

SRPT+WINQ 0 1.91

SRPT+LUS 0 0

Geneticalgorithm

Nearest neighbour algorithm

Test error

wi

Training and test example generator

Testexamples

Trainingexamples

Fig. 4. Method for calculating optimum wi weights.


4.3. Comparison of the machine-learning algorithms

The distances between a new case and the trainingexamples have to be calculated and the shortest distancefound to calculate its class using the nearest neighbouralgorithm. The new case’s class will coincide with that ofthe ‘nearest’ training example. The formulation used tocalculate the distance (d(x,e)) between a new case (x) and atraining example (e) is

dðx; eÞ ¼

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiXn

i¼1

wiðaix � aieÞ2

s,

where n is the number of attributes considered; aix is thevalue of attribute i in case x; aie is the value of attribute i inexample e, and wi is the weight assigned to attribute i as afunction of its importance.

The previous section shows that n equals ten in thisparticular case. Another two more sophisticated versions ofthe nearest neighbour algorithm have also been applied inthis study. In the first of the two, an integer value of k ofthree is employed, so that the three nearest neighbours arecalculated for each x. In the second version, a value of k offive is used. Odd values of k are chosen to eliminatepotential ties. One of the main difficulties of the nearestneighbour algorithm is that the classification of new casesdepends on the weights wi selected. However, the value ofeach wi is not known a priori.

A genetic algorithm (Holland, 1975; Goldberg, 1989;Michalewicz, 1996) resolves this problem by determiningthe optimum values of wi. Fig. 4, shows an overview of themethod for calculating optimum wi weights. It can be seenthat the genetic algorithm employs the nearest neighbourmethod to calculate the classification error for given wi

values. This error is the ‘fitness’ for a given set of wi

weights. The genetic algorithm will calculate the optimumvalues of wi after a certain number of generations. Thesteps of the proposed genetic algorithm are as follows:

1.
Generation of a population of m individuals. 2. Selection of the best individual. 3. Calculation of a distribution of accumulated probability
as a function of the ‘fitness’ of each individual in thepopulation.

4.
Selection of m individuals generating m randomnumbers between zero and one, employing the recentlycalculated probability distribution.
5.
Simple crossover of the individuals selected in step fourwith a predetermined crossover probability (CP). Theparents are eliminated.
6.
Mutation with a predetermined mutation probability(MP).
7.
Selection of the best individual. If this has a ‘fitness’ thatis inferior to that of the best individual from theprevious generation, it is retained and the worstindividual of the present generation is eliminated.
8.
Return to step three if the number of generations is lessthan the maximum number of generations (NGmax).
Each of the m individuals of the population is formed bya vector of the type that follows:

ðw1;w2;w3 . . . ;w9;w10Þ,

where wi is the weight of attribute i. The most appropriatevalues of population size (m), CP, MP, and NGmax werealso studied. Optimal values obtained are: m ¼ 50,CP ¼ 0:7, MP ¼ 0:025 and NGmax ¼ 100.Fig. 5 shows the test example error (examples that have

not previously been dealt with) obtained with each of themachine-learning algorithms for the criterion of meantardiness. The nearest neighbour algorithm (k-NN withk ¼ 5) can be seen to provide the lowest test error (9%).Moreover, error fluctuation from 600 training examplesupwards is minimum. The BPN is in second place, with a12% test error, and the C4.5 inductive learning algorithmgenerates the greatest test error (16%). Furthermore, it canbe observed that both the neural network and the C4.5

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0%

5%

10%

15%

20%

25%

30%

35%

50 200 350 500 650 800 950Number of examples

Err

or p

erce

ntag

e

C4.5

k-NN (k=5)BPN

Fig. 5. Comparison of machine-learning algorithms for mean tardiness.

0%

5%

10%

15%

20%

25%

50 200 350 500 650 800 950Number of examples

Err

or p

erce

ntag

e

C4.5

k-NN (k=1)

BPN

Fig. 6. Comparison of machine-learning algorithms for mean flow time.

C4.5 inductive learning algorithm

Generator of new control attributes

Generator of test and training examples

Initial test examples

Modified test and training examples

Modified decision tree and set of decision rules

Initial trainingexamples

Fig. 7. The generator module of new control attributes.


have greater test error fluctuation than the nearestneighbour algorithm from 600 training examples onwards.

Similarly, Fig. 6 provides a summary of the resultsthat were obtained with each of the machine-learningalgorithms for the criterion of mean flow time. Itshows that the nearest neighbour algorithm obtains zerotest error. The C4.5 inductive learning algorithm is insecond place, with a 1% test error, with the BPNgenerating greatest test error (4%). Errors for this lattercriterion are lower due to there being five dispatching rulecombinations that are really used. In contrast, 12combinations are used for the criterion of mean tardiness(see Table 1).

The ideal configuration of the neural network that wasused for the criterion of mean tardiness has 10 input nodes(one for each control attribute), 16 nodes in the hiddenlayer, and 12 nodes in the output layer (one for eachdispatching rule combination). Similarly, the ideal config-uration of the neural network employed for the criterion ofmean flow time has 10 input nodes, 16 nodes in the hiddenlayer, and five nodes in the output layer.

4.4. Generating new control attributes

To allow a better identification of the manufacturingsystem’s state, a module was designed which automaticallydetermines the ‘useful’ arithmetic combinations of theoriginal attributes by using simulation data which origin-ally served to obtain test and training examples. Togetherwith the C4.5 algorithm, this module generates the bestcontrol attribute combinations for the manufacturingsystem that is being used. The basic arithmetic operatorsconsidered are adding, subtracting, multiplying and divid-ing. Although others can be used, these above fouroperators were chosen for two reasons:

1.
The more operators used, the more search timeincreases.
2.
As the process is recursive, fairly complex attributes canbe generated from basic operators.
Fig. 7 provides an overview of how the module works. Apseudo-code for the generator of the new control attributesis listed next:

1.
Determination of the combinations of the presentattributes.
2.
Generation of new training and test examples accordingto earlier combinations.
3.
Identification of the ‘useful’ combinations. These are inthe decision tree and in the set of decision rulesgenerated by C4.5.
4.
If the new decision tree and/or the set of decision ruleshave fewer classification errors, go back to step one. Ifnot, stop the algorithm.
In fact, the decision can be made to continue thealgorithm at step four, as fewer classification errors may beobtained in the following iteration or iterations, eventhough error has not been improved in the presentiteration. By applying the proposed module, the following‘useful’ control attribute combinations were obtained forthe criterion of mean tardiness:

1.
U1+U2
2.
U1+U4
3.
U2+U3
4.
U1�U2

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5%


5.

Err

or p

erce

ntag

e

Fig

me

U2�U4

6.
U3�U4 4%
e
7. U3/U4
2%

3%

Err

or p

erce

ntag C4.5

k-NN (k=1)

BPN

The proposed module is also applied for the criterion ofmean flow time, and the following combinations ofattributes were determined to be ‘useful’:

0%

1%

1.
U1�U2
600 750 900
2. U3�U4 Number of examples 3. U1/U2
Fig. 9. Comparison of machine learning algorithms for the criterion of
4. U2/U3
mean flow time with the generator module of new control attributes.

It should be noted that only combinations of attributesUi are relevant for both criteria. Besides, U1 and U2 arepresent in most combinations due to the fact that machines1 and 2 have a greater workload. Fig. 8 shows the test errorobtained with each of the machine-learning algorithms forthe criterion of mean tardiness when the generator moduleof new control attributes was applied. It shows that thenearest neighbour algorithm gives the lowest test error(8%). Similarly, the BPN has a test error of 12%, and theC4.5 inductive learning algorithm generates the largest testerror (13%). The C4.5 algorithm is also shown to lead to alarger error fluctuation than the nearest neighbour algo-rithm and the BPN. A comparison of this figure with Fig. 5shows how test error has decreased. Only training sets of600 examples or more were used, as lower errors areobtained upwards of this training set size.

Furthermore, Fig. 9 provides a summary of the resultsobtained for each of the machine-learning algorithms forthe criterion of mean flow time. It can be seen that thenearest neighbour algorithm and the C4.5 inductivelearning algorithm have zero test error. In contrast, theBPN generates the largest test error (2%). Errors are onceagain considerably smaller that those obtained for thecriterion of mean tardiness, as the number of classes islower. Test errors for this figure are also lower than for Fig.6, because of the new control attributes applied. A finalpoint to be noted is that the ideal neural network for thecriterion of mean tardiness has 17, 15 and 12 neurons in theinput, hidden and output layers respectively. Similarly, for

0%

5%

10%

15%

20%

600 750 900Number of examples

C4.5

k-NN (k=5)

BPN

. 8. Comparison of machine learning algorithms for the criterion of

an tardiness with the generator module of new control attributes.

the criterion of mean flow time the ideal neural networkhas 14, 10 and five neurons.

4.5. Learning-based scheduling

To select the best combination of dispatching rulesaccording to the FMS’s state in real time we mustimplement the ‘scheduling knowledge’ in the FMS simula-tion model. A further key issue is the choice of themonitoring period, as the frequency used to test the controlattributes to decide whether the dispatching rules change ornot, determines the performance of the manufacturingsystem. Multiples of the average total processing time for ajob are taken (see for example, Wu and Wysk, 1989; Kimand Kim, 1994; Jeong and Kim, 1998) to select thismonitoring period. In this study, 2.5, 5, 10 and 20 timeunits are used as monitoring periods.Two different scenarios are also proposed for the

manufacturing system. In the first of them, changes aregenerated in the FMS at given time periods, as a functionof a random variable, equally distributed among theintegers from 50 to 500 time units. In the second scenario,this random variable ranges between 2.5 and 250 timeunits. Therefore, in this latter scenario the FMS willundergo a greater number of changes. Nine hundredtraining examples will be used for both performancecriteria in the light of the results in the previous section.Finally, it should be pointed out that five independentreplicas are made over 100 000 times units.A summary of the results obtained is provided in Table

2. To increase readability, the values in the table arerelative to the lowest mean tardiness and mean flow timeobtained (these are assigned a value of one), with amonitoring period of 2.5 time units, as this was the best.Mean tardiness and mean flow time values in the tablecorrespond to the average of the five replicas. Table 2demonstrates not only that the best alternative is to employa scheduling system based on machine learning, but alsothat the nearest neighbour algorithm (k-NN) provides thebest results. Mean tardiness values for the C4.5 algorithmand the BPN are similar, and worse than the valueobtained with the nearest neighbour algorithm. The

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Table 2

Mean tardiness (MT) and mean flow time (MFT) for the proposed

strategies

Strategy used MT for

first

scenario

MT for

second

scenario

MFT for

first

scenario

MFT for

second

scenario

SPT+SPT 4.1228 5.4703 2.1223 2.4183

SPT+NINQ 1.2134 1.2173 1.0455 1.0500

SPT+WINQ 1.2068 1.1964 1.0481 1.0476

SPT+LUS 2.5154 2.5819 1.5208 1.5277

EDD+SPT 3.5316 4.7024 2.2199 2.6260

EDD+NINQ 1.5325 1.6737 1.3361 1.3991

EDD+WINQ 1.5271 1.6819 1.3358 1.4030

EDD+LUS 2.8872 3.2830 1.8767 2.0614

MDD+SPT 3.5436 4.7435 2.3141 2.6908

MDD+NINQ 1.1358 1.1406 1.2356 1.2569

MDD+WINQ 1.1433 1.1521 1.2394 1.2620

MDD+LUS 2.3953 2.5228 1.7848 1.8646

SRPT+SPT 4.5211 6.1213 2.2947 2.6706

SRPT+NINQ 1.3824 1.4119 1.1392 1.1477

SRPT+WINQ 1.3860 1.4034 1.1448 1.1486

SRPT+LUS 2.8449 3.0129 1.6815 1.7195

k-NN 1.0000 1.0000 1.0000 1.0000

BPN 1.0221 1.0258 1.0129 1.0114

C4.5 1.0267 1.0294 1.0052 1.0023


combinations MDD+NINQ and MDD+WINQ are thebest strategies of those that use a fixed combination ofdispatching rules. However, mean tardiness values arehigher than the alternative that uses CBR by between13.58% and 15.21%.

Similarly, for the criterion of mean flow time, thescheduling systems based on the nearest neighbour algo-rithm and on C4.5 provide the best results. With the BPN,mean flow time values are slightly higher to those for theother two algorithms. Furthermore, it can be seen that thecombinations SPT+NINQ and SPT+WINQ generate theleast mean flow time from amongst the strategies that applya fixed combination of rules. However, mean flow timevalues are greater than the alternative of the nearestneighbour algorithm by between 4.55% and 5%.

To round off this study, the scheduling system based onthe nearest neighbour algorithm is compared with the otheralternatives by analysis of variance (ANOVA). Thisscheduling system is shown to be better than these with asignificance level of less than 0.05. The only exceptionoccurs between the nearest neighbour algorithm and C4.5according to the mean flow time criterion.

5. Conclusions

This paper makes a comparison of three machine-learning algorithms used for dynamically scheduling jobsin a FMS. A generator module of new control attributes isalso incorporated by which test error obtained with themachine-learning algorithms can be reduced, therebyimproving the manufacturing system’s performance. Theperformance of the FMS employing the scheduling system

based on the nearest neighbour algorithm is compared withthe other strategies, and the system proposed is shown toobtain lower mean tardiness and mean flow time values.The only exception occurs with the scheduling systemsbased on the nearest neighbour algorithm and on C4.5 forthe criterion of mean flow time as test errors in both thesealgorithms are the same. Although the selected FMS isquite generic both in its configuration and in the jobs’characteristics, and it has been widely used by otherauthors (see for example, Shaw et al., 1992; Kim et al.,1998; Min et al., 1998), the obtained results cannot begeneralised to any type of FMS.Future research might include consideration of more

decision types in the proposed FMS. In the same way otherFMS configurations could be studied. A simulator mightalso be incorporated, as sometimes ‘scheduling knowledge’leads to there being two or more theoretically rightdispatching rules for certain given control attribute values.In such cases, where the decision based on ‘schedulingknowledge’ is not clear, a simulator would be extremelyuseful to determine which rule to apply. Finally, aknowledge base refinement module could be added, whichwould automatically modify the knowledge base whenmajor changes in the manufacturing system occur.

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