复杂非凸约束优化难题与迭代动态多样进化算法

进化算法的迅速发展,为非凸约束优化问题的求解提供了有效途径,但目前常用优化算法还未能全面满足更为复杂的约束条件或目标分布对寻优方式灵活应变能力的特别需求.首先,本文研究发现,当优化问题在全局最优解的某一较小邻域内,依然分布有复杂的局部极值或可行域分布时,大多数进化算法中不灵活的探索与挖掘方式将会在寻优后期导致误收敛现象发生.其次,为解决这一难题,本文继续对问题特征与算法规则进行了深入探讨,并提出用于解决该类问题的迭代动态多样进化算法(IDDEA).该算法利用多智能体创建一种新型占优评估策略,并以此为基础设计出较优子区域的划分方式.本文所提子区域的划分,在充分发挥动态多样搜索进化方式的探索能力前提下迭代推进,逐步缩小寻优空间,进而使得寻优采样在收敛的同时,依然保持原有探索与挖掘的灵活权衡模式.再次,本文还提出一种最小惩罚函数,为IDDEA引入一种自适应惩罚机制,来动态调整不可行代理的适应度分配,从而有效避免了选择罚系数的难题.最后,IDDEA在若干工程优化设计问题中的成功应用表明,本文在合理的问题分析基础上,提供了更加有效的算法设计思路与成果.

Iterative Dynamic Diversity Evolutionary Algorithm for Constrained Optimization

Evolutionary algorithms (EAs) were shown to be effective for complex constrained optimization problems. However, inflexible exploration in general EAs would lead to losing the global optimum nearby the ill-convergence regions. In this paper, we propose an iterative dynamic diversity evolutionary algorithm (IDDEA) with contractive subregions guiding exploitation through local extrema to the global optimum in suitable steps. In IDDEA, a novel optimum estimation strategy with multi-agents evolving diversely is suggested to efficiently compute dominance trend and establish a subregion. In addition, a subregion converging iteration is designed to redistrict a smaller subregion in current subregion for next iteration, which is based on a special dominance estimation scheme. Meanwhile, an infimum penalty function is embedded into IDDEA to judge agents and penalize adaptively the unfeasible agents with the lowest fitness of feasible agents. Furthermore, several engineering design optimization problems taken from the specialized literature are successfully solved by the present algorithm with high reliable solutions.