Volume 6, Issue 3
Direct Gravitational Search Algorithm for Global Optimisation Problems

Ahmed F. Ali & Mohamed A. Tawhid

East Asian J. Appl. Math., 6 (2016), pp. 290-313.

Published online: 2018-02

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  • Abstract

A gravitational search algorithm (GSA) is a meta-heuristic development that is modelled on the Newtonian law of gravity and mass interaction. Here we propose a new hybrid algorithm called the Direct Gravitational Search Algorithm (DGSA), which combines a GSA that can perform a wide exploration and deep exploitation with the Nelder-Mead method, as a promising direct method capable of an intensification search. The main drawback of a meta-heuristic algorithm is slow convergence, but in our DGSA the standard GSA is run for a number of iterations before the best solution obtained is passed to the Nelder-Mead method to refine it and avoid running iterations that provide negligible further improvement. We test the DGSA on 7 benchmark integer functions and 10 benchmark minimax functions to compare the performance against 9 other algorithms,and the numerical results show the optimal or near optimal solution is obtained faster.

  • Keywords

Gravitational search algorithm, direct search methods, Nelder-Mead method, integer programming problems, minimax problems.

  • AMS Subject Headings

49K35, 90C10, 68U20, 68W05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-6-290, author = {}, title = {Direct Gravitational Search Algorithm for Global Optimisation Problems}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {6}, number = {3}, pages = {290--313}, abstract = {

A gravitational search algorithm (GSA) is a meta-heuristic development that is modelled on the Newtonian law of gravity and mass interaction. Here we propose a new hybrid algorithm called the Direct Gravitational Search Algorithm (DGSA), which combines a GSA that can perform a wide exploration and deep exploitation with the Nelder-Mead method, as a promising direct method capable of an intensification search. The main drawback of a meta-heuristic algorithm is slow convergence, but in our DGSA the standard GSA is run for a number of iterations before the best solution obtained is passed to the Nelder-Mead method to refine it and avoid running iterations that provide negligible further improvement. We test the DGSA on 7 benchmark integer functions and 10 benchmark minimax functions to compare the performance against 9 other algorithms,and the numerical results show the optimal or near optimal solution is obtained faster.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.030915.210416a}, url = {http://global-sci.org/intro/article_detail/eajam/10800.html} }
TY - JOUR T1 - Direct Gravitational Search Algorithm for Global Optimisation Problems JO - East Asian Journal on Applied Mathematics VL - 3 SP - 290 EP - 313 PY - 2018 DA - 2018/02 SN - 6 DO - http://dor.org/10.4208/eajam.030915.210416a UR - https://global-sci.org/intro/eajam/10800.html KW - Gravitational search algorithm, direct search methods, Nelder-Mead method, integer programming problems, minimax problems. AB -

A gravitational search algorithm (GSA) is a meta-heuristic development that is modelled on the Newtonian law of gravity and mass interaction. Here we propose a new hybrid algorithm called the Direct Gravitational Search Algorithm (DGSA), which combines a GSA that can perform a wide exploration and deep exploitation with the Nelder-Mead method, as a promising direct method capable of an intensification search. The main drawback of a meta-heuristic algorithm is slow convergence, but in our DGSA the standard GSA is run for a number of iterations before the best solution obtained is passed to the Nelder-Mead method to refine it and avoid running iterations that provide negligible further improvement. We test the DGSA on 7 benchmark integer functions and 10 benchmark minimax functions to compare the performance against 9 other algorithms,and the numerical results show the optimal or near optimal solution is obtained faster.

Ahmed F. Ali & Mohamed A. Tawhid. (2020). Direct Gravitational Search Algorithm for Global Optimisation Problems. East Asian Journal on Applied Mathematics. 6 (3). 290-313. doi:10.4208/eajam.030915.210416a
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