Multi-population genetic algorithm with ER network for solving flexible job shop scheduling problems

A genetic algorithm (GA) cannot always avoid premature convergence, and multi-population is usually used to overcome this limitation by dividing the population into several sub-populations (sub-population number) with the same number of individuals (sub-population size). In previous research, the questions of how a network structure composed of sub-populations affects the propagation rate of advantageous genes among sub-populations and how it affects the performance of GA have always been ignored. Therefore, we first propose a multi-population GA with an ER network (MPGA-ER). Then, by using the flexible job shop scheduling problem (FJSP) as an example and considering the total individual number (TIN), we study how the sub-population number and size and the propagation rate of advantageous genes affect the performance of MPGA-ER, wherein the performance is evaluated by the average optimal value and success rate based on TIN. The simulation results indicate the following regarding the performance of MPGA-ER: (i) performance shows considerable improvement compared with that of traditional GA; (ii) for an increase in the sub-population number for a certain TIN, the performance first increases slowly, and then decreases rapidly; (iii) for an increase in the sub-population size for a certain TIN, the performance of MPGA-ER first increases rapidly and then tends to remain stable; and (iv) with an increase in the propagation rate of advantageous genes, the performance first increases rapidly and then decreases slowly. Finally, we use a parameter-optimized MPGA-ER to solve for more FJSP instances and demonstrate its effectiveness by comparing it with that of other algorithms proposed in other studies.