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This paper proposes a per-machine linear dispatching rule learning approach to improve the scheduling of re-entrant flow shop such as semiconductor fab. Finding an optimal schedule of a complex manufacturing system is intractable; hence, a dispatching rule as a heuristic approach is widely used in actual practice. Also, to develop a good dispatching rule, an automated methodology for developing heuristics, also known as a hyper-heuristic, has been studied extensively. However, most of the literature has focused on finding a single-sophisticated dispatching rule, in which every machine uses the same rule. Such an approach often shows suboptimal performance when the optimal dispatching rule is different on each machine. To solve this problem, we introduce a simple and effective per-machine dispatching rule learning approach, in which each machine has one linear dispatching rule that is optimised by the Gradient-based Evolutionary Strategy (GES). This method is sample-efficient and can be applied to non-differentiable objective functions such as average Cycle Time. The proposed approach was mainly compared to two popular methods based on Genetic Programming (GP) and the Genetic Algorithm (GA) on a four-station and eight-machine re-entrant flow shop. Numerical results show that the proposed approach outperforms widely used methods.

Learning per-machine linear dispatching rule for heterogeneous multi-machines control