Application of Heuristic and Metaheuristic Algorithms in Solving Constrained Weber Problem with Feasible Region Bounded by ArcsReport as inadecuate

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Mathematical Problems in Engineering - Volume 2017 2017, Article ID 8306732, 13 pages -

Research Article

Faculty of Computer Science, Goce Delčev University, Goce Delčev 89, 2000 Štip, Macedonia

Department of Mathematics and Informatics, Faculty of Science and Mathematics, University of Niš, Višegradska 33, 18000 Niš, Serbia

Department of Systems Analysis and Operations Research, Reshetnev University, Prosp. Krasnoyarskiy Rabochiy 31, Krasnoyarsk 660037, Russia

Correspondence should be addressed to Predrag S. Stanimirović

Received 26 February 2017; Accepted 15 May 2017; Published 14 June 2017

Academic Editor: Domenico Quagliarella

Copyright © 2017 Igor Stojanović et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The continuous planar facility location problem with the connected region of feasible solutions bounded by arcs is a particular case of the constrained Weber problem. This problem is a continuous optimization problem which has a nonconvex feasible set of constraints. This paper suggests appropriate modifications of four metaheuristic algorithms which are defined with the aim of solving this type of nonconvex optimization problems. Also, a comparison of these algorithms to each other as well as to the heuristic algorithm is presented. The artificial bee colony algorithm, firefly algorithm, and their recently proposed improved versions for constrained optimization are appropriately modified and applied to the case study. The heuristic algorithm based on modified Weiszfeld procedure is also implemented for the purpose of comparison with the metaheuristic approaches. Obtained numerical results show that metaheuristic algorithms can be successfully applied to solve the instances of this problem of up to 500 constraints. Among these four algorithms, the improved version of artificial bee algorithm is the most efficient with respect to the quality of the solution, robustness, and the computational efficiency.

Author: Igor Stojanović, Ivona Brajević, Predrag S. Stanimirović, Lev A. Kazakovtsev, and Zoran Zdravev



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