【摘要】 由于采用罚函数法将有约束多目标优化问题转化为无约束多目标优化问题会使求解不合理,因此,文章首先在无约束Pareto排序遗传算法的基础上,提出了一个简单、实用的能分别考虑目标函数和约束函数,而又可以避免采用罚函数的全新排序方法。接着,针对小生境技术在遗传后期依旧会出现遗传漂移现象和共享半径不易确定等缺陷,提出了一种易于实现的超量惩罚策略来替代小生境技术,用以改进种群的多样性。此外,还采用了Pareto解集过滤器、邻域变异和群体重组等策略对算法的寻优能力进行改进,并最终形成了一种求解有约束多目标优化问题的Pareto遗传算法(CMOPGA),还给出了具体的算法流程图。最后采用两个数值算例对算法的求解性能进行了测试。数值试验表明,采用CMOPGA可方便地求得问题的Pareto前沿,并能使求得的Pareto最优解集具有可靠、均布、多样等特点。更多还原

【Abstract】 As usual, penalty function methods are used to transform a constrained into an unconstrained multiobjectiveoptimization problem.This way, however, may lead to unreasonable searching in Pareto GAs.So a new ranking approachwithout using penalty function methods is presented to handle a constrained multiobjective optimization problem.Thisapproach can deal with objective and constraint functions separatively.Owing to the occurrence of genetic drift in latergenerations and the difficulty in determining the sharing radius when using niche technique, an easily realized penaltystrategy for excess individuals is proposed to improve the diversity of population.In addition, some techniques, such asPareto filter, neighborhood mutation, and recombination, are applied to the genetic algorithms.On the basis of such im-provements and techniques, a ranking- based genetic algorithm for constrained multiobjective optimization problems isformed (CMOPGA), and its calculating flow chart is advanced.Finally, two numerical examples are given to test the per-formance of CMOPGA.The results of examples demonstrate that the reliable, uniformly distributed, and diverse Pareto op-timal solutions can be found conveniently by CMOPGA for multiobjective problems.更多还原