# Cyber Firefly Algorithm Based on Adaptive Memory Programming for Global Optimization
## 1 Introduction  
Many challenging problems in modern engineering and business domains challenge the design of satisfactory algorithms. Traditionally, researchers resort to either mathematical programming approaches or heuristic algorithms. However, mathematical programming approaches are plagued by the curse of problem size and the heuristic algorithms have no guarantees to near-optimal solutions. Recently, metaheuristic approaches have come as an alternative between the two extreme approaches. The metaheuristic approaches can be classified into two classes, evolution-based and memory-based algorithms. The evolutionary algorithms (EAs) iteratively improve solution quality by decent operations inspired by nature metaphors, creating several novel algorithms, such as genetic algorithms, artificial immune systems, ant colony optimization, and particle swarm optimization. The memory-based metaheuristic approaches guide the search course to go beyond the local optimality by taking full advantage of adaptive memory manipulations. Typical renowned methods in this class include tabu search, path relinking, scatter search, variable neighborhood search, and greedy randomized adaptive search procedures (GRASP). The metaheuristic approaches contained in the two classes have developed rather independently, and only a few works investigate the possible synergy between them [1]. [PERSON] and [PERSON] [2] proposes the COSEARCH approach which combines the tabu search and a genetic algorithm for solving the quadratic assignment problem. [PERSON] et al. [3] proposes an approach called HPSOTSwhich enables the particle swarm optimization to circumvent local optima by restraining the particle movement based on the use of tabu memory. A hybrid of the ant colony optimization and the GRASP is proposed by [PERSON] et al. [4] for cluster analysis. However, the two metaheuristics are separately used to tackle the feature selection and clustering problems, respectively. [PERSON] and [PERSON] [5] proposes a hybrid genetic algorithm (GA) with variable neighborhood search (VNS) to the number partitioning problem. Their hybrid GA-VNS runs the GA as the main algorithm and the VNS procedure for improving individuals within the population. [PERSON] et al. [6] introduces the cyber swarm algorithm which gives more substance to the particle swarm optimization (PSO) by incorporating the adaptive memory programming (AMP) strategies introduced in the scatter search and path-relinking (SS/PR) template. The adjective \"cyber\" emphasizes the connection between the evolutionary swarm metaheuristics and the AMP metaheuristics. The cyber swarm algorithm outperforms several state-of-the-art metaheuristics on complex benchmark functions. The experimental results of the above-noted works disclose a promising research area that the marrying of the approaches from the two classes of metaheuristics can create significant benefit that is hardly obtained by the approaches from each class alone. More recently, two evolution-based algorithms [7; 8], namely the glowworm swarm optimization (GSO) and the firefly algorithm (FA), were proposed. The two algorithms were inspired by the bioluminescence process that enables the light-mediated swarming behavior for mating or foraging. The intensity of the light and the distance between the light source and the observer determine the attractiveness degree that causes the moving maneuver. This form of metaphor can be used to develop a swarm-based optimization algorithm where a swarm of glowworms/fireflies represent a set of candidate solutions. The light intensity is evaluated by the objective value of the light source and the distance between the glowworms/fireflies implicitly defines the eligible neighbors since the light observed by an agent decays with the distance. The glowworms/fireflies are attracted by visible light sources and fly towards them. Therefore, the solutions represented by the glowworms/fireflies improve their objective value through the swarming behavior. Several improvements of FA have been proposed.