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 is a key component in multi-objective EAs (MOEAs), and it is performed in a greedy, deterministic manner. That is, the next-generation population is formed by selecting the first population-size ranked solutions (based on some selection criteria, e.g., non-dominated sorting, crowdedness and indicators) from the collections of the current population and newly-generated solutions. In this paper, we question this practice. We analytically present that introducing randomness into the population update procedure in MOEAs can be beneficial for the search. More specifically, we prove that the expected running time of a well-established MOEA (SMS-EMOA) for solving a commonly studied bi-objective problem, OneJumpZeroJump, can be exponentially decreased if replacing its deterministic population update mechanism by a stochastic one. Empirical studies also verify the effectiveness of the proposed stochastic population update method. This work is an attempt to challenge a common practice for the population update in 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（EAs）因其基于种群搜索的特性，已被广泛且成功地应用于解决多目标优化问题。种群更新是多目标进化算法（MOEAs）中的关键组成部分，通常采用贪婪且确定性的方式进行。即，下一代种群通过从当前种群和新生成解的集合中，基于某些选择标准（例如非支配排序、拥挤度或指标）选取前种群规模的排序解而形成。本文对这一实践提出质疑。我们分析表明，在MOEAs的种群更新过程中引入随机性可能有助于搜索。更具体地说，我们证明，如果将已成熟的MOEA（SMS-EMOA）中的确定性种群更新机制替换为随机机制，其在解决常见双目标问题OneJumpZeroJump时的期望运行时间可指数级减少。实证研究也验证了所提出的随机种群更新方法的有效性。本研究旨在挑战MOEAs中种群更新的常见做法，其积极成果可能具有更广泛的适用性，应鼓励在相关领域探索开发新的MOEAs。