Comprehensive learning gravitational search algorithm for global optimization of multimodal functions

Fuzzy Strategy Grey Wolf Optimizer for Complex Multimodal Optimization Problems

Traditional grey wolf optimizers (GWOs) have difficulty balancing convergence and diversity when used for multimodal optimization problems (MMOPs), resulting in low-quality solutions and slow convergence. To address these drawbacks of GWOs, a fuzzy strategy grey wolf optimizer (FSGWO) is proposed in this paper. Binary joint normal distribution is used as a fuzzy method to realize the adaptive adjustment of the control parameters of the FSGWO. Next, the fuzzy mutation operator and the fuzzy crossover operator are designed to generate new individuals based on the fuzzy control parameters. Moreover, a noninferior selection strategy is employed to update the grey wolf population, which makes the entire population available for estimating the location of the optimal solution. Finally, the FSGWO is verified on 30 test functions of IEEE CEC2014 and five engineering application problems. Comparing FSGWO with state-of-the-art competitive algorithms, the results show that FSGWO is superior. Specifically, for the 50D test functions of CEC2014, the average calculation accuracy of FSGWO is 33.63%, 46.45%, 62.94%, 64.99%, and 59.82% higher than those of the equilibrium optimizer algorithm, modified particle swarm optimization, original GWO, hybrid particle swarm optimization and GWO, and selective opposition-based GWO, respectively. For the 30D and 50D test functions of CEC2014, the results of the Wilcoxon signed-rank test show that FSGWO is better than the competitive algorithms.