An evolutionary bi-objective approach to the capacitated facility location problem with cost and CO2 emissions

It is strategically important to design efficient and environmentally friendly distribution networks. In this paper we propose a new methodology for solving the capacitated facility location problem (CFLP) based on combining an evolutionary multi-objective algorithm with Lagrangian Relaxation where financial costs and CO2 emissions are considered simultaneously. Two levels of decision making are required: 1) which facilities to open from a set of potential sites, and 2) which customers to assign to which open facilities without violating their capacity. We choose SEAMO2 (Simple Evolutionary Multi-objective Optimization 2) as our multi-objective evolutionary algorithm to determine which facilities to open, because of its fast execution speed. For the allocation of customers to open facilities we use a Lagrangian Relaxation technique. We test our approach on large problem instances with realistic qualities, and validate solution quality by comparison with extreme solutions obtained using CPLEX.