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On deciding when to stop metaheuristics: Properties, rules and termination conditions

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  • Corominas, Albert

Abstract

Most metaheuristics lack a termination condition based on reasonable premises and guaranteeing the quality of the solution provided by the algorithm. We propose a methodological frame that distinguishes the concepts of properties of the final incumbent solution, rules and termination conditions. The frame is applied to discuss the use of popular stopping rules (such as maximum number of iterations and maximum number of iterations without improvement) in the resolution of global optimization and combinatorial optimization problems via random restart metaheuristics. This allows finding simple formulas for determining the maximum number of iterations corresponding to diverse combinations of problem types and properties desired for the final incumbent solution. The suggestions for further research include the application of the probabilistic theory of records to the study of terminal conditions for metaheuristics.

Suggested Citation

  • Corominas, Albert, 2023. "On deciding when to stop metaheuristics: Properties, rules and termination conditions," Operations Research Perspectives, Elsevier, vol. 10(C).
    • Handle: RePEc:eee:oprepe:v:10:y:2023:i:c:s2214716023000180
    DOI: 10.1016/j.orp.2023.100283
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    References listed on IDEAS

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    1. Ran Etgar & Yuval Cohen, 2022. "Optimizing termination decision for meta-heuristic search techniques that converge to a static objective-value distribution," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(1), pages 249-271, March.
    2. V. Bartkutė & L. Sakalauskas, 2009. "Statistical Inferences for Termination of Markov Type Random Search Algorithms," Journal of Optimization Theory and Applications, Springer, vol. 141(3), pages 475-493, June.
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