A Dynamic Neighborhood Learning-Based Gravitational Search Algorithm

Balancing exploration and exploitation according to evolutionary states is crucial to meta-heuristic search (M-HS) algorithms. Owing to its simplicity in theory and effectiveness in global optimization, gravitational search algorithm (GSA) has attracted increasing attention in recent years. However, the tradeoff between exploration and exploitation in GSA is achieved mainly by adjusting the size of an archive, named <inline-formula> <tex-math notation="LaTeX">$ {K_{\textrm {best}}}$ </tex-math></inline-formula>, which stores those superior agents after fitness sorting in each iteration. Since the global property of <inline-formula> <tex-math notation="LaTeX">$ {K_{\textrm {best}}}$ </tex-math></inline-formula> remains unchanged in the whole evolutionary process, GSA emphasizes exploitation over exploration and suffers from rapid loss of diversity and premature convergence. To address these problems, in this paper, we propose a dynamic neighborhood learning (DNL) strategy to replace the <inline-formula> <tex-math notation="LaTeX">$ {K_{\textrm {best}}}$ </tex-math></inline-formula> model and thereby present a DNL-based GSA (DNLGSA). The method incorporates the local and global neighborhood topologies for enhancing the exploration and obtaining adaptive balance between exploration and exploitation. The local neighborhoods are dynamically formed based on evolutionary states. To delineate the evolutionary states, two convergence criteria named limit value and population diversity, are introduced. Moreover, a mutation operator is designed for escaping from the local optima on the basis of evolutionary states. The proposed algorithm was evaluated on 27 benchmark problems with different characteristic and various difficulties. The results reveal that DNLGSA exhibits competitive performances when compared with a variety of state-of-the-art M-HS algorithms. Moreover, the incorporation of local neighborhood topology reduces the numbers of calculations of gravitational force and thus alleviates the high computational cost of GSA.