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.

本论文研究了 GSEMO 算法在多目标优化中优化群体多样性的方法，阐述了该算法在解决 Pareto - 最优问题中的优势，并得到当问题规模为奇数时，预期时间内收敛到具有最优多样性的种群的证明，分析中涉及了种群的随机漫步等相关理论。