Hybrid firefly algorithm with grouping attraction for constrained optimization problem

Abstract

Firefly algorithm (FA) is a new random swarm search optimization algorithm, which simulates the mutual attraction and movement process of flashing fireflies. The different attraction models in FAs have the different number of fitness comparisons and attractions. Too many attractions may result in search oscillations, too few attractions may lead to premature convergence, and too many fitness comparisons may lead to higher computational time complexity. To avoid above problems, a new grouping attraction model is proposed, which can effectively reduce the number of attractions and fitness comparisons. Inspired by the idea of particle swarm optimization position update, the firefly with higher fitness in the group are added with the guidance of the firefly with best fitness. To reduce the probability of the stagnation occurrence and premature convergence of the FA caused by less attractions and fitness comparisons, combination mutation operator is introduced to FA, which can better balance the exploration and exploitation capabilities of the FA. Therefore, hybrid firefly algorithm with grouping attraction (HFA-GA) is given for constrained optimization. Experiments are conducted using CEC 2017 constrained optimization problems and four practical engineering optimization problems. The results show that the HFA-GA can efficiently improve the quality of solutions.