基于两阶段搜索算法的多峰函数优化

摘要

Multimodal optimization aims to search multiple optima (global and/or local optima)simultaneously, which gives rise to a challenging task for traditional optimization algorithms.This paper proposes a two-stage algorithm to solve multimodal optimization problems.In the first stage,NCDE with neighborhood mutation strategy tries its best to find as many approximate positions of optimal solutions as possible on the fitness landscape.After NCDE runs a certain number of iterations,DMC method is employed to divide the entire population into multiple clusters,and then CMA-ES algorithm is used to perform fine search on each cluster which is found by NCDE.Additionally,search point replenishment strategy is put forward to balance cluster size and to increase search capability of our algorithm in the beginning of the running.Extensive comparative experiments is made between our proposed approach and 9 state-of-the-art algorithms on two benchmark sets, the results show that the new algorithm is effective and superior to the other algorithms on the majority of test functions.%多峰优化问题需要搜索多个最优值（全局最优／局部最优），这给传统的优化算法带来很大程度上的挑战。本文提出了一种两阶段算法求解多峰优化问题。第一阶段采用带有邻域变异策略的排挤差分演化算法进行粗粒度搜索，在适应度景观上尽可能多的找到最优解的大概位置。搜索一定代数之后，调用DMC聚类方法把搜索种群划分成多个聚类，然后在每个聚类上调用协方差矩阵自适应演化策略算法进行精细搜索。另外，本文还提出搜索点补充策略用于平衡每个聚类的大小及增加算法初期的搜索能力。我们提出的方法和9个较新的经典算法在两个基准测试集上进行了大量对比测试，结果表明新算法是有效的，在大多数测试函数上都优于其它算法。