Bi-objective Optimization of a Multi-product multi-period Fuzzy Possibilistic Capacitated Hub Covering Problem: NSGA-II and NRGA Solutions

Document Type: Original Manuscript


1 Faculty of Industrial and Mechanical Engineering, Qazvin Branch, Islamic Azad University, Qazvin, Iran

2 Department of Industrial Engineering, , Qazvin Branch, IslamicAzad University, Qazvin, Iran



The hub location problem is employed for many real applications, including delivery, airline and telecommunication systems and so on. This work investigates on hierarchical hub network in which a three-level network is developed. The central hubs are considered at the first level, at the second level, hubs are assumed which are allocated to central hubs and the remaining nodes are at the third level. In this research, a novel multi-product multi-objective model for capacitated hierarchical hub location problem with maximal covering under fuzzy condition first is suggested. Cost, time, hub and central hub capacities are considered as fuzzy parameters, whereas manyparameters are uncertainty and indeterministic in the real world. To solve the proposed fuzzy possibilistic multi-objective model, first, the model is converted to the equivalent auxiliary crisp model by hybrid method and then is solved by two meta-heuristic algorithms such as Non-Dominated Sorting Genetic Algorithm (NSGA-II) and Non-Dominated Ranked Genetic Algorithm (NRGA) using MATLAB software The statistical results report that there is no significant difference between means of two algorithms exception CPU time criteria. In general, in order to show efficiency of two algorithms, we used Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), the resultsclearly show that the efficiency of NRGA is better than NSGA-II and finally, figures are achieved  by MATLAB software that analyze the conflicting between two objectives.


  • The hierarchical hub network under multi-product situation is developed.
  • Two conflicting objectives are considered.
  • A fuzzy possibilistic programming model which deals with uncertainty is proposed.
  • Using ANOVA (statistical method) and TOPSIS (DM method) for comparing two solution methodologies (NSGA-II and NRGA) are proposed.
  • Changing in the Pareto solution and CPU time results, relies on changing the number of central hubs.


Main Subjects

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