The evolutionary diversity optimization aims at finding a diverse set of solutions which satisfy some constraint on their fitness. In the context of multi-objective optimization this constraint can require solutions to be Pareto-optimal. In this paper we study how the GSEMO algorithm with additional diversity-enhancing heuristic optimizes a diversity of its population on a bi-objective benchmark problem OneMinMax, for which all solutions are Pareto-optimal. We provide a rigorous runtime analysis of the last step of the optimization, when the algorithm starts with a population with a second-best diversity, and prove that it finds a population with optimal diversity in expected time $O(n^2)$, when the problem size $n$ is odd. For reaching our goal, we analyse the random walk of the population, which reflects the frequency of changes in the population and their outcomes.

翻译：进化多样性优化旨在寻找满足某些适应度约束的多样化解集。在多目标优化背景下，该约束可要求解为帕累托最优。本文研究带有额外多样性增强启发式的GSEMO算法如何优化其在双目标基准问题OneMinMax（所有解均为帕累托最优）上种群的多样性。我们对该优化过程的最后一步进行严格的运行时分析——当算法从具有次优多样性的初始种群出发时，证明其在问题规模$n$为奇数的情况下，能够在期望时间$O(n^2)$内找到具有最优多样性的种群。为实现这一目标，我们分析了种群的随机游走过程，该过程反映了种群变化的频率及其结果。