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Global versus local search: the impact of population sizes on evolutionary algorithm performance

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Abstract

In the field of Evolutionary Computation, a common myth that “An Evolutionary Algorithm (EA) will outperform a local search algorithm, given enough runtime and a large-enough population” exists. We believe that this is not necessarily true and challenge the statement with several simple considerations. We then investigate the population size parameter of EAs, as this is the element in the above claim that can be controlled. We conduct a related work study, which substantiates the assumption that there should be an optimal setting for the population size at which a specific EA would perform best on a given problem instance and computational budget. Subsequently, we carry out a large-scale experimental study on 68 instances of the Traveling Salesman Problem with static population sizes that are powers of two between \((1+2)\) and \(({262144}+{524288})\) EAs as well as with adaptive population sizes. We find that analyzing the performance of the different setups over runtime supports our point of view and the existence of optimal finite population size settings.

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Notes

  1. This could be a manifestation of the NFLT.

  2. The question of whether there is a population size threshold above or below which the expected running time becomes polynomial would then, again intuitively, be answered with probably not.

  3. “We suspect the increase of generations to convergence is probably due to the overall increase in probability that a mutation will take place in the population and in the increased time it takes for a greater number of chromosomes to completely converge.” [28].

  4. In [55, 97, 98], we found that an ejection chain method using the stem-and-cycle structure, the Lin–Kernighan heuristic and Tabu Search can outperform MNS, respectively. However, hybrids of MNS and EAs or Ant Colony Optimization outperform similar hybrids of these algorithms.

  5. We also tested \((\mu ,\lambda )\) EAs, but like Lin and Chen [53], we found that these performed worse than the \((\mu +\lambda )\) EAs, so we excluded them from the discussion for the sake of brevity.

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Acknowledgments

The authors at UBRI would like to acknowledge support from the National Natural Science Foundation of China under Grants 61175065, 61329302, and 61150110488, the Fundamental Research Funds for the Central Universities, the Technological Fund of Anhui Province for Outstanding Youth under Grant 1108085J16, the Special Financial Grant 201104329 from the China Postdoctoral Science Foundation, the Chinese Academy of Sciences (CAS) Fellowship for Young International Scientists 2011Y1GB01, and the European Union 7th Framework Program under Grant 247619. The third author would like to acknowledge support from the University of Newcastle Faculty of Science and Information Technology’s Strategic Initiatives Research Fund (Grant 10.31415). The experiments reported in this work were executed on the supercomputing system in the Supercomputing Center of University of Science and Technology of China.

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  1. Joint USTC-Birmingham Research Institute in Intelligent Computation and Its Applications (UBRI), School of Computer Science and Technology, University of Science and Technology of China, Hefei, 230027, Anhui, China

    Thomas Weise, Yuezhong Wu & Ke Tang

  2. School of Design, Communication and Information Technology, Faculty of Science and Information Technology, The University of Newcastle, Callaghan, NSW, 2308, Australia

    Raymond Chiong

  3. Faculty of Electrical Engineering and Computer Science, Hochschule Zittau/Görlitz, 02826, Görlitz, Germany

    Jörg Lässig

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  1. Thomas Weise
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Correspondence to Thomas Weise.

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Weise, T., Wu, Y., Chiong, R. et al. Global versus local search: the impact of population sizes on evolutionary algorithm performance. J Glob Optim 66, 511–534 (2016). https://doi.org/10.1007/s10898-016-0417-5

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