A comparison between linear and non-linear combinations of priority rules for solving flexible job shop scheduling problem

Priority rules (PRs) have gained importance in the literature since they are suitable for solving especially large-scale scheduling problems in the industry. There are different types of PRs, of which composite PRs (CPRs), i.e., combinations of multiple rules, are known to have better performance in general. In this study, a basis for the generation of CPRs from linear and non-linear combinations of different PRs is defined and a comparison is made between these two approaches. Genetic algorithm and particle swarm optimization are operated for linear combination, and gene expression programming is used for non-linear combination, whose details are given. The employed benchmarks are from the flexible job shop scheduling problem, but the algorithms can also be employed to solve different scheduling problems. Along with the rules obtained based on the two approaches, a comparison is made between the famous simple PRs (SPRs) in the literature in terms of solution quality and time. The results show that usually, the non-linear combination provides better results. Since there is no process for rule extraction for SPRs, their computation time is very low. Both the used benchmarks and source codes are made available to the readers.