Abstract: To efficiently solve nonlinear optimization problems with multiple constraints in engineering design,a Modified Equilibrium Optimizer (MEO) was proposed.In the initial stage,the global search ability of the algorithm was enhanced by lens opposition-based learning,and the optimization information of particles in the population was further enriched.Then the exploitation and exploration phases were dynamically balanced by exponential adjustment factor.Finally,the optimal particle concentration was updated by using the dimensional-by-dimension Gaussian mutation mechanism and greedy strategy to avoid premature convergence.Two complex function sets of IEEE CEC2019 and IEEE CEC2020 with different rotation matrices were used to test the optimization performance of the proposed algorithm.Moreover,the statistical significance of algorithm was verified by Friedman test and Wilcoxon rank sum test.Experimental results showed that MEO performed well in the optimization accuracy and stability.By solving seven engineering design problems of different complexity,it was proved that MEO had good optimization efficiency and application space.

Key words: equilibrium optimizer algorithm, engineering problems, lens opposition-based learning, Gaussian variation

摘要： 针对工程设计领域中带有多个约束条件的非线性优化问题,提出一种改进平衡优化器算法(MEO)。通过引入镜头成像反向学习策略,增强算法在初始阶段的全局搜索能力,丰富粒子种群的位置信息,随后利用指数调节因子动态平衡勘探和开发能力,最后通过逐维高斯变异机制和贪婪策略更新最优粒子的浓度,避免早熟收敛。使用具有不同旋转矩阵的IEEE CEC2019和IEEE CEC2020两个复杂函数集测试所提算法在优化方面的性能,并且通过Friedman检验和Wilcoxon秩和检验验证算法的显著性,实验结果表明,MEO在寻优精度和稳定性方面表现优异。通过求解7个不同复杂程度的工程设计问题,证明MEO具有良好的优化效率和应用空间。

关键词: 平衡优化器算法, 工程问题, 镜头成像反向学习, 高斯变异