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Direct Gravitational Search Algorithm for Global Optimisation Problems

Part of: Algorithms - Computer Science Optimality conditions

Published online by Cambridge University Press:  20 July 2016

Ahmed F. Ali  and
Mohamed A. Tawhid
Ahmed F. Ali*
Affiliation:
Department of Computer Science, Faculty of Computers & Informatics, Suez Canal University, Ismailia, Egypt Department of Mathematics and Statistics, Faculty of Science, Thompson Rivers University, Kamloops, BC, CanadaV2C 0C8
Mohamed A. Tawhid*
Affiliation:
Department of Mathematics and Statistics, Faculty of Science, Thompson Rivers University, Kamloops, BC, CanadaV2C 0C8 Department of Mathematics and Computer Science, Faculty of Science, Alexandria University, Moharam Bey 21511, Alexandria, Egypt
*
*Corresponding author. Email addresses:ahmed_fouad@i.suez.edu.eg (A. F. Ali), Mtawhid@tru.ca (M. A. Tawhid)
*Corresponding author. Email addresses:ahmed_fouad@i.suez.edu.eg (A. F. Ali), Mtawhid@tru.ca (M. A. Tawhid)
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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 algorithmdirect search methodsNelder-Mead methodinteger programming problemsminimax problems

MSC classification

Secondary: 49K35: Minimax problems 90C10: Integer programming 68U20: Simulation 68W05: Nonnumerical algorithms
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 6 , Issue 3 , August 2016 , pp. 290 - 313
Copyright
Copyright © Global-Science Press 2016 

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