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.
['Yamin Alizadeh', 'Reza Tavakkoli-Moghaddam', 'Sadoullah Ebrahimnejad']
A new multi-objective model for a capacitated hub covering problem solving by two multi-objective evolutionary algorithms