An improved firefly algorithm for global continuous optimization problems

Abstract Global continuous optimization is populated by its implementation in many real-world applications. Such optimization problems are often solved by nature-inspired and meta-heuristic algorithms, including the firefly algorithm (FA), which offers fast exploration and exploitation. To further strengthen FA’s search for global optimum, a Levy-flight FA (LF-FA) has been developed through sampling from a Levy distribution instead of the traditional uniform one. However, due to its poor exploitation in local areas, the LF-FA does not guarantee fast convergence. To address this problem, this paper provides an adaptive logarithmic spiral-Levy FA (AD-IFA) that strengthens the LF-FA’s local exploitation and accelerates its convergence. Our AD-IFA is integrated with logarithmic-spiral guidance to its fireflies’ paths, and adaptive switching between exploration and exploitation modes during the search process. Experimental results show that the AD-IFA presented in this paper consistently outperforms the standard FA and LF-FA for 29 test functions and 6 real cases of global optimization problems in terms of both computation speed and derived optimum.