School of Manufacturing Science and Engineering, Southwest University of Science and Technology, Mianyang, China.
School of Mechanical Engineering, Sichuan University, Chengdu, China.
PLoS One. 2020 May 29;15(5):e0233759. doi: 10.1371/journal.pone.0233759. eCollection 2020.
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.
遗传算法（GA）并不能总是避免早熟收敛，通常使用多群体来克服这一限制，即将群体划分为几个具有相同个体数量（子群体大小）的子群体（子群体数量）。在以前的研究中，网络结构由子群体组成，如何影响子群体之间有利基因的传播速度，以及如何影响 GA 的性能，这些问题一直被忽视。因此，我们首先提出了一种具有 ER 网络的多群体 GA（MPGA-ER）。然后，通过使用灵活作业车间调度问题（FJSP）作为示例，并考虑总个体数（TIN），我们研究了子群体数量和大小以及有利基因的传播速度如何影响 MPGA-ER 的性能，其中性能是基于 TIN 通过平均最优值和成功率来评估的。模拟结果表明 MPGA-ER 的性能如下：（i）与传统 GA 相比，性能有了显著提高；（ii）对于给定 TIN 的子群体数量增加，性能先缓慢增加，然后迅速下降；（iii）对于给定 TIN 的子群体大小增加，MPGA-ER 的性能先快速增加，然后趋于稳定；（iv）随着有利基因传播速度的增加，性能先快速增加，然后缓慢下降。最后，我们使用参数优化的 MPGA-ER 来解决更多的 FJSP 实例，并通过与其他研究中提出的其他算法进行比较来证明其有效性。
