一种自适应调整权重向量的多目标进化算法

A multi-objective evolutionary algorithm for adjusting weight vectors adaptively

基于分解的多目标进化算法(multi-objective evolutionary algorithm based on decomposition,MOEA/D)作为一种重要的多目标优化方法,已经成功地应用于解决各种多目标优化问题。然而,MOEA/D算法在解决具有高维目标和复杂帕累托前沿(Pareto frontier,PF)的问题时,容易陷入局部最优并难以获得可行解。本文提出一种改进的MOEA/D算法,包括3个优化策略:首先,使用拉丁超立方抽样方法代替随机方法初始化种群,得到分布均匀的初始种群,同时对权重向量关联解的策略进行优化;其次,提出一种稀疏度函数,用于计算种群中个体的稀疏度并维护外部种群;最后,提出了自适应调整权向量的方法,用于引导种群收敛到帕累托前沿,并且有效平衡种群的多样性和收敛性。将提出算法和4种对比算法在DTLZ和WFG系列问题以及多目标旅行商问题(multi-objective travel salesman problem,MOTSP)上进行对比实验,实验结果表明本文提出自适应调整权重向量的多目标进化(MOEA/D with cosine similarity adaptive weight adjustment,MOEA/D-CSAW)算法在处理具有复杂帕累托前沿和高维多目标的问题时,算法的综合性能要优于对比算法。

As an important method for multi-objective optimization,the multi-objective evolutionary algorithm based on decomposition(MOEA/D)has been successfully applied to solve various multi-objective optimization problems.However,when solving problems with high-dimensional objective and complex Pareto frontier,MOEA/D tends to fall into local optima and struggles to obtain feasible solutions.This paper proposes an improved MOEA/D algorithm,which includes three optimization strategies.Firstly,the Latin Hypercube Sampling method is used instead of random methods to initialize the population,obtaining a uniformly distributed initial population,and optimizing the strategy for weight vector associated solutions.Secondly,a sparsity function is proposed to calculate the sparsity of individuals in the population and maintain the external population.Lastly,a method for adaptively adjusting the weight vector is proposed to guide the population convergence to the Pareto frontier and balance the diversity and convergence of the population effectively.Comparative experiments were conducted on the proposed algorithm and four contrast algorithms using DTLZ and WFG test series problems,as well as the multi-objective traveling salesman problem(MOTSP).The experimental results show that MOEA/D with cosine similarity adaptive weight adjustment(MOEA/D-CSAW),outperforms the compared algorithms in terms of overall performance when dealing with problems with complex Pareto frontiers and high-dimension multiple objectives.