基于全局排序的高维多目标优化研究

目标数超过4的高维多目标优化是目前进化多目标优化领域求解难度最大的问题之一,现有的多目标进化算法求解该类问题时,存在收敛性和解集分布性上的缺陷,难以满足实际工程优化需求.提出一种基于全局排序的高维多目标进化算法GR-MODE,首先,采用一种新的全局排序策略增强选择压力,无需用户偏好及目标主次信息,且避免宽松Pareto支配在排序结果合理性与可信性上的损失;其次,采用Harmonic平均拥挤距离对个体进行全局密度估计,提高现有局部密度估计方法的精确性;最后,针对高维多目标复杂空间搜索需求,设计新的精英选择策略及适应度值评价函数.将该算法与国内外现有的5种高性能多目标进化算法在标准测试函数集DTLZ{1,2, 4,5}上进行对比实验,结果表明,该算法具有明显的性能优势,大幅提升了4~30维高维多目标优化的收敛性和分布性.

Research of Global Ranking Based Many-Objective Optimization

Many-Objective optimization problem (MOP) with more than four objectives are among the most difficult problems in the field of evolutionary multi-objective optimization. In fact, existing multi-objective evolutionary algorithms (MOEAs) can not fulfill the engineering requirement of convergence, diversity and stability. In this paper, a new kind of many-objective evolutionary algorithm is proposed. The algorithm adopts a global ranking technique to favor convergence by improving selection pressure without need of the user's preference or objective information, avoiding loss of rationality and credibility due to the use of relaxed Pareto domination relations. In addition, a new global density estimation method based on the harmonic average distance is presented. Finally, a new elitist selection strategy is designed. Simulation results on DTLZ{1,2,4,5} test problems with 4~30 objectives show that the proposed algorithm consistently provides good convergence as the number of objectives increases, outperforming five state-of-the-art MOEAs.