Multi-objective optimization for a closed-loop network design problem using an improved genetic algorithm

This paper develops a multi-objective Mixed Integer Programming model for a closed-loop network design problem. In addition to the overall costs, the model optimizes overall carbon emissions and the responsiveness of the network. An improved genetic algorithm based on the framework of NSGA II is developed to solve the problem and obtain Pareto-optimal solutions. An example with 95 cities in China is presented to illustrate the approach. Through randomly generated examples with different sizes; the computational performance of the proposed algorithm is also compared with former genetic algorithms in the literature employing the weight-sum technique as a fitness evaluation strategy. Computational results indicate that the proposed algorithm can obtain superior Pareto-optimal solutions.