Hybrid multi-strategy firefly algorithm for solving optimization problems with constraints

We propose a hybrid multi-strategy firefly algorithm (HMSFA-PC) for solving constrained optimization problems. Firstly, an improved dynamic penalty function strategy is proposed to preprocess the constrained optimization problem so as to convert it into an unconstrained optimization problem. Secondly, the firefly algorithm itself is improved: the Lévy flights search mechanism is adopted to effectively increase the search range; a random expansion factor is introduced to improve the attraction model of the algorithm so that the population breaks through the constraint, effectively avoiding premature convergence and maintaining the population convergence; an adaptive dimensional reorganization mechanism is proposed to maintain the population convergence. The adaptive dimensional reorganization mechanism is proposed to select individuals with greater variability according to different iteration periods to interact with information and learn from each other, effectively improving the diversity of the population. To test the performance of the algorithm in dealing with unconstrained optimization problems, it is compared with some typical algorithms on the benchmark test function; to test the performance of the algorithm to deal with constrained optimization problems, it is compared with some top constraint solving algorithms on actual constraint test problems. The results show that the HMSFA-PC has the advantages of fast convergence and high convergence accuracy when dealing with unconstrained optimization problems, and still has good optimization performance when solving real constrained optimization problems with the collaboration of dynamic penalty functions. © 2024 Northeast University. All rights reserved.