# Cyber Firefly Algorithm Based on Adaptive Memory Programming for Global Optimization
## 1 Introduction
[PERSON] proposed the LFA [9] by combining his original FA with Levy flight. [PERSON] et al. employed the variable step size strategy to create the VESSFA [10] variant. The dynamic adaptive inertia weight was adopted in WFA [11] to use the short-term memory of previous moving velocity. [PERSON] et al. developed CLFA [12] which applies chaos theory and logical mapping to determine the optimal FA parameters. The Tidal Force formula was used in FAtidal [13] to improve the balance between exploitation and exploration search behaviors. The most recent improvement was GDAFA [14] which uses global-oriented positional update and dynamically adjusts the step size and attractiveness to avoid being trapped in local optima. The DsFA [15] employed dynamic step change strategy to balance the global and local search capabilities, such that the search course is not likely trapped in local optimum. From a long-term perspective of metaheuristic development, we anticipate that the GSO and the FA can be made more effective by incorporating the notions from the memory-based approaches, as validated in many previous attempts. Based on the prevailing framework of the cyber swarm algorithm [6] that integrates key elements of the two types of metaheuristic methods, we propose the Cyber Firefly Algorithm (CFA) to proliferate the advantages of the original form of the GSO and the FA. The CFA conceptions include the employment of multiple guiding fireflies, the embedding of the pattern search, firefly swarm rebuilding by the multi-start search, and the responsive strategies based on objective landscape analysis. The robustness of the CFA has been compared against the GSO, FA, and several state-of-the-art metaheuristic methods. The result as demonstrated in our statistical analyses and comprehensive experiments showed the CFA manifests a more effective form of GSO and FA. Most FA variants intend to improve the position update mechanism such as by using Levy flight [9], variable step size strategy [10], adaptive inertia weight [11], and dynamically adjusting strategy [14]. Our CFA differs with these variants by facilitating a more intelligent step size control mechanism which performs landscape analysis in the objective space to adaptively tune the step size according to the profiles of the incumbent fitness landscape. The novelty of this paper stems at creating a more effective form of GSO and FA approaches by bridging the advantages of evolution-based and memory-based metaheuristics. In particular, this paper investigates whether the CSA template is viable for improving GSO and FA as CSA has been shown in [6] for improving PSO. Our experimental results show that the proposed CFA prevails GSO, FA, and several state-of-the-art metaheuristics on benchmark datasets. This justifies the generalization capability of the CSA template and one can follow the template to create an effective version of interested metaheuristics. The remainder of this paper is organized as follows. Section 2 presents a literature review and Section 3 proposes the CFA and the employed features. Section 4 presents the results of intensive experiments. Finally, conclusions and future research possibilities are given in Section 5.