基于超球形模糊支配的高维多目标粒子群优化算法

高维多目标优化问题（MAOP）会随着待优化问题维度的增加形成巨大的目标空间，导致在目标空间中非支配解的比例急剧增加，削弱了进化算法的选择压力，降低了进化算法对MAOP的求解效率。针对这一问题，提出一种以超球型支配关系降低种群中非支配解数量的粒子群优化（PSO）算法。算法以模糊支配策略来维持种群对MAOP的选择压力，并通过全局极值的选择和外部档案的维护来保持种群个体在目标空间中的分布。在标准测试集DTLZ和WFG上的仿真结果表明，所提算法在求解MAOP时具备较优的收敛性和分布性。

Many-objective particle swarm optimization algorithm based on hyper-spherical fuzzy dominance

With the increase of the dimension of the problem to be optimized, Many-objective Optimization Problem (MAOP) will form a huge target space, resulting in a sharp increase of the proportion of non-dominant solutions. And the selection pressure of evolutionary algorithms is weakened and the efficiency of evolutionary algorithms for solving MAOP is reduced. To solve this problem, a Particle Swarm Optimization (PSO) algorithm using hyper-spherical dominance relationship to reduce the number of non-dominant solutions was proposed. The fuzzy dominance strategy was used to maintain the selection pressure of the population to MAOP. And the distribution of individuals in the target space was maintained by the selection of global extremum and the maintenance of external files. The simulation results on standard test sets DTLZ and WFG show that the proposed algorithm has better convergence and distribution when solving MAOP.