بررسی الگوریتم کرم شب تاب تصادفی

ABSTRACT On the Randomized Firefly Algorithm

Automatic problem solving with a digital computer has been the eternal quest of researchers in mathematics, computer science and engineering. The majority of complex problems (also NP-hard problems [1]) cannot be solved using exact methods by enumerating all the possible solutions and searching for the best solution (minimum or maximum value of objective function). Therefore, several algorithms have been emerged that solve problems in some smarter (also heuristic) ways. Nowadays, designers of the more successful algorithms draw their inspirations from Nature. For instance, the collective behavior of social insects like ants, termites, bees and wasps, or some animal societies like flocks of bird or schools of fish have inspired computer scientists to design intelligent multi-agent systems [2].

For millions of years many biological systems have solved complex problems by sharing information with group members [3]. These biological systems are usually very complex. They consists of particles (agents) that are definitely more complex than molecules and atoms, and are capable of performing autonomous actions within an environment. On the other hand, a group of particles is capable of intelligent behavior which is appropriate for solving complex problems in Nature. Therefore, it is no coincidence that these biological systems have also inspired computer scientists to imitate their intelligent behavior for solving complex problems in mathematics, physics, engineering, etc. Moreover, interest in researching various biological systems has increased recently. These various biological systems have been influenced by swarm intelligence (SI) that can be viewed as an artificial intelligence (AI) discipline concerned with the designing of intelligent systems.

It seems that the first use of the term ‘swarm intelligence’ was probably by Beni and Wang [4] in 1989 in the context of a cellular robotic system. Nowadays, this term also extends to the field of optimization, where techniques based on swarm intelligence have been applied successfully. Examples of notable swarm intelligence optimization techniques are ant colony optimization [5], particle swarm optimization [6], and artificial bees colony (ABC) [7, 8]. Today, the more promising swarm intelligence optimization techniques include the firefly algorithm (FA) [9–14], the cuckoo search [15], and the bat algorithm [16, 17].

Stochastic optimization searches for optimal solutions by involving randomness in some constructive way [18]. In contrast, if optimization methods provide the same results when doing the same things, these methods are said to be deterministic [19].

If the deterministic system behaves unpredictably, it arrives at a phenomenon of chaos [19]. As a result, randomness in SI algorithms plays a huge role because this phenomenon affects the exploration and exploitation in search process [20]. These companions of stochastic global search represent the two cornerstones of problem solving, i.e., exploration refers to moves for discovering entirely new regions of a search space, while exploitation refers to moves that focus searching the vicinity of promising, known solutions to be found during the search process. Both components are also referred to as intensification and diversification in another terminology [21]. However, these refer to medium- to long- term strategies based on the usage of memory (Tabu search), while exploration and exploitation refer to short-term strategies tied to randomness [20].

Essentially, randomness is used in SI algorithms in order to explore new points by moving the particles towards the search space. In line with this, several random distributions can be helpful. For example, uniform distribution generates each point of the search space using the same probability. On the other hand, Gaussian distribution is biased towards the observed solution, that is that the smaller modifications occur more often than larger ones [22]. On the other hand, the appropriate distribution depends on the problem to be solved, more precisely, on a fitness landscape that maps each position in the search space into fitness value. When the fitness landscape is flat, uniform distribution is more preferable for the stochastic search process, whilst in rougher fitness landscapes Gaussian distribution should be more appropriate.

This chapter deals with an FA algorithm that uses different randomization methods, like Uniform, Gaussian, Lévy flights, Chaotic maps, and the Random sampling in turbulent fractal cloud. Whilst the observed randomization methods are well known and widely used (e.g., uniform, Gaussian, Lévi flights, and chaotic maps), the random sampling in turbulent fractal cloud is taken from astronomy and, as we know, it is the first time used for the optimization purposes. Here, two well-known chaotic maps are also taken into account, i.e., Kent and Logistic.

The goal of our experimental work is to show how the different randomized methods influence the results of the modified FA. In line with this, a function optimization problem was solved by this algorithm. A suite of ten well-known functions were defined, as defined in the literature.

The structure of the rest of the chapter is as follows: Sect.2 describes a background information of various randomization methods. In Sect.3, the randomized firefly algorithms are presented. Experiments and results are illustrated in Sect.4. The chapter is finished summarizing our work and the directions for further development are outlined.