Stepping ahead Firefly Algorithm and hybridization with evolution strategy for global optimization problems

Abstract Intelligent optimization algorithms based on swarm principles have been widely researched in recent times. The Firefly Algorithm (FA) is an intelligent swarm algorithm for global optimization problems. In literature, FA has been seen as an efficient and robust optimization algorithm. FA is an algorithm that has obtained good to best results in complex problems. Therefore, there are many instances of modification, and hybridization of FA with other optimizing algorithms, but further improvements are still possible. This research first proposes a new modification of FA by introducing a novel and unique stepping ahead parameter. The concept is based on being proactive rather than reactive, which is the normal behaviour of a standard FA. The notion behind stepping ahead is to send a firefly ahead then the best known position to look for even better solution. Second, a new design of a hybrid of the newly modified FA with Covariance Matrix Adaptation Evolution Strategy (CMAES) to improve the exploitation further while maintaining good exploration in the fireflies is presented. The main use of CMAES in this hybrid algorithm is to provide diversity to fireflies, as a result it improves exploitation. Traditionally, hybridization has combined two or more algorithms in terms of structure only, and consideration was not given to the increase in time complexity or diversity. In this paper, the two algorithms are not run in separate cycles rather CMAES is placed inside the FA. Through this novelty, CMAES is initiated inside FA loop and an extra loop is avoided and at the same time CMAES diversifies FA solutions. The structure of algorithm together with the strength of individual solution are used. The newly established modified FA and hybrid are used to solve selected sixty five global optimization benchmark problems together with eight real-world problems from CEC 2011. The proposed algorithms have outperformed FA algorithm in both benchmark and real-world problems. The optimal solutions found by FA in benchmark problems was 69.2% while FA-Step algorithm achieved 73.9% and FA-CMAES algorithm obtained 92.3%. In real-world problem, FA obtained 37.5%, FA-Step was 50% while FA-CMAES was 75%. The results invariably show that the proposed algorithms perform significantly better than the standalone methods as well as the algorithms from the literature.

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