A probability guided evolutionary algorithm for multi-objective green express cabinet assignment in urban last-mile logistics

In the past decade, urban last-mile logistics (ULML) has attracted increasing attention with the growth of e-commerce. Under this background, express cabinet has been gradually advocated to improve the efficiency of ULML. This paper focuses on the multi-objective green express cabinet assignment problem (MGECAP) in ULML, where the objectives to be minimised are the total cost and the energy consumption. MGECAP is concerned with optimising the purchase and assignment decision of express cabinets, which is different from conventional assignment problems. To solve MGECAP, firstly, the integer programming model and the corresponding surrogate model are established. Secondly, problem-dependent heuristics, including the solution representation, genetic operators, and repair strategy of infeasible solutions, are proposed. Thirdly, a probability guided multi-objective evolutionary algorithm based on decomposition (PG-MOEA/D) is proposed, which can balance the limited computation resource among sub-problems during the iterative process. Meanwhile, a feedback strategy is put forward to alternatively generate new solutions when the probability condition is not satisfied. Finally, numerical results and a real-life case study demonstrate the effectiveness and the practical values of the PG-MOEA/D.