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Gravitational search algorithm with both attractive and repulsive forces

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Abstract

The gravitational search algorithm (GSA) is a meta-heuristic optimization algorithm which is inspired by the gravity force. This algorithm uses Newton’s gravity and motion laws to calculate the masses interactions and shows high performance in solving optimization problems. The premature convergence is the common drawback of heuristic search algorithms in high-dimensional problems, and GSA is not an exception. In this paper, a new version of GSA is proposed to improve the power of GSA in exploration and exploitation. The proposed algorithm has both attractive and repulsive forces. In this algorithm, the heavy particles attract some particles and repulse some others, in which the forces are inversely proportional to their distances. For better evaluation, the GSA with both attractive and repulsive forces (AR-GSA) is tested using CEC 2013 benchmark functions and the results are compared with some well-known meta-heuristic algorithms. The simulation results show that AR-GSA can improve the convergence rate, the exploration, and the exploitation capabilities of GSA.

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Authors and Affiliations

  1. Department of Electrical Engineering, Shahid Bahonar University of Kerman, Kerman, Iran

    Hamed Zandevakili & Ali Mahani

  2. Department of Electrical Engineering, Graduate University of Advanced Technology, Kerman, Iran

    Esmat Rashedi

Authors
  1. Hamed Zandevakili
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  2. Esmat Rashedi
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  3. Ali Mahani
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Correspondence to Hamed Zandevakili.

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Conflict of interest

Hamed Zandevakili, Esmat Rashedi, and Ali Mahani declare that they have no conflict of interest.

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This article does not contain any studies with human participants or animals performed by any of the authors.

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Communicated by V. Loia.

Appendix A: Complexity analysis method

Appendix A: Complexity analysis method

To compute the computational complexity of the algorithms the following phases should be done (http://www.ntu.edu.sg/home/EPNSugan/index_files/CEC2013/CEC2013.htm):

  1. (a)

    Run the test program below:

    for i \(=\) 1:1,000,000

    $$\begin{aligned} x= & {} 0.55 + (\hbox {double}) i;\\ x= & {} x+ x; x=x./2; x=x*x; x=\hbox {sqrt}(x);\\ x= & {} \hbox {log}(x); x=\hbox {exp}(x); y=x/x; \end{aligned}$$

    end

    Computation time for the above \(=\) \(T_0\);

  2. (b)

    Evaluate the computation time just for Function 14. For 200,000 evaluations of a certain dimension D, it gives \(T_1\);

  3. (c)

    The complete computation time for the algorithm with 200,000 evaluations of the same D-dimensional benchmark function 14 is T2.

  4. (d)

    Execute step c five times and get 5 \(T_2\) values. \(\hat{{T}}_2 =\hbox {mean}(T_2)\).

The complexity of the algorithm is reflected by: \(T_0, T_1,\hat{{T}}_2, (\hat{{T}}_2 -T_1 )/T_0\).

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Zandevakili, H., Rashedi, E. & Mahani, A. Gravitational search algorithm with both attractive and repulsive forces. Soft Comput 23, 783–825 (2019). https://doi.org/10.1007/s00500-017-2785-2

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