Niching methods have been developed to maintain the population diversity, to investigate many peaks in parallel, and to reduce the effect of genetic drift. We present the first rigorous runtime analyses of restricted tournament selection (RTS), embedded in a (μ+1) EA, and analyse its effectiveness at finding both optima of the bimodal function TwoMax. In RTS, an offspring competes against the closest individual, with respect to some distance measure, amongst w (window size) population members (chosen uniformly at random with replacement), to encourage competition within the same niche. We prove that RTS finds both optima on TwoMax efficiently if the window size w is large enough. However, if w is too small, RTS fails to find both optima even in exponential time, with high probability. We further consider a variant of RTS selecting individuals for the tournament without replacement. It yields a more diverse tournament and is more effective at preventing one niche from taking over the other. However, this comes at the expense of a slower progress towards optima when a niche collapses to a single individual. Our theoretical results are accompanied by experimental studies that shed light on parameters not covered by the theoretical results and support a conjectured lower runtime bound.

中文翻译：

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双峰优化的受限比赛选择的运行时分析。

已经开发了Niching方法来维持种群多样性，并行研究许多峰，并减少遗传漂移的影响。我们展示了嵌入在 (μ+1) EA 中的受限锦标赛选择 (RTS) 的第一个严格运行时分析，并分析了其在找到双峰函数 TwoMax 的最优值方面的有效性。在 RTS 中，后代在 w（窗口大小）种群成员（随替换随机选择）中，就某种距离度量而言，与最接近的个体竞争，以鼓励同一生态位内的竞争。我们证明，如果窗口大小 w 足够大，RTS 可以有效地找到 TwoMax 上的最优值。但是，如果 w 太小，RTS 即使在指数时间内也无法找到两个最优值，而且概率很高。我们进一步考虑了一种 RTS 的变体，它在不替换的情况下为锦标赛选择个人。它产生了更多样化的锦标赛，并且更有效地防止了一个利基市场接管另一个利基市场。然而，当一个利基崩溃到一个人时，这会以较慢的进展为代价。我们的理论结果伴随着实验研究，这些研究揭示了理论结果未涵盖的参数并支持推测的运行时下限。