Selection hyper-heuristics (HHs) are automated algorithm selection methodologies that choose between different heuristics during the optimisation process. Recently, selection HHs choosing between a collection of elitist randomised local search heuristics with different neighbourhood sizes have been shown to optimise standard unimodal benchmark functions from evolutionary computation in the optimal expected runtime achievable with the available low-level heuristics. In this paper, we extend our understanding of the performance of HHs to the domain of multimodal optimisation by considering a Move Acceptance HH (MAHH) from the literature that can switch between elitist and non-elitist heuristics during the run. In essence, MAHH is a non-elitist search heuristic that differs from other search heuristics in the source of non-elitism.

We first identify the range of parameters that allow MAHH to hillclimb efficiently and prove that it can optimise the standard hillclimbing benchmark function OneMax in the best expected asymptotic time achievable by unbiased mutation-based randomised search heuristics. Afterwards, we use standard multimodal benchmark functions to highlight function characteristics where MAHH outperforms elitist evolutionary algorithms and the well-known Metropolis non-elitist algorithm by quickly escaping local optima, and ones where it does not. Since MAHH is essentially a non-elitist random local search heuristic, the paper is of independent interest to researchers in the fields of artificial intelligence and randomised search heuristics.

选择超启发式 (HH) 是在优化过程中在不同启发式之间进行选择的自动算法选择方法。最近，选择 HH 在具有不同邻域大小的精英随机局部搜索启发式集合之间进行选择已被证明可以从进化计算中优化标准单峰基准函数，从而在可用的低级启发式可实现的最佳预期运行时间中。在本文中，我们通过考虑文献中可以在运行期间在精英和非精英启发式之间切换的移动接受 HH (MAHH)，将我们对 HH 性能的理解扩展到多模态优化领域。从本质上讲，MAHH 是一种非精英搜索启发式算法，与其他搜索启发式算法在非精英搜索的来源上有所不同。

我们首先确定允许 MAHH 有效爬山的参数范围，并证明它可以在基于无偏突变的随机搜索启发式可实现的最佳预期渐近时间内优化标准爬山基准函数OneMax。之后，我们使用标准的多模态基准函数来突出显示 MAHH 通过快速逃避局部最优而优于精英进化算法和著名的Metropolis非精英算法的函数特征，以及那些没有的函数特征。由于 MAHH 本质上是一种非精英随机局部搜索启发式，因此该论文对人工智能和随机搜索启发式领域的研究人员具有独立的兴趣。