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PAOLO PRIORE*, DAVID DE LA FUENTE, RAÚL PINO, JAVIER PUENTE. Escuela Técnica Superior de Ingenieros Industriales, Universidad de Oviedo, ...
Dynamic scheduling of flexible manufacturing systems using neural networks and inductive learning

PAOLO PRIORE*, DAVID DE LA FUENTE, RAÚL PINO, JAVIER PUENTE

Escuela Técnica Superior de Ingenieros Industriales, Universidad de Oviedo, Campus de Viesques, 33203, Gijón, Spain Phone: 985182107 Fax: 985182010 e-mail: [email protected] *: corresponding author Keywords : scheduling, neural networks, inductive learning, FMS, simulation Word count: 5244

Dynamic scheduling of flexible manufacturing systems using neural networks and inductive learning

P. Priore, D. de la Fuente, R. Pino and J. Puente School of Industrial Engineering, University of Oviedo, Spain

ABSTRACT Dispatching rules are usually applied to schedule jobs in Flexible Manufacturing Systems (FMSs) dynamically. Despite their frequent use, one of the drawbacks that they display is that the state the manufacturing system is in dictates the level of performance of the rule. As no rule is better than all the other rules for all system states, it would highly desirable to know which rule is the most appropriate for each given condition, and to this end this paper proposes a scheduling approach that employs inductive learning and backpropagation neural networks. Using these latter techniques, 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. A module that generates new control attributes is also designed in order to improve the “scheduling knowledge” that is obtained. Simulation results show that the proposed approach leads to significant performance improvements over existing dispatching rules. Keywords : scheduling, neural networks, inductive learning, FMS, simulation

INTRODUCTION One of the most commonly applied solutions to the scheduling problem in FMSs involves using dispatching rules, which have been evaluated for performance by many researchers (see for example, Choi and Malstrom, 1988; Denzler and Boe, 1987; Egbelu and Tanchoco, 1984; Henneke and Choi, 1990; Montazeri and Van Wassenhove, 1990; Stecke and Solberg, 1981; Tang et al., 1993). Almost all the above studies point to the fact that rule performance depends on the criteria that are chosen, and the system’s configuration and conditions (utilisation level of the system, relative loading, due date tightness, and so on). It would thus be interesting to be able to change dispatching rules at the right moment dynamically.

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The literature describes two basic approaches to modify dispatching rules. The first approach is to select a rule at the appropriate moment by simulating a set of pre-established dispatching rules and opting for the one that provides the best performance (see for example, Ishii and Talavage, 1991; Jeong and Kim, 1998; Kim and Kim, 1994; Wu and Wysk, 1989). The second approach, involving artificial intelligence, requires a set of earlier system simulations (training examples) to determine what the best rule is for each possible system state. A machine learning algorithm (Michalski et al., 1983) is trained to acquire knowledge through these training examples, and this knowledge is then used to make intelligent decisions in real time (see for example, Kim et al., 1998; Min et al., 1998; Nakasuka and Yoshida, 1992; Shaw et al., 1992). The training examples are generated by defining a set of control attributes that identify the manufacturing system’s state at each particular time. Machine learning, which is related to the field of artificial intelligence, solves problems by using knowledge it had acquired while solving earlier problems in the past similar in nature to the problem at hand. These previously resolved problems are referred to by the terms training cases or training examples. Knowledge is then acquired using these training examples and the machine learning algorithm. Knowledge is then validated using test cases or examples (i.e. examples that have not previously been dealt with). Training or test examples are usually made up of a number of attributes that define the characteristics of these examples. Furthermore, there is a special attribute called the class, which is the solution to each example. Two frequently applied machine learning algorithm types in many applications are inductive learning and neural networks. Aytug et al. (1994) and Priore et al. (2001) provide a review in which machine learning is applied to solving scheduling problems. Nevertheless, there are hardly any studies in the literature that compare the different types of machine learning algorithms used in scheduling problems. This paper therefore presents a scheduling approach that uses and compares inductive learning and neural networks. To improve the manufacturing system’s performance, a new approach is also proposed whereby new control attributes that are arithmetical combinations of the original 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 machine learning is then presented. This is followed by the experimental study, which describes a new approach to determine new control attributes from the original ones. The two machine learning algorithms used are also compared. Finally, the

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proposed scheduling approach is compared with the alternative of using a combination of dispatching rules constantly. A summary of the results obtained concludes the paper.

NEURAL NETWORKS AND INDUCTIVE LEARNING “Backpropagation neural networks”, or multilayer perceptron (Rumelhart et al., 1986), which will be applied in this work, figure amongst those networks that are most well-know and most widely used as pattern classifiers or function approximators (Freeman y Skapura, 1991; Lippman, 1987). An overview of a neural network of this type can be seen in Figure 1. It shows that there is a single hidden layer and there are no connections between neurons in the same layer in this particular case. The backpropagation training algorithm is used in this type of neural networks. This algorithm calculates the most adequate connection weights (wij , w’jk) and thresholds (u j , u’k) so that the difference between the network output (zµk) and the desired one (o µk) is minimised. If one imagines a neural network with an input layer of n 1 neurons, a hidden layer of n 2 neurons, and an output layer of n 3 neurons, and if the outputs of the input, hidden and output layers are called xi , yj and zk respectively, then this difference is calculated (assuming p training examples) by the following:

(

E wij , u j , w' jk , u ' k

)

1 = 2

∑∑ ( p

n3

o kµ

µ =1 k =1

2



zkµ

)

(1)

where:  z kµ = f   

n2

∑ w'

 y µj = f   

µ jk ⋅ y j

j =1

n1

∑w i =1

ij

 − u' k   

 ⋅ xiµ − u j   

(2)

(3)

Function f is known as the neural network transfer function. Once the network has been trained (i.e. once the weights and thresholds have been calculated), it is then ready to classify new examples or cases.

Take in Figure 1

Furthermore, inductive learning algorithms use a set of training examples to generate a decision tree. The original idea of this algorithm type comes from the works of Hoveland and Hunt at the end of

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the fifties, and leads to concept learning systems (Hunt et al., 1966) in the following decade. The idea is to recursively divide the initial set of training examples into subsets composed of single-class collections of examples. The C4.5 algorithm (Quinlan, 1993) is the most commonly applied inductive learning algorithm. This algorithm also generates a set of decision rules from the decision tree, whereby the class of new cases can be determined.

SCHEDULING USING NEURAL NETWORKS AND INDUCTIVE LEARNING Two contrasting features need to be fulfilled for a real-time scheduling system that dynamically modifies dispatching rules to work properly (Nakasuka and Yoshida, 1992): 1.

Rule selection must take into account a variety of information about the manufacturing system in real time.

2.

Rule selection must be completed fast enough for real operations not to be delayed.

One way of doing this is to employ some class of knowledge about the relationship between the manufacturing system’s state and the rule to be applied at that moment. However, one of the most difficult problems is precisely how this knowledge is to be acquired. Machine learning algorithms, such as inductive learning or neural networks, are used to do this. However, the training examples and the learning algorithm must be adequate for this knowledge to be useful. Moreover, in generating the training examples, the attributes selected are crucial to the performance of the scheduling system (Chen and Yih, 1996). Figure 2 shows a scheduling system that employs machine learning. The training and test examples needed by the machine learning algorithm must first be generated. The generator of examples employs an FMS simulation model to this end, and generates different FMS states (with different rates of arrival of parts, diverse relative work loads for the manufacturing system, different due date tightnesses, etc.). The best dispatching rule to be applied is calculated for each state (i.e. the class of this state, or example, is obtained), and a training or test example is thus obtained. The machine learning algorithm employs the training examples to generate the knowledge required to make future scheduling decisions. This knowledge will be in the form of decision rules or trees when an inductive learning algorithm is used, or will be in the form of weights and thresholds if a neural network is employed. The real time control system using the ‘scheduling knowledge’, the manufacturing system’s state and performance,

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choose the best dispatching rule for job scheduling. Further training examples may possibly be needed in order to refine the knowledge about the manufacturing system depending on the performance of the latter.

Take in Figure 2

EXPERIMENTAL STUDY The proposed FMS The FMS which was used in the experimental study was a Mazak FMS. Mazak is a company which designs and sells FMSs. A simulation model using the WITNESS programme was developed to mimic the Mazak FMS. The latter, as shown in Figure 3, has four machining centres, a washing machine, thirty two work-in-process storage racks, and a crane (the material handling system). Each machining centre has its own input and output buffer. In addition, each machining centre has different interchangeable tool magazines, enabling it to process various operations by mounting different tool magazines. However, in this experimental study, we presume that the Mazak FMS has a pre-set policy for tooling arrangement.

Take in Figure 3

Two types of decision are studied in this system. The first of them is the selection by the machine of parts assigned to it. The dispatching rules applied to do this in this FMS are: SPT (Shortest Processing Time), EDD (Earliest Due Date), MDD (Modified Job Due Date) and SRPT (Shortest Remaining Processing Time). These rules, which order the different jobs that are competing for the use of a particular machine as a result of different priority schemes, were selected because of their fine performance in several earlier studies (Kim et al., 1998; Min et al., 1998; Shaw et al., 1992). A priority index is assigned to each job and the one with the lowest index will be selected first. The calculation of the priority index for each rule is carried out as follows: SPT

p ij

EDD

di

MDD

max {t+Pij , d i }

SRPT

Pij

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where d i is the due date of job i; p ij is the processing time of operation j of job i; Pij is the remaining processing time for job i at the beginning of operation j, and t is the moment when the scheduling decision is taken. Due date of job i (d i ) is calculated, following Baker (1984), by the following expression: d i = t i + pi ∗ F

(4)

where F is the flow allowance factor which measures due date tightness; ti is the moment when job i arrives at the system, and p i is the total processing time of job i. As an operation can be carried out on different machines, the second type of decision involves the selection of the machines by the parts. The dispatching rules used in this case are (Kim et al., 1998; Min et al., 1998; O’Keefe and Kasirajan, 1992): SPT (Shortest Processing Time), which selects the machine that will carry out the operation in the shortest time; NINQ (Number in Queue), which selects the machine with the fewest number of jobs in the buffer; WINQ (Work in Queue), which selects the machine whose input buffer contains the smallest total amount of work, and LUS (Lowest Utilised Station), which selects the machine with the smallest total utilisation rate.

Generating training and test examples The training and test examples can only be generated if the control attributes that describe the state that the manufacturing system is in are first defined. These attributes are the following: 1.

F: flow allowance factor which measures due date tightness (Baker, 1984).

2.

NAMO: number of alternative machines for an operation.

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.

The following expressions are used to calculate the latter two attributes: RBM =

10 ∗ max ( U 1 , U 2 , U 3 , U 4 , U 5 ) MU

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(5)

10 ∗

( U 1 − MU ) 2 + ( U 2 − MU ) 2 + ( U 3 − MU ) 2 + ( U 4 − MU ) 2 + ( U 5 − MU ) 2 4

RSDU =

MU

(6)

To obtain the training and test examples needed for the learning stage the following suppositions were made: 1.

Jobs arrive at the system following a Poisson distribution.

2.

Processing times for each operation are sampled from an exponential distribution with a mean of one.

3.

The number of alternative machines for an operation varies between one and four.

4.

The arrival rate varies in such a way that the overall use of the system fluctuates between 55% and 95%.

5.

The value of factor F ranges between one and ten. Since mean tardiness and mean flow time in the system are the two criteria that are most

commonly used in the literature on scheduling, they were also applied to measure system performance in our experimental study. In all, 1100 different control attribute combinations were randomly generated, of which 1000 were training examples, and 100 were used as test examples. Sixteen simulations were actually needed to generate a example, as there are four rules for each of the decisions to be taken.

The application of neural networks Backpropagation neural networks are particularly used to solve classification problems such as the one being considered in this work. The ideal configuration of the neural network used for the criterion of mean tardiness was found to have 11 input nodes (one for each control attribute), 16 nodes in the hidden layer, and 12 nodes in the output layer (one for each dispatching rule combination). The number of neurons in the hidden layer was obtained by a iterative search process that calculated the number of neurons that would provide the best results. Similarly, the ideal configuration of the neural network employed for the criterion of mean flow time was found to have 11 input nodes, 16 nodes in the hidden layer, and 5 nodes in the output layer. Table I provides a summary of the results obtained using different-sized sets of training examples for the criteria of mean tardiness and mean flow time. Generally, it can be seen that as the number of training examples increases, test example error decreases considerably. Table I also shows that test error fluctuates between 16% and 12% upwards of 450 training examples for the criterion of mean tardiness.

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Furthermore, for the criterion of mean flow time, test error is observed to oscillate between 6% and 4% upwards of 500 training examples. Errors for this latter criterion are lower due to there being five dispatching rule combinations (SPT+SPT, SPT+NINQ, SPT+WINQ, MDD+WINQ, SRPT+WINQ) that are really used. In contrast, twelve combinations (SPT+SPT, SPT+NINQ, SPT+WINQ, SPT+LUS, EDD+SPT,

EDD+NINQ,

EDD+WINQ;

EDD+LUS,

MDD+SPT,

MDD+NINQ,

MDD+WINQ,

MDD+LUS) are used for the criterion of mean tardiness.

Take in Table I

The application of C4.5 The results of applying the C4.5 inductive learning algorithm to the same test and training examples can be seen in Table II. This algorithm generates a decision tree and a set of rules, which are applied to determinate the dispatching rule to be used at each particular moment. It can be seen that errors obtained with C4.5 are lower for the criterion of mean flow time. However, for the criterion of mean tardiness the neural network obtains less test error.

Take in Table II

There now follows a sample of the set of rules that resulted from applying 950 training examples for the criterion of mean flow time: Rule 1: IF NAMO