求解约束优化问题的ε-DE算法

ε-Differential Evolution Algorithm for Constrained Optimization Problems

差分进化(differential evolution,简称DE)算法解决约束优化问题(constrained optimization problems,简称COPs)时通常采用可行解优先的比较规则,但是该方法不能利用种群中不可行解的信息.设计了可以利用不可行解信息的ε-DE算法.该算法通过构造一种比较准则,使得进化过程可以充分利用种群中优秀不可行解的信息.该准则通过引入种群约束允许放松程度的概念,在进化初始阶段使可行域边界上且拥有较优目标函数的不可行解进入种群;随着进化代数增加,种群约束允许放松程度不断减小,使得种群中不可行解数量减少,直到种群约束允许放松程度为0,种群完全由可行解组成.此外,还选择了一种改进的DE算法作为搜索算法,使得进化过程具有较快的收敛性.13个标准Benchmark函数实验仿真的结果表明:ε-DE算法是目前利用DE算法解决COPs问题中效果最好的.

Differential evolution algorithm usually solves the constrained optimization problems by the feasible solutions priority rule, but the method can not use the infeasible solutions information populations, ε-DE algorithm is designed and can use the information of infeasible solutions. By designing new comparison rules, the infeasible solutions with better objective function are made full use of in the evolution process. The concept of population constraint relax degree is introduced in the comparison rules. During the evolution initial phase, the infeasible solutions with better objective function and near the boundary of the feasible region are incorporated in the population. With the evolutionary generation increasing, the decrease in the population constraint relax degree decreases the number of infeasible solutions in the population. Unless the population constraint relax degree is 0, the population is entirely composed of feasible solutions. In addition, an improved DE algorithm is chosen as the search algorithm, so a faster convergence is gotten. The simulation results of 13 benchmark functions prove that ε-DE is most competitive in all DE algorithms for solving COPs.