基于两阶段搜索算法的多峰函数优化
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摘要
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.
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 forw ard 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.
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 forw ard 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.
引文
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[18]Bandaru S,Deb K.A parameterless-niching-assisted biobjective approach to multimodal optimization[A].Proc of IEEE Congress on Evolutionary Computation[C].Cancun:IEEE,2013.95-102.
[2]彭虎,吴志健,等.基于精英区域学习的动态差分进化算法[J].电子学报,2014,42(8):1522-1530.Peng Hu,Wu Zhi-jian,et al.Dynamic differential evolution algorithm based on elite local learning[J].Acta Electronica Sinica,2014,42(8):1522-1530.(in Chinese)
[3]李康顺,韦蕴珊,等.小生境演化算法下的WDCT图像压缩方法[J].电子学报,2014,(4):809-814.Li Kang-shun,Wei Yun-shan,et al.WDCT image compression based on niching evolutionary algorithm[J].Acta Electronica Sinica,2014,42(4):809-814.(in Chinese)
[4]郑金华,刘磊,等.一种自适应小生境分布性保持策略[J].电子学报,2012,40(11):2330-2335.Zheng Jin-hua,Liu Lei,et al.An adaptive niche for keeping the diversity of solutions in multi-objective evolutionary algorithm[J].Acta Electronica Sinica,2012,40(11):2330-2335.(in Chinese)
[5]Qu B Y,Suganthan P N,Liang J J.Differential evolution w ith neighborhood mutation for multimodal optimization[J].IEEE Transactions on Evolutionary Computation,2012,16(5):601-614.
[6]Hansen N,Ostermeier A.Completely derandomized selfadaptation in evolution strategies[J].Evolutionary Computation,2001,9(2):159-195.
[7]Hansen N.The CMA Evolution Strategy:A Comparing Review[M].Berlin:Springer,2006.75-102.
[8]Preuss M.Niching the CMA-ES via nearest-better clustering[A].Proceedings of the 12th Annual Conference Companion On Genetic and Evolutionary Computation[C].Portland:ACM,2010.1711-1718.
[9]Stoean C,Preuss M,Stoean R,et al.Multimodal optimization by means of a topological species conservation algorithm[J].IEEE Transactions on Evolutionary Computation,2010,14(6):842-864.
[10]Li X D,et al.Benchmark Functions for CEC'2013 Special Session and Competition on Niching M ethods for M ultimodal Function Optimization[R].M elbourne:RM IT University,Evolutionary Computation and M achine Learning Group,2013.1-10.
[11]Vitela J E,Castaos O.A sequential niching memetic algorithm for continuous multimodal function optimization[J].Applied Mathematics and Computation,2012,218(17):8242-8259.
[12]Pereira M W,et al.A topological niching covariance matrix adaptation for multimodal optimization[A].Proc of IEEE Congress on Evolutionary Computation[C].Betjing:IEEE,2014.2562-2569.
[13]Shir O M,Emmerich M,Back T.Adaptive niche radii and niche shapes approaches for niching w ith the CM A-ES[J].Evolutionary Computation,2010,18(1):97-126.
[14]Auger A,Hansen N.A restart CMA evolution strategy w ith increasing population size[A].Proc of IEEE Congress on Evolutionary Computation[C].Edinburgh,Scotland:IEEE,2005.1769-1776.
[15]Gao W,Yen G G,Liu S.A cluster-based differential evolution w ith self-adaptive strategy for multimodal optimization[J].IEEE Transactions on Cybernetics,2014,44(8):1314-1327.
[16]Qu B Y,Suganthan P N.A distance-based locally informed particle sw arm model for multimodal optimization[J].IEEE Transactions on Evolutionary Computation,2013,17(3):387-402.
[17]Li X D.A Multimodal particle swarm optimizer based on fitness euclidean-distance ratio[A].Proc of The 9th Annual Conference on Genetic and Evolutionary Computation[C].London:ACM,2007.78-85.
[18]Bandaru S,Deb K.A parameterless-niching-assisted biobjective approach to multimodal optimization[A].Proc of IEEE Congress on Evolutionary Computation[C].Cancun:IEEE,2013.95-102.