Abstract

This paper presents the Constructive Cooperative Coevolutionary (mathrm {C}^3) algorithm, applied to continuous large-scale global optimisation problems. The novelty of mathrm {C}^3 is that it utilises a multi-start architecture and incorporates the Cooperative Coevolutionary algorithm. The considered optimisation problem is decomposed into subproblems. An embedded optimisation algorithm optimises the subproblems separately while exchanging information to co-adapt the solutions for the subproblems. Further, mathrm {C}^3 includes a novel constructive heuristic that generates different feasible solutions for the entire problem and thereby expedites the search. In this work, two different versions of mathrm {C}^3 are evaluated on high-dimensional benchmark problems, including the CEC’2013 test suite for large-scale global optimisation. mathrm {C}^3 is compared with several state-of-the-art algorithms, which shows that mathrm {C}^3 is among the most competitive algorithms. mathrm {C}^3 outperforms the other algorithms for most partially separable functions and overlapping functions. This shows that mathrm {C}^3 is an effective algorithm for large-scale global optimisation. This paper demonstrates the enhanced performance by using constructive heuristics for generating initial feasible solutions for Cooperative Coevolutionary algorithms in a multi-start framework.

Highlights

  • Many practical real-world optimisation problems within engineering can be considered as global optimisation problems

  • Considering the statistically significant differences, C3jDErpo is the best algorithm or among the best in 28 of the 36 tests compared to CCjDErpo and jDErpo, and C3PSO in 23 of the 36 tests compared to CCPSO and Particle Swarm Optimiser (PSO)

  • These results were compared with 9 other large-scale global optimisation algorithms representing the state-of-the-art, next to the previously used CCjDErpo, jDErpo, CCPSO and PSO algorithms

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Summary

Introduction

Many practical real-world optimisation problems within engineering can be considered as global optimisation problems. A well-known multi-start method, the Continuous Greedy Randomised Adaptive Search Procedure (CGRASP) (Hirsch et al 2010), is relevant for the work presented in this paper. Another metaheuristic, that is adopted in this work, is the Cooperative Coevolutionary (CC) algorithm (Potter and De Jong 1994). That is adopted in this work, is the Cooperative Coevolutionary (CC) algorithm (Potter and De Jong 1994) This algorithm requires that the optimisation problem is decomposed into subproblems. Those works propose different versions of CC to improve the performance on non-separable problems These different versions of CC mainly focus on regrouping the parameters into different subproblems.

Background
Greedy randomised adaptive search procedure
Cooperative coevolutionary algorithm
Phase I: constructive heuristic
Phase II: cooperative coevolution
Results and discussion
Convergence analysis
Computational effort
Robustness analysis
Results CEC’2013 LSGO functions
Conclusions and future work
Benchmark functions
Full Text
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