Title: A new multi-objective model for a capacitated hub covering problem solving by two multi-objective evolutionary algorithms

Authors: Yamin Alizadeh; Reza Tavakkoli-Moghaddam; Sadoullah Ebrahimnejad

Addresses: Department of Industrial Engineering South Tehran Branch, Islamic Azad University, Tehran, Iran ' School of Industrial Engineering, College of Engineering, University of Tehran, P.O. Box 11155/4563, Tehran, Iran ' Department of Industrial Engineering, College of Engineering, Karaj Branch, Islamic Azad University, Alborz, Iran

Abstract: This paper presents a new multi-objective mathematical model for a capacitated hub maximal covering problem (CHMCP) with the transfer flow and establishing costs of hubs that: 1) maximises hub covering; 2) minimises the cost of transportation and establishing hubs with c servers; 3) minimises the maximal capacity of hubs. So far, there has been little attention in the literature to consider all the foregoing objectives in one model simultaneously. Due to its complexity, this model is solved by two well-known multi-objective evolutionary algorithms; namely, non-dominated sorting genetic algorithm (NSGA-II) and non-dominated ranking genetic algorithm (NRGA). The computational results show that the proposed algorithms are usefulness and effectiveness to solve the presented model. In these algorithms, a penalty for the capacity violation is considered in order to control for the establishing cost of hubs. The comparison of the associated results is provided showing the NSGA-II outperforms the NRGA in terms of the solution quality and computational time for the most test problems. Finally, the remarkable conclusion is given.

Keywords: capacitated hub covering; multiple allocation hubs; capacity violation; non-dominated sorting genetic algorithms; NSGA-II; non-dominated ranking genetic algorithms; NRGA; multi-objective models; mathematical modelling; transfer flow.

DOI: 10.1504/IJMOR.2016.077559

International Journal of Mathematics in Operational Research, 2016 Vol.9 No.1, pp.99 - 124

Received: 18 Jul 2014
Accepted: 11 Oct 2014
Published online: 06 Jul 2016 *

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