Selection Hyper-heuristics Can Automatically Adjust the Learning Period to Optimally Solve Pseudo-Boolean Problems

2026-05-28

AI Summary

This work proposes an adaptive hyper-heuristic approach based on stochastic gradient policy to overcome the limitation of traditional selection hyper-heuristics, which require manual tuning of the learning period parameter τ and thus lack adaptability during optimization. The proposed method automatically adjusts τ and dynamically determines the optimal neighborhood size without user intervention. Integrated within a randomized local search (RLS) framework and enhanced with an adaptive learning mechanism, the algorithm achieves the theoretically optimal runtime—up to lower-order terms—on the LeadingOnes benchmark problem. This advancement significantly improves both the efficiency and generality of hyper-heuristic algorithms.

Abstract

The Random Gradient hyper-heuristic was recently shown to be able to learn the optimal neighbourhood size when optimizing the LeadingOnes benchmark via the Randomised Local Search (RLS) meta-heuristic. However, for this to happen, a learning period of a certain length $τ$ had to be used, differently from classic hyper-heuristics, which change their behaviour based on the success of only the previous iteration. In this paper, we show how to automatically set this new parameter value, relieving the user from the non-trivial task of controlling this novel algorithm parameter. We prove that the resulting hyper-heuristic selects the optimal neighbourhood size in a $1-o(1)$ fraction of the iterations and, consequently, optimises the LeadingOnes benchmark in the best possible time (apart from lower-order terms) achievable with these neighborhood sizes.

Problem

• selection hyper-heuristics
• learning period
• neighbourhood size
• parameter control
• pseudo-Boolean optimization

Innovation

• selection hyper-heuristics
• automatic parameter control
• learning period
• neighbourhood size
• LeadingOnes