<p>The focus of this paper is to provide an authentic approach to solving bi-objective optimization problems. The target problem is a novel extension of a multi-period $p$-mobile hub location problem, which takes into account the impact of the traveling time at the hubs' network, the time spent at each hub for processing the flows, and the delay caused by congestion at hubs with specific capacities. We first develop a mixed-integer mathematical model corresponding to the context problem. Afterward, a hybrid meta-heuristic algorithm will be proposed to solve the unveiled model that operates based on simultaneously employing a novel evaluation procedure, a clustering technique, and a genetic approach. The experiments validate that the proposed algorithm performs significantly better than several state-of-the-art algorithms. Furthermore, the decisive effect of two considerable factors: congestion and service time, are also analyzed.</p>

<pre>The focus of this paper is to propose a bi-objective mathematical model for a new extension of a multi-period p-mobile hub location problem and then to devise an algorithm for solving it. The developed model considers the impact of the time spent traveling at the hubs' network, the time spent at hubs for processing the flows, and the delay caused by congestion at hubs with specific capacities. Following the unveiled model, a hybrid meta-heuristic algorithm will be devised that simultaneously takes advantage of a novel evaluation function, a clustering technique, and a genetic approach for solving the proposed model.</pre>

<pre>The focus of this paper is to propose a bi-objective mathematical model for a new extension of a multi-period p-mobile hub location problem and then to devise an algorithm for solving it. The developed model considers the impact of the time spent traveling at the hubs' network, the time spent at hubs for processing the flows, and the delay caused by congestion at hubs with specific capacities. Following the unveiled model, a hybrid meta-heuristic algorithm will be devised that simultaneously takes advantage of a novel evaluation function, a clustering technique, and a genetic approach for solving the proposed model.</pre>