A comparison between metaheuristics for solving a capacitated fixed charge transportation problem with multiple objectives

The main focus of this work is to formulate and solve a Fixed Charge Transportation Problem (FCTP) considering multiple modes of transport with different capacities. The condition for the feasibility is that the total capacity of all the modes of transport at each origin must be at least the total quantity of commodity available at the origin. The problem is modeled as a multi-objective minimization problem with two conflicting objectives: the total transportation cost and the total transportation time. For this purpose, crossover and mutation operators have been designed to make them suitable for the problem. The problem is solved by a modified NSGA-II, obtained by adapting the newly developed genetic operators in the metaheuristic structure of NSGA-II. Five numerical example problems of various sizes are solved using the modified NSGA-II. For a fair comparison of the perfor-mance of the modified NSGA-II, the same example problems are solved using two other algorithms: modified SPEA-2 and a modified GrEA, obtained by incorporating the same newly developed crossover and mutation respectively into SPEA-2 and GrEA. The results obtained by the modified NSGA-II, modified SPEA-2 and modified GrEA are compared using four performance metrics: RNI value, HV, Spacing and GS. The modified NSGA-II performs best for all example problems according to the metrics RNI value and GS, and for all the example problems except the example Problem 3 according to the metrics HV and spacing. For the example Problem 3, the modified GrEA yields the best performance with respect to the metrics HV and spacing. The modified SPEA2 performs worst in terms of all the metric values for all the example problems. Finally, some potential future research directions are discussed in the conclusion.