en Mathematical Modeling and Applications of OR Mathematical Modeling and Applications of OR پژوهشی Original <span style="font-size:11pt"><span style="line-height:normal"><span style="text-autospace:none"><span new="" roman="" style="font-family:" times=""><i><span style="font-size:10.0pt"><span style="letter-spacing:-.25pt">Enhancing the efficacy and productivity of transportation system has been on the most common issues in recent decades, noteworthy to the industrial managers and expert so that the products are delivered to the clients at right time and the least costs. Therefore, there are two important issues; one is to create hub as the as intermediaries for streaming from multiple origins to multiple destinations and also responding to the tours of every hub at the proper time. The other is a route where the vehicles should pay at time window of each destination node. On the other hand, these problems may cause cost differences between hub and interruption of their balance. Accordingly, this paper presents a model dealing with cost balancing among the vehicles as well as reducing the total cost of the system. Given the multi-objective and NP-Hard nature of the issue, a multi-objective imperialist competitive algorithm (MOICA) is suggested to provide Pareto solutions. The provided solutions are at small, average and large scales are compared with the solutions provided by Non-Dominated Sorting Genetic Algorithm (NSGA-II) algorithm. Then, its performance is determined using the index for evaluating the algorithm performance efficacy to solve the problem at large dimensions.</span></span></i></span></span></span></span><br> &nbsp; Location-Routing Problem, Multiple Allocation, Hard Time Window, MOICA Algorithm 156 167 http://iors.ir/journal/browse.php?a_code=A-10-6049-1&slc_lang=en&sid=1 Amir-Mohammad Golmohammadi a-golmohammadi@araku.ac.ir 00031947532846002832 00031947532846002832 Yes Department of Industrial Engineering, Arak University, Arak, Iran. Hamidreza Abedsoltan abedsoltan@ut.ac.ir 00031947532846002833 00031947532846002833 No School of Industrial Engineering, College of Engineering, University of Tehran