基于超平面投影的高维多目标进化算法

针对高维多目标优化问题（MaOPs），为了更好地在收敛性和分布性之间保持平衡，提出基于超平面投影的高维多目标进化算法（HPEA）.通过归一化技术构造单位超平面，将种群个体垂直投影到单位超平面上，消除收敛程度的影响；通过改进的Harmonic平均距离，评估单位超平面上投影点的拥挤密度；结合收敛信息构造λ-distance，更好地平衡解集收敛性与分布性.为了检验所提算法的性能，将之用于求解3~10个目标的9类标准测试函数，与目前国内外具有代表性的5种高维多目标进化算法对比可知，该算法相对于其他算法具有优势，能够在提高算法收敛性的同时，保证解集的分布性.
Abstract: A many-objective evolutionary algorithm based on hyperplane projection (HPEA) was proposed in order to better balance between convergence and distribution in many-objective optimization problems (MaOPs). The normalization method was used to construct a unit hyperplane and the population was projected onto the unit hyperplane for removing the influence of the convergence degree of individuals. Then an improved Harmonic mean distance was used to calculate the crowding density of the projected points in the above unit hyperplane. The λ-distance was constructed to better balance between convergence and distribution of solutions by considering the convergence information. Nine standard benchmark problems with three to ten objectives were tested to demonstrate the effectiveness of the proposed algorithm. The algorithm was compared with five state-of-the-art many-objective evolutionary algorithms (MaOEAs). The experimental results show that the proposed algorithm has more advantage than other algorithms, which can ensure the uniform distribution and improve the convergence.