Machine Learning Approaches for Flow Shop Scheduling Problems with Alternative Resources, Sequence-dependent Setup Times and Blocking

Transcription

1 Machine Learning Approaches for Flow Shop Scheduling Problems with Alternative Resources, Sequence-dependent Setup Times and Blocking Frank Benda 1, Roland Braune 2, Karl F. Doerner 2 Richard F. Hartl 2 1 Corresponding author. Department of Business Administration, University of Vienna 2 Department of Business Administration, University of Vienna frank.benda@univie.ac.at, roland.braune@univie.ac.at, karl.doerner@univie.ac.at, richard.hartl@univie.ac.at Abstract The paper deals with different machine learning approaches for solving flow shop scheduling problems with alternative resources, sequence-dependent setup times, and blocking. The basis of these approaches is an Industry 4.0 application configuration of the industrial partner Syngroup a business consultancy with clients in manufacturing. The aim of the first approach is to generate a generalised priority rule in form of a decision tree (DT) for dispatching jobs. The DT is built using high quality solutions that are obtained using a constraint programming (CP) formulation. To be able to collect enough training examples the basic cyber-physical system (CPS) configuration was modified to an abstract model. Novel aspects include a unified representation of job sequencing and machine assignment decisions, and the generation of random forests (RF) to reduce overfitting behaviour. To show the performance of the proposed approaches, three different instance scenarios with four different job load sets were implemented, based on randomised problem data. Computational results indicate that this machine learning approach performs well in instance sets with a medium and high job load as well as in the practical application setting. The second machine learning approach deals with Genetic Programming (GP) for the same problem definition. Instead of pairwise precedences between material movements as in the first approach, in this case the available jobs are ranked using a tree-based priority rule generated with the GP. Preliminary experiments indicate that the performance of the DT and RF approach can be surpassed in particular settings. 1 Introduction The industrial partner Syngroup a business consultancy located in Vienna develops decision support systems and Industry 4.0 applications. The Syngroup makes use of a CPS for demonstrating the new possibilities of their Industry 4.0 applications by comparing the handson results of human players versus the autonomous planning system. The configuration of the CPS shop floor is shown in Fig. 1. The machines consist of three preprocessing buffer slots, a processing slot, and a transport buffer slot from which the jobs in the shape of little balls are transported to the next stage. This configuration represents a typical shop floor for many production processes, such as furniture and window construction. The CPS simulates the production sequence of jobs and the adjustment of the sequence in unforeseen events (i.e. machine breakdowns). The idea of this physical model is to demonstrate the effect of different control policies (that is, dispatching rules) on global performance measures, like the overall lead time. For this purpose, a decision tree (DT) approach is proposed. The contribution is threefold: first, solution information is extracted from a Constraint Programming (CP) formulation to generate the training data. Second, the job sequencing is combined with the machine assignment. The decision does not only contain the next job to be moved but also onto which machine the job should be transported to. This approach allows for more complex decision making. And third, the DT is embedded in a random forest (RF) approach to reduce overfitting behaviour. The second machine learning approach deals with the same basic configuration. As for the DT and RF approach, the goal is to generate a generalised priority rule that performs well in different instance scenarios. Due to the well performing DT and RF approach, a Genetic Programming (GP) approach is introduced to compete with and undercut the results of the DTs and RFs. The contribution of this project is the newly formed set of terminals and functions. These sets contain a higher degree of complexity due to the restricted transport resource, setup times, and blocking behaviour. To the best of our knowledge, this complexity level has not been dealt with in the literature until now.

2 Figure 1: CPS shop floor configuration 2 Decision Tree and Random Forest Approach The objective of the first approach is to show that a DT and RF learning approach can perform well as a generalisable dispatching rule. For this purpose the CPS configuration of the industrial partner is analysed, as introduced in Section 1. In the next step an abstract model was implemented based on that CPS configuration. The configuration of the shop floor of the industrial partner is shown in Fig Solution Method Applying the resulting decision tree as priority rule to other instances should result in decreased lead times compared to the results of common dispatching rules. For building the decision tree training data has to be generated. Therefore, three instance sets were set up with different configurations. The instances of an instance set were solved approximately optimal using constraint programming. In the next step the resulting production sequences of every instance were simulated with the help of a deterministic shop floor simulation tool. The decision tree s required training data is provided by exploiting the important information out of this simulation process of the CP results. It is split into three different parts: paired comparisons of possible material movements as proposed by Olafsson and Li [1], attributes for comparing the values of the paired comparisons, and the target classes Yes and No of which material movement should be preferred as suggested by Shahzad and Mebarki [3]. To avoid the decision tree to overfit the training data, a second approach was conducted: the random forest approach. For preventing overfitting, one of the techniques to apply usually is pruning [2]. However, preliminary tests with pruning were conducted with only limited success, as it did not lead to the expected effect of a better accuracy of the trees or decrease of the overall lead time. Hence, RFs are employed as a more advanced, yet easy to use approach for this purpose. 2.2 Experimental Setup Three different instance scenarios were defined to examine the effect of machine blocking and a high degree of capacity utilisation on the transport resource (crane blocking). But also a mixture of both aspects was considered. Finally, an instance scenario that is even closer to the CPS configuration has been introduced. Each of these instance scenarios contains three different job load sets: low load (6-15 jobs), medium load (12-44 jobs), and high load (21-72 jobs). For every set 80 instances were randomly generated with an instance generator. With the help of these instances the DTs are trained and built using the CP formulation, as discussed before. Then, the tree is being evaluated conducting a cross-validation procedure. 2.3 Computational Results The results may be summarized as follows: Applying the decision tree or random forest as a priority rule to new instances results in significantly reduced lead times compared to the results of common dispatching rules in the bigger part of the test instances. Dealing with instances with less jobs to be produced, less information can be exploited out of the CP results leading to less training data for the decision tree. In these cases the dispatching

3 rules provide slightly better results than the decision tree or random forest approach. The basic principle of the two priority rules under consideration is simply choose the job with the shortest processing time. Priority rule 1 (PR1) was extended taking setup time into consideration. It selects the job with the shortest processing time on the next machine combined with the inevitable setup time on that machine. Priority rule 2 (PR 2) adds the factor of machine workload to PR1. Although PR2 includes PR1, nevertheless PR1 was considered in the results. The reason for this is the analysis of the effect regarding the overall lead time improvement adding machine workload to the priority rule. The comprehensive comparison of all the approaches now consists of the CP results compared with the DT approach, RF approach, PR1 without machine workloads, and PR2 including machine workloads. After having conducted the cross-validation, the next step is to choose a training set out of the job load sets and instance scenarios that is used for building a generalised DT. For this purpose the best performing DT was chosen. In the next step these trees were applied to all the other sets. As the trees have been trained on a particular training set and now are tested on different sets, their extrapolation capabilities in this case are analysed. The results are shown in Table 1. They indicate that the generalised DT and the RF perform well in a medium and high job load set but as before not so well in a low job load set compared to PR1 and PR2. The configurations shown in these tables state the height of a DT for the DT approach and number of trees/sample ratio/attribute ratio for the RF approach. After several performance tests, three different job load sets with the corresponding configuration have been chosen to build the DT and RFs for the CPS adaptation scenario (see Table 2). The whole job load set (80 instances) is used for building the DT and RFs. In the next step the resulting DT and RFs are directly tested against the CPS problem with real-time transport using the shop floor simulator. In this case the benchmark is the dispatching rule approach of the industrial partner. Note that total lead times, measured in minutes and seconds, are reported instead of deviations. The main objective regarding the real-world model configuration of Syngroup was achieved by decreasing their lead time significantly, as shown in Table 2. The results of this comparison provides evidence that the lead time of the CPS application introduced by the industrial partner can be undercut considerably. The results for both configurations can be improved by applying the DT. In particular, it has to be emphasised that the RF approach is able to improve the benchmark result of the industrial partner by more than 3 minutes on the larger instance. 3 Genetic Programming Approach The results achieved with the DT and RF approach turned out to be promising. For this reason a second machine learning approach is proposed based on the configuration of the industrial partner and the abstract model introduced above, namely a Genetic Programming (GP) approach. The GP approach is developed for the basic problem of the industrial partner and tested against the results of the CP, DT, and RF. In contrast to the first approach, the goal is not to obtain an indication whether a material movement should be preferred over another, but rather a numerical ranking of movable jobs. The aim is to find a generalised tree-based priority rule that performs well compared to the CP results and that undercuts the results of the DT and RF approach. 3.1 Solution Method As for the DT and RF approach, the goal is to generate a generalised priority rule that performs well in different instance scenarios. Due to the well performing DT and RF approach, a GP approach is introduced to compete with and undercut the results of the DTs and RFs. The contribution of this approach is the newly formed set of terminals and functions. These sets contain a higher degree of complexity due to the restricted transport resource, setup times, and blocking behaviour. To the best of our knowledge, this complexity level has not been dealt with in the literature until now. Firstly, the function and terminal sets are defined. The function and terminal sets form the modules with which the expression trees are built. The function set usually contains basic mathematical operators, such as addition, subtraction, multiplication, and division. It is contemplated to also implement comparing operators, for example equals, greater/equal than, and less/equal than, or if-else-conditions. The terminal set consists of processing time, crane position in relation to job position, transport time, blocking the recent machine, recent machine workload, workload on next stage, for example. As the processing time of the same job type may vary between parallel machines in the next processing step the job ranking cannot be separated from the machine assignment. Hence, the terminal set contains attributes regarding the transport resource, machines, and jobs. Secondly, the range of the GP parameters are configured, as shown in Table 3. The initial population of a GP run is generated using the grow and full method using a randomization parameter. In the next step the training instances are chosen randomly out of each instance set, as introduced for the DT and RF approach. For every GP run 20 instances within a set are used as training instances. The fitness level is then calculated for every expression tree in a population by accumulating the overall makespans for each of the training instances. 16 GP runs for each training instance set and each GP configuration are conducted due to the randomly generated initial population of expression trees. The goal is to achieve a wider variety within the initial expression tree population. The expression tree achieving the best overall makespan out of these 16 runs is chosen as the resulting tree. Finally, after the termination criterion is met, the fi-

4 Table 1: Results for the generalised DT and RF Instance scenario Approach Instance Job Machine bottleneck Crane bottleneck Mixed scenario load Job load set set low med high low med high low med high CP PR PR DT MB high RF Mixed high Table 2: CPS adaptation results Approach Training scenario Job load set Configuration Syngroup 08:38 15:52 PR1 09:05 16:12 PR2 09:09 13:27 DT CPS adaptation high 20 08:19 15:13 RF CPS adaptation high 50/0.5/1 09:34 14:27 RF Machine bottleneck medium 50/0.5/0.5 09:01 12:46 Table 3: GP parameter configuration Parameter Range Population size Generations Tournament size 4-9 Elites 0-20% Mutation 0-30% Max. depth 4-7

5 nal priority rule will be validated based on the test instances. Again, the goal is to compute an estimate for the off-training-set error. This will primarily be accomplished using a larger hold-out set of problem instances, because the expected computational effort may render a k-fold cross-validation very difficult to perform within a reasonable time frame at least on a single workstation PC. The CP, DT, and RF results of the first approach will then be compared with those achieved by the GP approach. 3.2 Computational Results Preliminary experiments suggest that the overall makespans for the hold-out set of problem instances undercut the performance of the DT and RF approach in particular settings. In some cases the results of the CP formulation are outperformed. Though, further test runs regarding the configuration of the population size, number of generations, tournament size, mutation chance, and number of elites have to be conducted. References [1] Olafsson S, Li X (2010) Learning effective new single machine dispatching rules from optimal scheduling data. Int J Prod Econ 128(1): [2] Quinlan JR (1993) C4.5: Programs for Machine Learning. Morgan Kaufmann Publishers Inc., San Francisco, USA [3] Shahzad A, Mebarki N (2012) Data mining based job dispatching using hybrid simulation-optimization approach for shop scheduling problem. Eng Appl Artif Intell 25(6):