基于黎曼球面的多目标演化算法

基于黎曼球面的多目标演化算法 A Multi-Objective Evolutionary Algorithm Based on Riemann-Sphere 彭晟 PENG Sheng 1 first-author 李元香 LI Yuanxiang 1 武汉大学软件工程国家重点实验室 武汉大学软件工程国家重点实验室 State Key Laboratory of Software Engineering,Wuhan University State Key Laboratory of Software Engineering,Wuhan University 对于求解多目标优化问题提出了一种基于黎曼球面的多目标演化算法（RSEA）.它的特点在于:先在目标空间中采用无穷远点作为采样基点来对Pareto最优前沿进行采样;再将无界的多目标函数空间同构映射到黎曼球面上,进而在黎曼球面上对产生的新个体是否加入精英文档进行判定,以此提高了算法的均匀性与多样性,加快了算法的收敛速度.数值实验表明,新算法与NSGA2,SPEA2算法相比,性能有明显的提高. A new multi-objective evolutionary algorithm named Riemann-sphere multi-objective evolutionary algorithm （RSEA） is proposed in this paper. First The RSEA takes the infinity as the sampling center. Then by Stereographic projection,the object-space is mapped onto the Riemann-Sphere. Moreover,spherical distance is used to evaluate whether the new individuals join the elitist space or not. Using this method,it can accelerate the rate of convergence as well as the distribution and diversity. The numerical experiments show that the performance of the RSEA is better than that of NSGA2,SPEA2. 演化算法 黎曼球面 多目标优化 Pareto最优前沿 evolutionary algorithm Riemann-sphere multi-objective optimization Pareto optimal front 10.14188/j.1671-8836.2010.04.006 O221.6 国家自然科学基金资助项目（60773009） 2010-04-01 2021-04-01 4 56