An in-depth metaheuristic approach to design a sustainable closed-loop agri-food supply chain network

As an essential component of human life, agricultural products play a very important role in guaranteeing that individuals get all the essential nutrition. Governments and industries spend great financial resources, define short- and long-term goals, and organize their policies to develop a steady agri-food supply chain and provide fresh, healthy products to their societies. This work proposes a new mixed-integer linear programming model to propose an agri-food supply chain network design for the coconut industry under sustainable terms. This study mainly aims to solve a multi-objective closed-loop supply chain, considering both forward and reverse product movements. The model attempts to manage the net present value of total cost for specific planning horizons while monitoring environmental pollution and job opportunities within the network. Given the NP-hard nature of the network, the solution approach embraces a set of recently developed metaheuristics to overcome its complexity effectively. To this end, six multi-objective optimizers and three hybrid algorithms are utilized, among which the multi-objective artificial rabbit optimizer is first developed and applied in this study. Hence, the model's compatibility with real conditions is investigated using fifteen practical tests. The results of interval plots and the Friedman statistical test emphasize that optimizers can solve all sizes of problems. However, the Non-Dominated Sorting Genetic Algorithm-II (NSGA-II) outperforms solving practical tests according to both the results of statistical tests and the novel hybrid Multi-Criteria Decision Making (MCDM) framework.