Evolutionary generation of dispatching rule sets for complex dynamic scheduling problems
Introduction
Production scheduling is concerned with the allocation of resources, e.g. machines, to the processing of a number of jobs. The task is to determine a schedule that optimises a given performance criterion such as the makespan. One of the most complex scheduling problems is the job shop problem, in which each job consists of a number of operations that need to be performed on distinct work centres in a prescribed order, where the order in which a job visits the work centres is job-specific. In this work, a work centre is defined as a set of (1 to m) identical machines with the same functionality.
A widely used approach to real-world scheduling, where problems are often characterised by a highly complex and dynamic environment, are dispatching rules. Dispatching rules are simple heuristics that, whenever a machine is available, determine the job with the highest priority of the jobs waiting to be processed next on that machine. The computation of priorities is typically based on local information, which allows dispatching rules to be executed quickly, irrespective of the complexity of the overall problem. Moreover, because each scheduling decision is made at the latest possible moment, i.e. immediately before its implementation, dispatching rules naturally possess the ability to react to dynamic changes. Other advantages of dispatching rules include their simple and intuitive nature, their ease of implementation within practical settings, and their flexibility to incorporate domain knowledge and expertise (Aytug et al., 2005, Geiger et al., 2006).
On the other hand, the lack of a global perspective on the problem of dispatching rules is also their biggest drawback. They take scheduling decisions on the basis of current local conditions without assessing the negative impact a decision might have on the decision-making at other work centres in the future. The limited horizon of dispatching rules also explains the absence of a single rule that outperforms all others across different shop configurations, operating conditions and objective functions (Blackstone et al., 1982, Haupt, 1989, Holthaus and Rajendran, 1997, Rajendran and Holthaus, 1999). The decision which rule to select generally depends on the specific problem at hand. In addition, some researchers have shown that it can be beneficial to select different rules at different work centres within a shop. This appears to be particularly true for problems where work centres vary with respect to their relative position in the system (LaForge and Barman, 1989, Mahmoodi et al., 1996, Barman, 1997) or their utilisation (Raman et al., 1989, Ruben and Mahmoodi, 1998, Bokhorst et al., 2008), or possess different characteristics altogether (Cigolini et al., 1999, Lee et al., 2003). In summary, the employed rules typically have to be customised to the problem in order to tap the full potential of a dispatching rule-based approach.
The development of customised dispatching rules is usually a tedious procedure requiring a significant amount of expertise, coding-effort and time. The challenge is to design local, decentralised rules which result in a good global performance of a complex production environment. Generally, this is achieved by a trial-and-error procedure, with candidate rules tested in a simulation model of the considered manufacturing system, modified, and retested until they fulfill the requirements for actual implementation (Geiger et al., 2006). This process can be automated by a hyper-heuristic. Hyper-heuristics are optimisation methods that operate on a search space of heuristics (Burke et al., 2010). In this work, evolutionary algorithms (EAs) are employed as hyper-heuristics to search for effective dispatching rules, and discrete-event simulation is used to evaluate the evolved rules.
In a previous paper (Pickardt et al., 2010), we apply a hyper-heuristic that is based on a special type of EA called genetic programming (GP) to create a single dispatching rule for a complex and dynamic job shop from semiconductor manufacturing. Here, we extend the method with another EA that, in a second stage, assigns a different dispatching rule to each work centre in the shop. This two-stage hyper-heuristic is tested by comparing its performance to that of the original GP hyper-heuristic and the standard rule-assignment hyper-heuristic without access to evolved rules.
The paper is organised as follows. Section 2 reviews the related literature, followed by a presentation of the three hyper-heuristics in Section 3. These are applied to a scenario from semiconductor manufacturing, described in Section 4 and results are reported in Section 5. Some investigations of the robustness of the generated dispatching rule sets are done in Section 6, and the paper concludes with a summary and some suggestions for future work.
Section snippets
Literature review
An early paper related to the generation of composite dispatching rules whose priority indices are mathematical functions of several job attributes is the one by Hershauer and Ebert (1975). They define composite rules as the weighted sum or product of common priority indices, and use Hooke–Jeeves pattern search to find the best weights for a job shop problem. They find that the effectiveness of their method strongly depends on aspects such as the format of the composite rules and the starting
Algorithm design
The implemented hyper-heuristics are all based on EAs, which are iterative, stochastic search procedures inspired by natural evolution. They maintain a set (population) of candidate solutions (individuals), and, in each iteration (generation), select good solutions from the population (survival of the fittest), and generate new solutions (children) by recombining (crossing over) two old solutions (parents) and/or randomly modifying (mutating) a solution. Over time, this process ‘evolves’ better
Application to a problem from semiconductor manufacturing
We apply the three hyper-heuristics to a complex scheduling problem from semiconductor manufacturing with dynamic, stochastic job arrivals. Shops encountered in that industry typically possess characteristics such as reentrant material flows, and machines with sequence-dependant setup times or batch processing capabilities (Uzsoy et al., 1992, Pfund et al., 2006, Wu et al., 2008), increasing the complexity of scheduling even beyond the classic job shop problem, which is already NP-hard (Garey
Experimental results
The three hyper-heuristics are run for 20 times, which results in 20 different evolved (sets of) rules. Common random numbers are used across the hyper-heuristics to give the same set of simulation experiments for the fitness evaluations of a replication. The performance of evolved and benchmark rules is measured by conducting 50 replications of the simulation experiment encompassing six years, where data collection starts after the 1 year of warm-up. Again, common random numbers are used in
Sensitivity analysis
The benchmark for the robustness of an evolved rule (set) is the rule that would be employed without the availability of a hyper-heuristic, i.e. WMOD_MCB. This rule is also likely to be robust as it does not require any parameters to be set. The sensitivity analysis is conducted for the best rule set from the two-stage hyper-heuristic with respect to changes in the arrival rates of the different products and the due date setting.
Conclusion
In this paper, we have developed a two-stage hyper-heuristic to automatically generate sets of dispatching rules for complex and dynamic scheduling problems. The approach combines a GP hyper-heuristic that evolves a composite rule from basic attributes (Hildebrandt et al., 2010, Pickardt et al., 2010), with an EA hyper-heuristic that assigns different rules to different work centres as proposed by Yang et al. (2007). We tested the two-stage procedure on a scenario from semiconductor
Acknowledgements
We would like to thank Robert Sarney for implementing a first version of the EA hyper-heuristic and the four anonymous referees for their valuable comments. This research has been supported by the German Research Council (DFG) under Grants BR 1592/7-1 and SCHO 540/17-1.
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