Abstract
Abstract
This paper deals with three characteristics of transportation costs, crowding and traffic costs, and the costs of hub installation. The main aim of this paper is to define the independent cost function in order to connect to the crowding rate and incurred cost in an exponential way not considered in the literature directly. In this function, the independent variable is the crowding and traffic rate input, and the output is the cost incurred. However, involving three separate objective functions namely total cost, congestion and hub installation costs are not considered up to now. Also, considering the contrast among three foregoing costs, each function is considered independently. Due to the NP-hardness of this kind of problem to solve this multi-objective mathematical model, at first we devised an efficient approach to navigate through the feasible solution space iteratively without using penalty function. To solve our developed multi-objective mathematical model we propose five multi-objective meta-heuristic algorithms, namely 1) NSGA-II with an elitism solution, 2) NSGA-II without an elitism solution, 3) NRGA with an elitism solution, 4) NRGA without an elitism solution, and 5) MOPSO. Finally, three criteria are used to compare the related results obtained by these five algorithms.
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