基于R2指标和目标空间分解的高维多目标粒子群优化算法

R2 indicator and objective space partition based many-objective particle swarm optimizer

基于R2指标和分解策略的多目标粒子群优化算法(R2-MOPSO)在求解2、3个目标优化问题时具有较好的收敛性和多样性,但在求解高维多目标优化问题时难度较大.对此,提出一种基于R2指标和目标空间分解的高维多目标粒子群优化算法(R2-MOPSO-II).首先借鉴R2指标和目标空间分解策略综合权衡选择过程的收敛性和多样性,设计双层档案维护策略;然后设计一种新的向导选择策略来连接目标空间和决策变量空间,进而提出一种基于双层档案的速度和位置更新策略以权衡粒子群优化算法的勘探和开采能力;最后通过引入高斯学习策略和精英学习策略防止粒子陷入局部最优前沿.数值仿真结果表明,所提出算法在求解DTLZ和WFG测试问题时具有较好的收敛性和多样性.

The R2 indicator and decomposition based multiple particle swarm optimizer(R2-MOPSO)is suitable for solving two and three objectives optimization problems in terms of the convergence and diversity.However,it is difficult for the R2-MOPSO to address many-objective optimization problems(MaOPs).Therefore,we propose an R2 indicator and objective space partition based many-objective particle swarm optimizer(R2-MOPSO-II)to solve MaOPs.Firstly,a new bi-level archive maintainence strategy is introduced to balance the convergence and diversity after considering the R2 indicator and the objective space partition strategy.Then,a new leader selection strategy gives the bridge between objective space and decision variable space.The modified velocity updated equation based on bi-level archive is introduced to balance the exploration and exploitation.Finally,the Gaussian learning strategy and the elitist learning strategy are embedded into the proposed algorithm to help the algorithm jump out of local Pareto front.The numerical simulation results show that the proposed algorithm has achieved better convergence and diversity for solving DTLZ and WFG test instances.