Abstract
Inspired by the collective behavior of fish schools, the fish school search (FSS) algorithm is a technique for finding globally optimal solutions. The algorithm is characterized by its simplicity and high performance; FSS is computationally inexpensive, compared to other evolution-inspired algorithms. However, the premature convergence problem is inherent to FSS, especially in the optimization of functions that are in very-high-dimensional spaces and have plenty of local minima or maxima. The accuracy of the obtained solution highly depends on the initial distribution of agents in the search space and on the predefined initial individual and collective-volitive movement step sizes. In this paper, we provide a study of different chaotic maps with symmetric distributions, used as pseudorandom number generators (PRNGs) in FSS. In addition, we incorporate exponential step decay in order to improve the accuracy of the solutions produced by the algorithm. The obtained results of the conducted numerical experiments show that the use of chaotic maps instead of other commonly used high-quality PRNGs can speed up the algorithm, and the incorporated exponential step decay can improve the accuracy of the obtained solution. Different pseudorandom number distributions produced by the considered chaotic maps can positively affect the accuracy of the algorithm in different optimization problems. Overall, the use of the uniform pseudorandom number distribution generated by the tent map produced the most accurate results. Moreover, the tent-map-based PRNG achieved the best performance when compared to other chaotic maps and nonchaotic PRNGs. To demonstrate the effectiveness of the proposed optimization technique, we provide a comparison of the tent-map-based FSS algorithm with exponential step decay (ETFSS) with particle swarm optimization (PSO) and with the genetic algorithm with tournament selection (GA) on test functions for optimization.
Highlights
With the increased use of artificial intelligence, decision support systems, forecasting, and expert systems in many enterprises, optimization problems arise more often in modern economic sectors.Such problems are widespread in computer science, engineering [1], and economics [2]
The accuracy of optimization results obtained by fish school search (FSS) heavily depends on the initial locations of agents in a fish school—the initial population X of solutions x i ∈ X—and the shape of the distribution produced by the pseudorandom number generators (PRNGs) that is used to generate individual and collective-volitive random movement vectors
The logistic map, which outperformed chaos-based PRNGs in Section 3.1, produces less accurate results when used as a PRNG in the fish school search evolution-inspired optimization algorithm with exponential step decay
Summary
With the increased use of artificial intelligence, decision support systems, forecasting, and expert systems in many enterprises, optimization problems arise more often in modern economic sectors. Zhiteng Ma et al in [33] used a modified version of the logistic map (1) to generate the initial locations of agents in the proposed chaotic particle swarm optimization algorithm. They conducted a series of experiments that verified the effectiveness of the implemented optimization technique. El-Shorbagy et al in [35] proposed a hybrid algorithm that integrates the genetic algorithm and a chaotic local search strategy to improve the convergence speed towards the globally optimal solution They considered several chaotic mappings, including the logistic map (1). The results of the numerical experiments show the outstanding advantage of tent-map-based chaotic PRNG performance, as well as the superiority of tent-map-based FSS with exponential step decay over PSO and GA
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