Many real-world multi-objective optimization problems (MOPs) are characterized by a large number of decision variables, where the decision variables are mostly set to zero in the Pareto optimal solutions. Although some multi-objective evolutionary algorithms (MOEAs) have been tailored for large-scale MOPs in recent years, most of them do not consider the sparse nature of Pareto optimal solutions, and their effectiveness to sparse MOPs has not been investigated. Therefore, this work aims to compare the performance of MOEAs on sparse MOPs by suggesting a comprehensive performance indicator. In comparison to existing indicators assessing the convergence and diversity of a solution set according to predefined reference points, the proposed indicator can assess the convergence, diversity, and sparsity without using any reference point. Based on the proposed indicator, an experiment is conducted to compare the performance of 11 state-of-the-art MOEAs on 60 test instances taken from benchmark suites and real-world applications. The statistical results show that some MOEAs are significantly better than the others for solving sparse MOPs, and the proposed indicator is effective for the performance assessment on sparse MOPs.

中文翻译：

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通过综合指标比较稀疏多目标优化进化算法的性能【研究前沿】


许多现实世界的多目标优化问题（MOP）都具有大量决策变量的特点，其中决策变量在帕累托最优解中大多设置为零。尽管近年来一些多目标进化算法（MOEA）已经针对大规模 MOP 进行了定制，但大多数算法都没有考虑 Pareto 最优解的稀疏性，并且它们对稀疏 MOP 的有效性尚未得到研究。因此，本工作旨在通过提出综合性能指标来比较 MOEA 在稀疏 MOP 上的性能。与根据预定义参考点评估解集的收敛性和多样性的现有指标相比，所提出的指标可以在不使用任何参考点的情况下评估收敛性、多样性和稀疏性。基于所提出的指标，进行了一项实验，比较 11 个最先进的 MOEA 在来自基准套件和实际应用程序的 60 个测试实例上的性能。统计结果表明，一些MOEA在解决稀疏MOP问题上明显优于其他MOEA，并且所提出的指标对于稀疏MOP问题的性能评估是有效的。