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Incremental cooperative coevolution for large-scale global optimization

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Abstract

Cooperative coevolution (CC) is an efficient framework for solving large-scale global optimization (LSGO) problems. It uses a decomposition method to divide the LSGO problems into several low-dimensional subcomponents; then, subcomponents are optimized. Since CC algorithms do not consider any imbalance feature, their performance degrades during solving imbalanced LSGO problems. In this paper, we propose an incremental CC (ICC) algorithm in which the algorithm optimizes an integrated subcomponent which subcomponents are dynamically added to it. Therefore, the search space of the optimizer is grown incrementally toward the original problem search space. Various search spaces are built according to three approaches, namely random-based, sensitivity analysis-based, and random sensitivity analysis-based methods; then, ICC explores these search spaces effectively. Random-based selects a subcomponent randomly for adding it to the current search space and the sensitivity analysis-based method uses a sensitivity analysis strategy to select a subcomponent. The random sensitivity analysis-based strategy is a hybrid of the random and sensitivity analysis-based methods. Theoretical analysis is provided to demonstrate that the proposed ICC-based algorithms are effective for solving imbalanced LSGO problems. Finally, the efficiency of these algorithms is benchmarked on the complex imbalanced LSGO problems. Simulation results confirm that ICC obtains a better performance overall.

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Authors and Affiliations

  1. Department of Electrical, Computer, and Software Engineering, University of Ontario Institute of Technology (UOIT), 2000 Simcoe Street North, Oshawa, ON, L1H 7K4, Canada

    Sedigheh Mahdavi & Shahryar Rahnamayan

  2. Department of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran

    Mohammad Ebrahim Shiri

Authors
  1. Sedigheh Mahdavi
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  2. Shahryar Rahnamayan
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  3. Mohammad Ebrahim Shiri
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Corresponding author

Correspondence to Shahryar Rahnamayan.

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The authors declare that they have no conflict of interest.

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This article does not contain any studies with human participants or animals performed by any of the authors.

Additional information

Communicated by V. Loia.

Appendix

Appendix

Tables 9, 10, and 11 present the normal coefficient corresponding to nonseparable subcomponents in the modified normal CEC-2010 test functions.

Table 9 Normal coefficients for functions (\(f_9\)–\(f_{13}\))
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Table 10 Normal coefficients for functions (\(f_{14}\)–\(f_{18}\))
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Table 11 Normal coefficients for functions (\(f_4\)–\(f_8\))
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Mahdavi, S., Rahnamayan, S. & Shiri, M.E. Incremental cooperative coevolution for large-scale global optimization. Soft Comput 22, 2045–2064 (2018). https://doi.org/10.1007/s00500-016-2466-6

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