A Multi Objective Model for Capacitated Hub Location Problem with Hierarchical Relations between Nodes, and its Solving by Meta heuristic Algorithm

In this research, Hub location problem was studied in an incomplete network with a Hierarchical structure. Allocation of nodes to the hub is single. Hub nodes and communication paths are capacitated. First objective function is as “Mini Max” type that used to minimize the maximum transfer time in the network. Second objective function is as “Mini Sum” type that considered to minimize the total transfer cost in the network. Eventually multi objective hub location problem is modeled with hierarchical structure, single assignment and capacitated using mixed integer programing. For numerical survey of the model, in the first the problem was solved in small size to be checked feasibility of model with GAMZ software and LP-Metric method. Due to the NP-Hard of problem, to solve the problem in medium and large size used Meta-heuristic methods. In this study used two Meta heuristic method as Noun-dominated sorting genetic algorithm (II) and multi-objective Aunt Lion optimizer algorithms. To compare the results used comparative criteria as the number of Pareto answers, maximum spread index, spacing metric and CPU time. Comparison of the results was done with a statistical method. Results showed Multi-objective Aunt Lion optimizer algorithm produced solution with more dispersion than Noun-dominated sorting genetic algorithm (II). In return Noun-dominated sorting genetic algorithm had faster solving speed than Multi-objective Aunt Lion optimizer algorithm.