Crossover Operators Between Multiple Scheduling Heuristics with Genetic Programming for Dynamic Flexible Job Shop Scheduling

Dynamic flexible job shop scheduling (DFJSS) is an important combinatorial optimisation problem that aims to optimise machine resources to improve production efficiency. Multi-tree genetic programming (MTGP) has been widely used to learn the routing rule and the sequencing rule for DFJSS simultaneously. Unlike traditional genetic programming that only operates crossover on a single tree, MTGP has various cases to conduct crossover since a genetic programming individual consists of more than one tree. Different crossover operators may affect the performance of MTGP for DFJSS. However, the investigation into different crossover operators in MTGP for DFJSS is rare. Specifically, it is not clear what influence will have on MTGP if involving both the routing rule and the sequencing rule for crossover. To this end, this paper provides a comprehensive investigation of four possible crossover cases between multiple scheduling heuristics with MTGP for DFJSS. The four operators are designed according to the number of trees/rules that crossover operator works on, and whether swapping full trees between parents. The results show that although the compared algorithms have comparable results in most scenarios, MTGP with both rules for crossover and the swapping strategy is ranked as the best one. Further analyses show that the sizes of learned rules are highly related to the crossover operators, and crossover involving more rules can increase the rule sizes, and vice versa. In addition, the population diversity and the number of unique features in the learned rules of MTGP with both rules for crossover are increased to learn effective rules.