基于动态关联的高维多目标进化算法

High-dimensional multi-objective evolutionary algorithm based on dynamic correlation

  • 摘要: 针对现有多目标进化算法在处理复杂Pareto边界问题时收敛性与多样性难以平衡的问题,提出了一种改进的动态关联策略(dynamic association model,DAM)和基于目标空间转换的自适应权值更新策略(objective-oriented transformation strategy,OTS)的高维多目标进化算法MOEA/D-DAM. 该算法通过DAM将权重向量与种群个体通过切比雪夫加权法进行关联,实现种群与权向量的动态关联,增强了种群的收敛性与多样性;采用基于目标空间转换的OTS通过对帕累托前沿曲率估计,当其曲率小于1时,将种群在目标空间进行坐标转换;采用目标向量之间的余弦相似度来衡量稀疏度,有效改善了个体在帕累托前沿上分布不均的问题使种群在保持多样性的同时快速收敛.MOEA/D-DAM与其他先进算法MOEA/D-UR、MOEA/D-URAW、MOEA/D-VOV、PeEA以及TS-NSGA-Ⅱ在DLTZ测试问题和WFG测试问题上进行仿真对比实验. 结果表明,MOEA/D-DAM在IGD性能指标上分别有43、48、52、49、40个问题表现优于其他算法,最优解占比为54.6%;在HV性能指标上有28、46、42、37、43个问题依次优于其他算法,最优解占比为42.1%. 该算法在求解复杂Pareto边界的高维多目标优化问题中表现出强大的竞争力,能够有效平衡收敛性与多样性.

     

    Abstract: In response to the drawbacks of existing multi-objective evolutionary algorithms in handling complex Pareto frontier issues, such as insufficient selection pressure and uneven distribution, a novel high-dimensional multi-objective evolutionary algorithm, MOEA/D-DAM, is proposed. This algorithm adopts a dynamic association model (DAM) and an adaptive weight update strategy based on target space transformation (OTS) to enhance the exploration capability, quality, and diversity of the algorithm. The DAM connects the weight vector with the population individuals through the Chebyshev weighting approach, achieving the dynamic association between the population and the weight vector. The OTS based on target space transformation and adaptive weight update, estimates the curvature of the Pareto frontier and adjusts the population coordinates via the target space coordinates when the curvature is less than 1. The algorithm effectively ameliorates the distribution of individuals on the Pareto frontier, enabling the population to converge rapidly while maintaining diversity. MOEA/D-DAM is compared with advanced algorithms MOEA/D-UR, MOEA/D-URAW, MOEA/D-VOV, PeEA, and TS-NSGA-Ⅱ on the DLTZ test problem and WFG test problem through simulation experiments. The experimental results indicate that MOEA/D-DAM outperforms other algorithms in the IGD performance indicator on 43, 48, 52, 49, and 40 problems, with a best solution ratio of 54.6%. It shows superior performance in the HV performance indicator on 28, 46, 42, 37, and 43 problems, with a best solution ratio of 42.1%. The algorithm demonstrates strong competitiveness in solving complex Pareto problems.

     

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