基于NSGA-Ⅱ的偏好分解的多目标优化算法研究

Many-object optimization algorithm with preference based on decomposition

对于多目标优化问题,传统的优化算法不能够很好地处理复杂的Pareto前沿(PF)上的收敛和分布问题,收敛性和分布性二者不能得到较好的平衡;利用改进后的边界交叉方法,超平面根据补足位移移动,形成新的标准目标向量,使得更多的个体分布落在可行区域;决策者偏好的高维多目标优化算法,能够有效地减小搜索空间,解决算法后期收敛放缓和种群退化的问题。本文提出基于偏好向量分解的多目标优化算法,基于NSGA-Ⅱ的偏好分解的多目标优化算法,将偏好信息作为促进解向最优解移动的条件,能够加快收敛速度,找到接近的真实的Pareto最优前沿解(POF)。本文将(NSGA-RPIPBI)和非支配排序遗传算法(NSGA-Ⅱ)、基于优势和分解的多目标进化算法(MOEA/DD)在多目标问题测试集DTLZ1-4上进行多维目标测试,NSGA-RPIPBI在解集的收敛性和分布性效果更好。

For multi-objective optimization problems,traditional optimization algorithms cannot handle the convergence and distribution problems on the complex Pareto front(PF)effectively,which causes that convergence and distribution cannot be well balanced.Utilizing the improved Penalty-Based Boundary Intersection(PBI),the hyperplane moves according to the complementary displacement to form a new standard coordinate system,so that more individuals are distributed in feasible areas.And for the high-dimensional target optimization algorithm,it can effectively reduce the search space,solving the situation of slow convergence and population degradation in the later stage of the algorithm.The multi-objective optimization algorithm based on preference vector decomposition(NSGA-RPIPBI)proposed in this paper uses preference information as a condition for promoting the solution to move to the optimal solution,which can speed up the convergence and find the close real Pareto Optimal Frontier Solution(POF).In this paper,NSGA-RPIPB,non-dominated sorting genetic algorithm(NSGA-Ⅱ)and multi-objective evolutionary algorithm based on advantage and decomposition(MOEA/DD)are tested on multi-objective problem test set DTLZ1-4,and the results shows that NSGA-RPIPBI has a better convergence and distribution effect on the solution set.