软件学报
軟件學報
연건학보
JOURNAL OF SOFTWARE
2013年
6期
1177-1195
,共19页
张贵军%何洋军%郭海锋%冯远静%徐建明
張貴軍%何洋軍%郭海鋒%馮遠靜%徐建明
장귀군%하양군%곽해봉%풍원정%서건명
多模态优化%广义凸%下界估计%差分进化%小生境
多模態優化%廣義凸%下界估計%差分進化%小生境
다모태우화%엄의철%하계고계%차분진화%소생경
multimodal optimization%abstract convex%underestimation%differential evolution%niching
针对多模态优化问题,提出了基于广义凸下界估计模型的改进差分进化算法。首先,基于模型变换方法将原优化问题转变为单位单纯形约束条件下的严格递增射线凸优化问题;其次,基于广义凸理论,利用差分进化算法中更新个体的适应度知识,建立原优化问题广义凸下界估计模型,设计实现了基于 N-叉树的估计模型快速计算方法;进而,综合考虑原问题目标值与其估计值之间的差异,提出一种基于有偏采样的小生境指标,并设计区域进化树更新策略来保证算法的局部搜索能力。数值实验结果表明,提出的算法能够有效地发现并维持一定数量的满意解模态,动态地实现全局模态搜索到模态内局部增强的自适应平滑过渡。对于给出的测试问题,能够发现所有的全局最优解以及一些较好的局部极值解。
針對多模態優化問題,提齣瞭基于廣義凸下界估計模型的改進差分進化算法。首先,基于模型變換方法將原優化問題轉變為單位單純形約束條件下的嚴格遞增射線凸優化問題;其次,基于廣義凸理論,利用差分進化算法中更新箇體的適應度知識,建立原優化問題廣義凸下界估計模型,設計實現瞭基于 N-扠樹的估計模型快速計算方法;進而,綜閤攷慮原問題目標值與其估計值之間的差異,提齣一種基于有偏採樣的小生境指標,併設計區域進化樹更新策略來保證算法的跼部搜索能力。數值實驗結果錶明,提齣的算法能夠有效地髮現併維持一定數量的滿意解模態,動態地實現全跼模態搜索到模態內跼部增彊的自適應平滑過渡。對于給齣的測試問題,能夠髮現所有的全跼最優解以及一些較好的跼部極值解。
침대다모태우화문제,제출료기우엄의철하계고계모형적개진차분진화산법。수선,기우모형변환방법장원우화문제전변위단위단순형약속조건하적엄격체증사선철우화문제;기차,기우엄의철이론,이용차분진화산법중경신개체적괄응도지식,건립원우화문제엄의철하계고계모형,설계실현료기우 N-차수적고계모형쾌속계산방법;진이,종합고필원문제목표치여기고계치지간적차이,제출일충기우유편채양적소생경지표,병설계구역진화수경신책략래보증산법적국부수색능력。수치실험결과표명,제출적산법능구유효지발현병유지일정수량적만의해모태,동태지실현전국모태수색도모태내국부증강적자괄응평활과도。대우급출적측시문제,능구발현소유적전국최우해이급일사교호적국부겁치해。
In this paper, a modified differential evolution algorithm, which is based on abstract convex lower approximation, is proposed for multimodal optimization. First, the original bound constrained optimization problem is converted to an increasing convex along rays (ICAR) function over a unit simplex by using the projection transformation method. Second, based on abstract convex theory, the study builds a lower approximation to original optimization problem by using a finite subset of biased sampling points comes from the population replacement scheme in the basic DE algorithm. Some properties of underestimation model are analyzed theoretically, and an N-ary tree data structure have also been designed and implemented to solve them. Furthermore, considering the difference between the original and its underestimated function values, the paper proposes a niche identify indicator based on biased DE sampling procedure, and also design a regional phylogenetic tree replacement strategy to enhance the exploitation capacity in niche. Experimental results confirm that the proposed algorithm can distinguish between the different attraction basins, and safeguard the consequently discovered solutions effectively. For the given benchmark problems, the proposed algorithm can find all the global optimal solutions and some good local minimum solutions.