A novel x -shaped binary particle swarm optimization
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METHODOLOGIES AND APPLICATION
A novel x-shaped binary particle swarm optimization Zahra Beheshti1,2
Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Definitive optimization algorithms are not able to solve high-dimensional optimization problems because the search space grows exponentially with the problem size and an exhaustive search will be impractical. Therefore, approximate algorithms are applied to solve them. A category of approximate algorithms are meta-heuristic algorithms. They have shown an acceptable efficiency to solve these problems. Among them, particle swarm optimization (PSO) is one of the well-known swarm intelligence algorithms to optimize continuous problems. A transfer function is applied in this algorithm to convert the continuous search space to the binary one. The role of the transfer function in binary PSO (BPSO) is very important to enhance its performance. Several transfer functions have been proposed for BPSO such as S-shaped, V-shaped, linear and other transfer functions. However, BPSO algorithm can sometimes find local optima or show slow convergence speed in some problems because of using the velocity of PSO and these transfer functions. In this study, a novel transfer function called x-shaped BPSO (XBPSO) is proposed to increase exploration and exploitation of BPSO in the binary search space. The transfer function uses two functions and improved rules to generate a new binary solution. The proposed method has been run on 33 benchmark instances of the 0–1 multidimensional knapsack problem (MKP), two discrete maximization functions and 23 minimization functions. The results have been compared with some well-known BPSO and discrete metaheuristic algorithms. The results showed that x-shaped transfer function considerably increased the solution accuracy and convergence speed in BPSO algorithm. The average error of compared algorithms on all 0–1 MKP benchmark instances indicated that XBPSO has the minimum error of 8.9%. Also, the mean absolute error (MAE) obtained by XBPSO on two discrete maximization functions is 0.45. Moreover, the proposed transfer function provides superior solutions in 18 functions from 23 minimization functions. Keywords Binary particle swarm optimization (BPSO) Transfer function S-shaped, V-shaped and linear transfer functions x-shaped transfer function
1 Introduction Many optimization problems are in the class of NP-hard problems. Exact algorithms are not able to solve these problems in a reasonable time, because the search space exponentially grows with increasing the problem dimension. Meta-heuristic algorithms, which are in the category
Communicated by V. Loia. & Zahra Beheshti [email protected] 1
Faculty of Computer Engineering, Najafabad Branch, Islamic Azad University, Najafabad, Iran
2
Big Data Research Center, Najafabad Branch, Islamic Azad University, Najafabad, Iran
of approximate algorithms, show good performance in solving these problems. One of the well-known metaheuri
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