基于角度邻域的多目标差分进化算法

Multiobjective differential evolution algorithm based on angle neighbourhood

针对如何实现差分进化算法求解多目标优化问题,提出了一种基于角度邻域的多目标差分进化算法,通过在选择操作中引入弱支配概念,实现了对多目标优化问题的求解.该算法通过计算目标空间中个体与权重向量的夹角来确定每个个体的邻域,并在此基础上引入了基于角度邻域的变异策略,使个体的变异在邻域内进行,保证进化方向.此外,该算法创建了一个外部存档用来保存进化过程中的非支配解,并定期对外部存档进行维护,大大改善了解集的分布性.大量的数值仿真实验结果表明通过角度确定邻域的方法比通过欧氏距离确定邻域的方法更加有效,算法所得解集的收敛性和分布性也均明显优于基于分解的差分多目标进化算法(multiobjective evolutionary algorithm based on decomposition and differential evolution,MOEA/D–DE)和非支配排序算法Ⅱ(nondominated sorting genetic algorithm II,NSGA).

To solve the multiobjective optimization problem by differential evolution algorithm, a multiobjective differential evolution algorithm based on angle neighborhood is proposed. The weak domination is introduced to obtain the capacity of solving the multiobjective optimization problem. The neighbourhood of each individual is determined by computing the angle between each individual and weight vector in the objective space. To ensure the evolutionary direction of individual, the mutation strategy based on angle neighbourhood is introduced to execute the mutation operation in angle neighborhood. Additionally, an external archive is established to save the non-dominated solutions obtained in evolutionary process. The archive is maintained regularly, and the distributivity of the approximate set has been greatly improved. A large amount of experimental results show that the neighbourhood determined by angle is more effective than the neighbourhood determined by Euclidean distance, and the convergence and distribution of the approximate set obtained by the proposed algorithm are obviously superior to multiobjective evolutionary algorithm based on decomposition and differential evolution（MOEA/D–DE） and nondominated sorting genetic algorithm Ⅱ（NSGAⅡ）.