Abstract
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.
Highlights
The genetic algorithm (GA) is a widely used evolutionary algorithm [1,2,3]
We found that the propagation rate of advantageous genes among sub-populations was limited by these network topologies; how the propagation rate affects the performance of multi-population genetic algorithm (MPGA) over a wider range is still not clear
Most existing literature measured the propagation rate of advantageous genes based on takeover time [12, 15], and studied the algorithm’s selection pressure from a theoretical perspective
Summary
The genetic algorithm (GA) is a widely used evolutionary algorithm [1,2,3]. When solving problems with GA, feasible solutions are first encoded in individuals, which can be conveniently processed by operators (e.g., crossover and mutation). In [15], the authors studied the propagation dynamics behavior of an evolutionary algorithm using scale-free networks from a theoretical perspective (it was measured by takeover time, i.e., the duration it takes until advantageous genes fill the whole population), thereby revealing the influencing mechanisms of different network structural parameters on the selection pressures of the algorithm. ▪Apply scale-free, small-world and random networks to limit possible crossover partners in a population, and study the performance of differently obtained algorithms on multiobjective optimization problems. Some scholars have used MPGA to solve FJSP [4, 22]; the number of sub-populations in their studies was very limited To this end, first, the network generated by the ER model [23] and the migration frequency are used to control the propagation behaviors of advantageous genes among sub-populations. A comparison of this MPGA-ER with other algorithms proposed in other studies demonstrates its effectiveness
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