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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.

  • AMS Subject Headings

49K35, 90C10, 68U20, 68W05

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-6-290, author = {Ahmed F. Ali and Mohamed A. Tawhid}, 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 AU - Ahmed F. Ali & Mohamed A. Tawhid JO - East Asian Journal on Applied Mathematics VL - 3 SP - 290 EP - 313 PY - 2018 DA - 2018/02 SN - 6 DO - http://doi.org/10.4208/eajam.030915.210416a UR - https://global-sci.org/intro/article_detail/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 and Mohamed A. Tawhid. (2018). 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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