A genetic algorithm with two-step rank-based encoding for closed-loop supply chain network design.

The closed-loop supply chain (CLSC) plays an important role in sustainable development and can help to increase the economic benefits of enterprises. The optimization for the CLSC network is a complicated problem, since it often has a large problem scale and involves multiple constraints. This paper proposes a general CLSC model to maximize the profits of enterprises by determining the transportation route and delivery volume. Due to the complexity of the multi-constrained and large-scale model, a genetic algorithm with two-step rank-based encoding (GA-TRE) is developed to solve the problem. Firstly, a two-step rank-based encoding is designed to handle the constraints and increase the algorithm efficiency, and the encoding scheme is also used to improve the genetic operators, including crossover and mutation. The first step of encoding is to plan the routes and predict their feasibility according to relevant constraints, and the second step is to set the delivery volume based on the feasible routes using a rank-based method to achieve greedy solutions. Besides, a new mutation operator and an adaptive population disturbance mechanism are designed to increase the diversity of the population. To validate the efficiency of the proposed algorithm, six heuristic algorithms are compared with GA-TRE by using different instances with three problem scales. The results show that GA-TRE can obtain better solutions than the competitors, especially on large-scale instances.