Explosion gravitation field algorithm with dust sampling for unconstrained optimization

Gravitation Field Algorithm (GFA) is a novel optimization algorithm derived from the Solar Nebular Disk Model (SNDM) in astronomy and inspired by the formation process of planets. Although it has achieved good performance when solving many unconstrained optimization problems, which demonstrated its promising application potential in many real-world problems, GFA still has much room for improvement, especially when it comes to the accuracy and efficiency of the algorithm.In this research, an improved GFA algorithm called Explosion Gravitation Field Algorithm (EGFA) is proposed for unconstrained optimization problems, with the introduction of two strategies: Dust Sampling (DS) and Explosion Operation. The task of DS is to locate the space that contains the optimal solution(s) by initializing the dust population randomly in the search space; while the Explosion Operator is to improve the accuracy of solutions and decrease the probability of the algorithm falling into local optima by generating the new population around the center dust to replace the original population.A comparison of experimental results on six classical unconstrained benchmark problems with different dimensions demonstrates that the proposed EGFA outperforms the original GFA and several classical metaheuristic optimization algorithms, such as Genetic Algorithm (GA) and Particle Swarm Optimization (PSO), in terms of accuracy and efficiency in lower dimensions. Additionally, the comparison of results on three real datasets indicate that EGFA performs better than the original GFA and k-means for solving clustering problems.