โ Scribed by Gao, Wanru; Neumann, Frank
No coin nor oath required. For personal study only.
Recently Ulrich and Thiele [14] have introduced evolutionary algorithms for the mixed multi-objective problem of maximizing fitness as well as diversity in the decision space. Such an approach allows to generate a diverse set of solutions which are all of good quality. With this paper, we contribute to the theoretical understanding of evolutionary algorithms for maximizing the diversity in a population that contains several solutions of high quality. We study how evolutionary algorithms maximize the diversity of a population where each individual has to have fitness beyond a given threshold value. We present a first runtime analysis in this area and study the classical problems called OneMax and LeadingOnes. Our results give first rigorous insights on how evolutionary algorithms can be used to produce a maximal diverse set of solutions in which all solutions have quality above a certain threshold value.
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