A self-adaptive strategy based firefly algorithm for constrained engineering design problems

Abstract Firefly algorithm (FA) is an effective meta-heuristic method, which has drawn extensive attentions and inspired many variants. However, it is difficult to balance the relation of the exploration and exploitation of FA. To this end, FA with self-adaptive strategy (SAFA) is proposed to improve the performance of the algorithm for constrained engineering design problems. Firstly, the characteristics of the standard FA are analyzed, and the essence of FA easily trapped into the local optima is revealed by theory analysis and case study. Secondly, a self-adaptive strategy for attraction model is proposed to improve the exploitation ability, and another self-adaptive strategy for stochastic model is developed to ensure a better balance between the exploration and exploitation. Thirdly, a self-adaptive penalty function is presented to treat constraint conditions. Then, the initial parameter setting is investigated, and the proper initial parameter value corresponding to the optimal performance of SAFA is obtained. And then, SAFA and other FA variants are used to optimize a set of classical and Congress on Evolutionary Computation (CEC) 2015 benchmark functions. Meanwhile, the contributions of self-adaptive strategies for attraction model and stochastic model are investigated with experimental analysis, respectively Finally, SAFA and other meta-heuristic methods are employed to solve constrained engineering design problems. The effects of SAFA with standard and self-adaptive penalty function are compared. Numerical experimental results show that self-adaptive strategies for attraction model and stochastic model improve the performance of FA, and SAFA obtains the best solutions on most of the benchmark functions. In addition, SAFA has the advantage in solving problems with different kind of dimensions, and maintains reasonable population diversity throughout the iteration compared with the other FA variants. Meanwhile, SAFA can reduce the computational complexity and ensure the solution accuracy in solving constrained optimization problems.