Multi-objective Firefly algorithm for enhanced balanced exploitation and exploration capabilities

The multi-objective Firefly algorithm has a single strategy for finding the best in the evolutionary process, which is easy to fall into the local optimum and leads to poor distribution and convergence of the population. To address this problem, this article proposes an enhanced multi-objective Firefly algorithm with balanced exploitation and exploration capability (MOFA-EBE). The convergence evaluation index is introduced to divide the population into two sub-regions according to the difference of convergence, namely, the development area and exploration area, and each sub-region is assigned its learning strategy to maximize the utilization of population information. Since the individuals in the development region are far from the Pareto front, the Levy flights mechanism is added to expand the search area and make them approach the Pareto front quickly under the guidance of the convergent global optimal particles to improve the convergence of the algorithm; since the individuals in the exploration region already have better convergence, they are assigned the most diverse and convergent global individuals for guidance and the Cauchy The variation mechanism is added to the Pareto frontier for continuous exploration to improve the distributivity of the algorithm. In the experimental part, the algorithm is compared with some multi-objective optimization algorithms on 19 benchmark test functions, and the effectiveness of the added strategy of MOFA-EBE is verified. The results show that MOFA-EBE is significantly superior to several other algorithms in terms of improving population convergence and distributivity.