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

arXiv 2605.29916 ↗First posted 28 May 2026cs.NE cs.AI cs.DScited by 0

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Abstract (arXiv)

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.

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References · 16

  1. 2020Self-Adjusting Evolutionary Algorithms for Multimodal Optimizationcited by 15
  2. 2018Better Runtime Guarantees Via Stochastic Dominationcited by 12
  3. 2021Stagnation Detection with Randomized Local Searchcited by 11
  4. 2022Theory-inspired Parameter Control Benchmarks for Dynamic Algorithm Configurationcited by 11
  5. 2018Theory of Parameter Control for Discrete Black-Box Optimization: Provable Performance Gains Through Dynamic Parameter Choicescited by 9
  6. 2021Stagnation Detection in Highly Multimodal Fitness Landscapescited by 8
  7. 2022Stagnation Detection Meets Fast Mutationcited by 8
  8. 2016Self-adaptation of Mutation Rates in Non-elitist Populationscited by 6
  9. 2015Optimal Parameter Choices Through Self-Adjustment: Applying the 1/5-th Rule in Discrete Settingscited by 5
  10. 2017The (1+λ) Evolutionary Algorithm with Self-Adjusting Mutation Ratecited by 4
  11. 2018Runtime Analysis for Self-adaptive Mutation Ratescited by 4
  12. 2019Hyper-Parameter Tuning for the (1+(λ,λ)) GAcited by 4
4 more
  1. 2023How the Move Acceptance Hyper-Heuristic Copes With Local Optima: Drastic Differences Between Jumps and Cliffscited by 4
  2. 2024Hyper-Heuristics Can Profit From Global Variation Operatorscited by 2
  3. 2025Speeding Up Hyper-Heuristics With Markov-Chain Operator Selection and the Only-Worsening Acceptance Operatorcited by 2
  4. 2024A Flexible Evolutionary Algorithm With Dynamic Mutation Rate Archivecited by 1

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