Evolutionary algorithm for multi-objective multi-index transportation problem under fuzziness

An Improved Genetic Algorithm (I-GA) for solving multi-objective Fuzzy Multi–Index Multi-objective Transportation Problem (FM-MOTP) is presented. Firstly, we introduce a new structure for the individual to be able to represent all possible feasible solutions. In addition, in order to keep the feasibility of the chromosome, a criterion of the feasibility was designed. Based on this criterion, the crossover and mutation were modified and implemented to generate feasible chromosomes. Secondly, an external archive of Pareto optimal solutions is used, which best conform a Pareto front. For avoiding an overwhelming number of solutions, the algorithm has a finite-sized archive of non-dominated solutions, which is updated iteratively at the presence of new solutions. Finally, the computational studies using two numerical problems, taken from the literature, demonstrate the effectiveness of the proposed algorithm to solve FM-MOTP Problem under fuzziness.