Evolutionary algorithms (EAs) have been widely and successfully applied to solve multi-objective optimization problems, due to their nature of population-based search. Population update, a key component in multi-objective EAs (MOEAs), is usually performed in a greedy, deterministic manner. That is, the next-generation population is formed by selecting the best solutions from the current population and newly-generated solutions (irrespective of the selection criteria used such as Pareto dominance, crowdedness and indicators). In this paper, we question this practice. We analytically present that stochastic population update can be beneficial for the search of MOEAs. Specifically, we prove that the expected running time of two well-established MOEAs, SMS-EMOA and NSGA-II, for solving two bi-objective problems, OneJumpZeroJump and bi-objective RealRoyalRoad, can be exponentially decreased if replacing its deterministic population update mechanism by a stochastic one. Empirical studies also verify the effectiveness of the proposed population update method. This work is an attempt to challenge a common practice in the design of existing MOEAs. Its positive results, which might hold more generally, should encourage the exploration of developing new MOEAs in the area.

翻译：进化算法因其基于种群搜索的特性，已广泛应用于多目标优化问题求解。种群更新作为多目标进化算法的关键组件，通常以贪婪、确定性的方式执行——即从当前种群和新生成解中选取最优个体构成下一代种群（无论采用何种选择准则，如帕累托支配、拥挤度或指标）。本文对这一常规做法提出质疑，并通过理论分析证明随机种群更新有助于提升多目标进化算法的搜索性能。具体而言，我们证明：将SMS-EMOA与NSGA-II这两种成熟多目标进化算法的确定性种群更新机制替换为随机机制后，其求解两类双目标问题（OneJumpZeroJump与双目标RealRoyalRoad）的期望运行时间可呈指数级降低。实验研究亦验证了所提种群更新方法的有效性。本研究旨在挑战现有MOEA设计中的常规实践，其积极结论可能具有更广泛的适用性，有望推动该领域新型多目标进化算法的探索与发展。