基于新模型的多目标遗传算法

A multi-objective genetic algorithm based on a new model

给出了个体的序和密度定义及目标空间中解的密度分布方差和均匀性分布指标函数,其中序是Pareto解的质量的一个度量,密度是Pareto解的分布均匀性的一个度量.对任意多个目标函数的优化问题转化成两个目标函数的优化问题,并对转化后的优化问题设计了遗传算法,同时把均匀性分布指标函数引入算法的变异操作中,用于自适应地调节搜索向Pareto最优解集移动和更好地获得解的均匀性分布,直到满足终止条件.数据实验表明该方法对Pareto解的质量及其均匀性分布是有效的.

The rank and density of the population are first defined and then the density distribution variance and uniform distribution index function of solutions in objective space are clearly given. The rank is a measure of the quality of solutions, and the density distribution variance is a measure of the uniformity of the distribution of solutions. Using these two measures as two objective functions, the multi-objective optimization problem is finally converted into a two objective optimization problem. For the transformed problem, a novel genetic algorithm is proposed. In designing the algorithm, the uniform distribution index function is integrated into the mutation operator to adaptively adjust the search. As a result, the solutions will gradually move to the entire Pareto front and their distribution will gradually become uniform.