A discrete gravitational search algorithm for solving combinatorial optimization problems

Dowlatshahi M. B., Nezamabadi-Pour H., Mashinchi M.

INFORMATION SCIENCES, vol.258, pp.94-107, 2014 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 258
  • Publication Date: 2014
  • Doi Number: 10.1016/j.ins.2013.09.034
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.94-107
  • Çanakkale Onsekiz Mart University Affiliated: No


Hydrogels based on p(4-VP) of different dimensions were prepared and, after chemical modification, were used in the removal of one of the most potent toxic materials, cyanide. Macro and micron p(4-VP) hydrogel swelling behavior was evaluated in various aquatic environments. HCl, bromoethane, 1-bromobutane, 1-bromohexane, and 2-bromoethylamine were used as quaternizing agents to generate positive charges on both p(4-VP) macrogels and microgels. The modified p(4-VP) macrogels and microgels were used in cyanide ion removal for the first time from aqueous environments. The p(4-VP)-HCl at macro and micro sizes removed almost 49 and 61 mg cyanide ions per gram hydrogel in deionized water after modification, respectively. Moreover, the absorption capacity of the modified p(4-VP) hydrogel did not change significantly in tap, drinking, and creek waters. Parameters that affect the absorption process, such as cyanide concentration, contact time, hydrogel amount, and contaminated water source, were investigated. Additionally, magnetic field responsive macro and micro p(4-VP) hydrogel composites provided many advantages, such as easy handling after cyanide absorption, e.g., ready removal of cyanide-loaded p(4-VP) composites with an externally applied magnetic field. Langmuir and Freundlich adsorption isotherms were applied to the data obtained for cyanide uptake from aqueous environments.

Metaheuristics are general search strategies that, at the exploitation stage, intensively exploit areas of the solution space with high quality solutions and, at the exploration stage, move to unexplored areas of the solution space when necessary. The Gravitational Search Algorithm (GSA) is a stochastic population-based metaheuristic that was originally designed for solving continuous optimization problems. It has a flexible and well-balanced mechanism for enhancing exploration and exploitation abilities. In this paper, a Discrete Gravitational Search Algorithm (DGSA) is proposed to solve combinatorial optimization problems. The proposed DGSA uses a Path Re-linking (PR) strategy instead of the classic way in which the agents of GSA usually move from their current position to the position of other agents. The proposed algorithm was tested on a set of 54 Euclidean benchmark instances of TSP with sizes ranging from 51 to 2392 nodes. The results were satisfactory and in the majority of the instances, the results were equal to the best known solution. The proposed algorithm ranked ninth when compared with 54 different algorithms with regard to quality of the solution. (C) 2013 Elsevier Inc. All rights reserved.