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A Novel Fitness Function for Genetic Programming in Dynamic Flexible Job Shop Scheduling

Dynamic flexible job shop scheduling (DF JSS) is a complex and challenging combinatorial optimisation problem. In DF JSS, job operations have to be processed on a set of machines, and thus machine assignment and operation sequencing decisions need to be made simultaneously in dynamic situations. Genetic programming (GP), as a hyper-heuristic approach, has been widely used to learn scheduling heuristics for DF JSS automati-cally. However, the traditional GP parent selection method based on fitness value only may not be sufficiently effective, since not all the subtrees of a GP individual are meaningful and can contribute to the goodness of the individual. This paper proposes a new GP algorithm with a novel fitness function by incorporating the subtree importance into the parent selection method. Specifically, the subtree importance is measured by the correlation coefficient between the behaviour of subtrees and the GP individual. The proposed algorithm is expected to improve the effectiveness of GP by capturing more useful subtrees for producing offspring to the next generation. This paper uses nine DF JSS scenarios to examine the effectiveness of the proposed algorithm. The results show that the proposed algorithm achieves slightly better performance in some of the scenarios while no worse in all other scenarios. Further analyses, including the effect of the designed fitness function and sizes of the learned scheduling heuristics, are also conducted.