Abstract
We take a theoretical approach to analysing conditions for terminating evolutionary algorithms. After looking at situations where much is known about the particular algorithm and problem class, we consider a more generic approach. Schemes that depend purely on the previous time to improvement are shown not to work. An alternative criterion, the \(\lambda \)-parallel scheme, does terminate correctly (with high probability) for any randomised search heuristic algorithm on any problem, provided certain conditions on the improvement probabilities are met. A more natural and less costly approach is then presented based on the runtime so far. This is shown to work for the classes of monotonic and path problems (for Randomised Local Search). It remains an open question whether it works in a more general setting.
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References
Bossek, J., Sudholt, D.: Do additional target points speed up evolutionary algorithms? Theor. Comput. Sci. 950, 20–38 (2023)
Cathabard, S., Lehre, P.K., Yao, X.: Non-uniform mutation rates for problems with unknown solution lengths. In: FOGA 2011: Proceedings of the 11th Workshop Proceedings on Foundations of Genetic Algorithms. ACM (2011)
Doerr, B., Doerr, C., Kötzing, T.: Solving problems with unknown solution length at almost no extra cost. Algorithmica 81, 703–748 (2019)
Doerr, B., Rajabi, A., Witt, C.: Simulated annealing is a polynomial-time approximation scheme for the minimum spanning tree problem. Algorithmica 86, 64–89 (2023)
Doerr, B.: Probabilistic tools for the analysis of randomized optimization heuristics. In: Doerr, B., Neumann, F. (eds.) Theory of Evolutionary Computation. NCS, pp. 1–87. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-29414-4_1
Doerr, B., Goldberg, L.A.: Drift analysis with tail bounds. In: Schaefer, R., Cotta, C., Kołodziej, J., Rudolph, G. (eds.) PPSN XI. LNCS, vol. 6238, pp. 174–183. Springer, Heidelberg (2021). https://doi.org/10.1007/978-3-642-15844-5_18
Einarsson, H., et al.: The linear hidden subset problem for the (1 + 1) EA with scheduled and adaptive mutation rates. Theor. Comput. Sci. 785, 150–170 (2019)
Ghoreishi, S., Clausen, A., Joergensen, B.: Termination criteria in evolutionary algorithms: a survey. In: 9th International Joint Conference on Computational Intelligence, pp. 373–384 (2017)
Liu, Y., Zhou, A., Zhang, H.: Termination detection strategies in evolutionary algorithms: a survey. In: GECCO 2018: Proceedings of the Genetic and Evolutionary Computation Conference, pp. 1063–1070. ACM (2018)
Lobo, F.G., Bazargani, M., Burke, E.K.: A cutoff time strategy based on the coupon collector’s problem. Eur. J. Oper. Res. 286, 101–114 (2020)
Rowe, J.E., Sudholt, D.: The choice of the offspring population size in the \((1, \lambda )\) evolutionary algorithm. Theor. Comput. Sci. 545, 20–38 (2014)
Witt, C.: Fitness levels with tail bounds for the analysis of randomised search heuristics. Inf. Process. Lett. 114, 38–41 (2014)
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Rowe, J.E. (2024). A Theoretical Investigation of Termination Criteria for Evolutionary Algorithms. In: Stützle, T., Wagner, M. (eds) Evolutionary Computation in Combinatorial Optimization. EvoCOP 2024. Lecture Notes in Computer Science, vol 14632. Springer, Cham. https://doi.org/10.1007/978-3-031-57712-3_11
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DOI: https://doi.org/10.1007/978-3-031-57712-3_11
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