一种基于信息熵的多种群遗传算法  

An information entropy-based multi-population genetic algorithm

作　　者：李纯莲[1] 王希诚[2] 赵金城[3] 武金瑛[2] 

机构地区：[1]大连理工大学计算机科学与工程系 [2]大连理工大学工业装备结构分析国家重点实验室,辽宁大连116024 [3]大连大学生物信息学与分子设计研究所,辽宁大连116622

出　　处：《大连理工大学学报》2004年第4期589-593,共5页Journal of Dalian University of Technology

基　　金：国家"973"计划资助项目(19990328);国家自然科学基金资助项目(10272030).

摘　　要：通过模型变换建立了一种约束优化的演化设计模型,并构造出求解此模型的多种群空间收缩遗传算法.利用最优解在各种群中的存在概率将信息熵概念引入进化过程,构造出一种含有熵的多目标优化模型,利用该模型可以直接显式地给出作为拉格朗日乘子的种群最优解存在概率,从而得出多种群遗传操作的空间收缩因子,控制各种群寻优搜索时解空间的收缩.用种群的多样性避免遗传进化的早熟现象,以空间收缩尺度作为停机判据,有效地控制了算法的收敛.数值算例显示,熵的介入使随机搜索类进化算法的寻优目的性大为增强,从而提高了演化设计的计算效率.An evolutionary design model for constraint optimization problems through transformation of optimization models is constructed, and then a multi-population genetic algorithm with narrowing of the search space is presented to solve the problem. By defining the probabilities that the optimal solution occurs in each population, information-entropy is introduced into evolution process. The probabilities can be obtained by explicitly solving the multi-objective optimization problem with information entropy: they are just Lagrange multipliers in the Kuhn-Tucker condition of the problem, and then the coefficients of narrowing of the searching space for multi-population genetic algorithm can be given by means of them and to control contraction of the solution space. The premature problem can be avoided by keeping diversity among different populations. The algorithm can be ensured by very rapid and steady convergence using solution space contraction criterion. The ability of searching optimization solution for the evolution algorithms is enhanced by introducing entropy. Numerical examples show that the method has very high accuracy and effectiveness.

关 键 词：信息熵 群遗传算法 准精确惩罚函数 拉格朗日乘子 约束优化 空间收缩尺度 

分 类 号：O236[理学—运筹学与控制论] TP18[理学—数学]