A competitive and collaborative-based multilevel hierarchical artificial electric field algorithm for global optimization

Abstract

Competitive and collaborative strategies and topologies are among the most essential concepts and greatly influence the optimization ability of population-based optimization algorithms. To update individuals' information, this article proposes a multilevel hierarchical artificial electric field algorithm with competitive and collaborative strategies (PAEFA). The proposed algorithm constructs a multilevel structure and places them in specific layers. The whole population is divided into two groups of winners and losers by pairwise comparison of their fitness in the same layer. Losers collaborate with their respective winners, whereas winners collaborate with individuals who are on the upper layers. In the proposed algorithm, each individual has their own learning mechanism, which can learn from more than one exemplar, rather than only from the global best. With the knowledge of this structure, the diversity of the population increases, which strengthens the performance of the scheme. To verify the adaptability of the proposed algorithm, extensive experiments are performed on the CEC 2017 test suite at 30, 50, and 100 dimensions. We have studied the diversity factor of PAEFA using all three dimensions. These experiments suggest that PAEFA outperforms over thirty state-of-the-art algorithms in terms of accuracy, statistical results, and convergence speed while achieving comparable computational time in most cases and showing the validity of results. The PAEFA algorithm achieves superior performance compared to other state-of-the-art algorithms on 87.60% and 80.05% of problems in terms of accuracy and statistical significance across all three dimensions, respectively.