An Improved Pareto Front for the Non-Linear Multi-Objective Fixed Cost Transportation Problem

In this paper, we investigate a non-linear multi-objective optimization fixed-cost transportation problem (MOFCTP) with multiple modes of transport with given capacities, having two opposing objectives: minimization of the total transportation cost and minimization of the total distribution time. The investigated problem is addressed using a modified NSGA-II, achieved by using a priority-based representation by ranking the allocation of routes based on priority levels rather than directly working with transportation quantities, adapting an efficient priority-based decoding procedure, and integrating into its framework newly developed genetic operators tailored to accommodate multiple modes of transportation. The achieved computational results for the five existing instances from the literature prove that our modified NSGA-II outperforms the current state-of-the-art algorithms for solving the non-linear MOFCTP with multiple modes of transport with given capacities, providing an improved Pareto front.