How the Duration of the Learning Period Affects the Performance of Random Gradient Selection Hyper-Heuristics

Abstract

Recent analyses have shown that a random gradient hyper-heuristic (HH) using randomised local search (RLSk) low-level heuristics with different neighbourhood sizes k can optimise the unimodal benchmark function LeadingOnes in the best expected time achievable with the available heuristics, if sufficiently long learning periods τ are employed. In this paper, we examine the impact of the learning period on the performance of the hyper-heuristic for standard unimodal benchmark functions with different characteristics: Ridge, where the HH has to learn that RLS1 is always the best low-level heuristic, and OneMax, where different low-level heuristics are preferable in different areas of the search space. We rigorously prove that super-linear learning periods τ are required for the HH to achieve optimal expected runtime for Ridge. Conversely, a sub-logarithmic learning period is the best static choice for OneMax, while using super-linear values for τ increases the expected runtime above the asymptotic unary unbiased black box complexity of the problem. We prove that a random gradient HH which automatically adapts the learning period throughout the run has optimal asymptotic expected runtime for both OneMax and Ridge. Additionally, we show experimentally that it outperforms any static learning period for realistic problem sizes.

On the runtime analysis of selection hyper-heuristics with adaptive learning periods

“…The length of the learning period is crucial for the success of the hyper-heuristic and can be determined in a self-adjusting manner as shown in [DLOW18]. These works were extended to other benchmark problems in [LOW20a].…”

Fast Immune System-Inspired Hypermutation Operators for Combinatorial Optimization

“…Since the optimal values for the distribution parameters γ and β are different in the exploitation and the exploration phases, future work may consider an adaptation of the parameters to automatically allow them to increase and decrease throughout the run [51]- [53]. Furthermore, the performance of the proposed operators should be evaluated experimentally for classical combinatorial optimisation problems, complementing the theoretical analyses of the worst-case performance, and for real-world applications.…”

Automatic adaptation of hypermutation rates for multimodal optimisation

“…The mechanism we propose to use to adapt the mutation rate in the (1+1) AIS is inspired by the 1/5 rule traditionally used in evolutionary computation for continuous optimisation [26]. The method has also been applied successfully in discrete optimisation to automatically adapt the offspring population size of crossover-based algorithms [16,17] and the duration of the learning period in online algorithm selection (i.e., hyper-heuristics) [20,30]. While commonly used in continuous optimisation, the 1/5 rule adaptation has rarely been rigorously studied to automatically adapt the mutation rate in combinatorial optimisation, with probably the only exception 2) respectively.…”