Escaping local optima is one of the major obstacles to function optimisation. Using the metaphor of a fitness landscape, local optima correspond to hills separated by fitness valleys that have to be overcome. We define a class of fitness valleys of tunable difficulty by considering their length, representing the Hamming path between the two optima and their depth, the drop in fitness. For this function class we present a runtime comparison between stochastic search algorithms using different search strategies. The ($$1+1$$1+1) EA is a simple and well-studied evolutionary algorithm that has to jump across the valley to a point of higher fitness because it does not accept worsening moves (elitism). In contrast, the Metropolis algorithm and the Strong Selection Weak Mutation (SSWM) algorithm, a famous process in population genetics, are both able to cross the fitness valley by accepting worsening moves. We show that the runtime of the ($$1+1$$1+1) EA depends critically on the length of the valley while the runtimes of the non-elitist algorithms depend crucially on the depth of the valley. Moreover, we show that both SSWM and Metropolis can also efficiently optimise a rugged function consisting of consecutive valleys.

中文翻译：

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如何在黑盒优化中摆脱局部最优：当非精英主义胜过精英主义时

逃避局部最优是功能优化的主要障碍之一。使用健身景观的比喻，局部最优对应于必须克服的健身山谷隔开的山丘。我们通过考虑它们的长度来定义一类可调难度的适应度谷，代表两个最优值之间的汉明路径及其深度，适应度的下降。对于这个函数类，我们展示了使用不同搜索策略的随机搜索算法之间的运行时比较。($$1+1$$1+1) EA 是一种简单且经过充分研究的进化算法，由于它不接受恶化的动作（精英主义），因此它必须跨越山谷以达到更高的适应度。相比之下，Metropolis 算法和强选择弱突变 (SSWM) 算法是种群遗传学中​​的一个著名过程，都能够通过接受恶化的动作来跨越健身谷。我们表明 ($$1+1$$1+1) EA 的运行时间主要取决于山谷的长度，而非精英算法的运行时间主要取决于山谷的深度。此外，我们表明 SSWM 和 Metropolis 还可以有效地优化由连续山谷组成的崎岖函数。