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

Abstract

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.

Keywords:

• urban last-mile logistics
• green express cabinet assignment
• energy consumption
• multi-objective optimisation
• evolutionary algorithm

Notes

1 Without loss of generality, we assume that the power function has an analytical form and it is integrable as well.

2 If site j is a newly opened site, the initial holding amount for each Type l is 0.

3 If demand of Type l at site j is 0 and α_il=1, then β_ij=0; or, β_ij may be set to 0, if it is limited by other real-life conditions.

4 The unit of rated power is watt (W), and the unit of the total energy consumption in Formula (10) is kilowatt-hour (kWh).

5 The generator of these instances can be downloaded at https://www.researchgate.net/publication/322076995_InstancesGenerator.

6 The practical data of this Case Study can be downloaded at https://www.researchgate.net/publication/322075785_Case_Study.

7 These non-dominated solutions can be downloaded at https://www.researchgate.net/publication/322075872_Nondominated_solutions_of_Case_study.

Additional information

Funding

This research was partially supported by National Natural Science Foundation of China [grant number 71572031], and Philosophy and Social Science Fund, Liaoning, China [L16AZY032].