This article investigates the performance of multistart next ascent hillclimbing and well-known evolutionary algorithms incorporating diversity preservation techniques on instances of the multimodal problem generator. This generator induces a class of problems in the bitstring domain which is interesting to study from a theoretical perspective in the context of multimodal optimization, as it is a generalization of the classical OneMax and TwoMax functions for an arbitrary number of peaks. An average-case runtime analysis for multistart next ascent hillclimbing is presented for uniformly distributed equal-height instances of this class of problems. It is shown empirically that conventional niching and mating restriction techniques incorporated in an evolutionary algorithm are not sufficient to make them competitive with the hillclimbing strategy.

We conjecture the reason for this behavior is the lack of structure in the space of local optima on instances of this problem class, which makes an optimization algorithm unable to exploit information from one optimum to infer where another optimum might be. When no such structure exists, it seems that the best strategy for discovering all optima is a brute-force one.

Overall, our study gives insights with respect to the adequacy of hillclimbers and evolutionary algorithms for multimodal optimization, depending on properties of the fitness landscape.

本文研究了多起点下一次爬山的性能以及在多模态问题生成器实例上结合多样性保存技术的著名进化算法。该生成器在位串域中引发了一类问题，从多模态优化背景下的理论角度研究这些问题很有趣，因为它是任意数量峰值的经典OneMax和TwoMax函数的推广。针对此类问题的均匀分布等高实例，提出了多起点下次爬山的平均情况运行时间分析。经验表明，进化算法中包含的传统生态位和交配限制技术不足以使它们与爬山策略竞争。

我们推测这种行为的原因是该问题类实例的局部最优空间中缺乏结构，这使得优化算法无法利用一个最优值的信息来推断另一个最优值可能在哪里。当不存在这样的结构时，发现所有最优的最佳策略似乎就是暴力策略。

总体而言，我们的研究根据适应度景观的属性，对登山者和多模式优化的进化算法的充分性提供了见解。