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The evolutionary diversity optimization aims at finding a diverse set ofsolutions which satisfy some constraint on their fitness. In the context ofmulti-objective optimization this constraint can require solutions to bePareto-optimal. In this paper we study how the GSEMO algorithm with additionaldiversity-enhancing heuristic optimizes a diversity of its population on abi-objective benchmark problem OneMinMax, for which all solutions arePareto-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, andprove 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 analysethe random walk of the population, which reflects the frequency of changes inthe population and their outcomes.

Rigorous Runtime Analysis of Diversity Optimization with GSEMO on OneMinMax