基于就近取值策略的离散多目标优化

Discrete multi-objective optimization based on the nearest value strategy

针对现有的离散变量处理方法在求解多目标优化问题中存在精度和可靠性不足的情况,结合离散变量优化问题和遗传算法两者的特点,提出一种能够处理离散变量的就近取值策略.此策略代替了传统对离散优化问题中离散变量的处理方法:将离散优化问题转化为连续优化问题,利用决策变量为连续的优化方法去解决该离散优化问题所对应的连续优化问题的最优解集,最后再按照特定的方法将该连续优化问题的最优解集离散化得到对应离散优化问题的最优解集.将此策略应用在传统多目标遗传算法NSGA-Ⅱ(Non-dominate Sort Genetic AlgorithmⅡ)的遗传算子中得到了离散交叉算子和离散变异算子,使得算法能够真正在离散空间中搜索寻优,并得到了一种基于就近取值策略的离散多目标优化算法(Dispersed Non-dominate Sort Genetic AlgorithmⅡ,DIS-NSGA-Ⅱ).在理论上本方法相比传统方法,对解决离散优化问题更合理,优化结果更精确,有较大优势.最后,通过实验对比现有两种最典型的离散变量处理方法验证了DIS-NSGA-Ⅱ对解决离散变量优化问题的有效性.

In this paper,in view of insurfficient precision and reliability of existing approaches to solve multi-objective optimization problems which include discrete variables,a new strategy called nearest valued based on characteristics both of multi-objective genetic algorithms and discrete optimization problems is proposed.Traditional strategy transforms discrete multi-objective optimization problems into continue multi-objective optimization problems and then takes advantage of strategies that deal with continue variables to optimize it.Furthermore,we have achieved optimal solution set of corresponding continue optimization problems.Finally,some special discretization methods are utilized to handle the problems and achieve discrete optimal solution set is reaplaced by nearest valued strategy. So,we get a DIS-NSGA-Ⅱ(dispersed non-dominate sort genetic algorithm Ⅱ )which is suitable for discrete multi-objective optimization problems from applying nearest valued strategy in geneic operators of traditional multiobjective optimization algorithm NSGA-Ⅱ (non-dominate sort genetic algorithm Ⅱ )and gain a discrete crossover operator and a mutation operator.The biggest advantage of DIS-NSGA-Ⅱ is that it can make optimization algorithm authentically optimizing in discrete decision variable space.In theory,nearest valued strategy has greater advantages that its processing strategy is more reasonale.In the end,the effectiveness of the algorithm is verified by comparing two kinds of typical algorithms and the data shows that the algorithm has greater advantages in dealing with discrete multi-pbjective optimization problems.