Multi-strategy ensemble firefly algorithm with equilibrium of convergence and diversity

Abstract

Balancing the convergence and diversity in the multi-objective firefly algorithm is essential for obtaining high precision and well distributed Pareto front. However, most existing algorithms cannot​ guarantee such balance, leading to a poor comprehensive performance. To address this limitation, this paper proposes a multi-strategy ensemble firefly algorithm with equilibrium of convergence and diversity (MEFA-CD). Firstly, an improved linear congruence method is used to generate the initial population with uniform distribution, to provide a good start for the subsequent population evolution and ensure the global search ability; Secondly, a hybrid learning strategy is utilized to identify the best elite solution according to the maximum fitness value. Combined with the current best solution, the firefly is guided to learn under the effect of compensation factor. On the one hand, it breaks through the population constraints, which yields a faster convergence to the Pareto optimal solution set. On the other hand, it expands the search range of the population, which improves the diversity and the accuracy of the Pareto optimal set; Finally, the crowding distance mechanism is used to delete the aggregation solution, which maintains the diversity of external files and ensures the local development ability of the population, and further improves the convergence of the algorithm. Experimental results show that, compared with other multi-objective optimization algorithms, the proposed algorithm has better performance in convergence and diversity, among which the optimization performance is improved by 61% compared with the standard MOFA.