AFO-ideal point method algorithm flowchart.

As China’s "double carbon" goal continues to advance, logistics as a key area of carbon emissions and low-carbon logistics center site selection are key links in the process. However, existing studies on logistics center location often ignore the impact of demand uncertainty, which leads to a waste of resources in the planning and construction processes. We take logistics cost and carbon emission as the objectives, and the multi-objective site selection model established based on stochastic programming theory takes demand uncertainty as a stochastic constraint. We transform the stochastic constraint model into a 0–1 mixed integer multi-objective planning model by utilizing the idea of equivalence transformation. The Aptenodytes Forsteri Optimization (AFO) algorithm is combined with the Ideal Point Method to solve the model, and the algorithm is compared with the Particle Swarm Optimization (PSO), Differential Evolutionary (DE), Tabu Search (TS), Sparrow Search (SS) algorithms, and the exact solver Linear Interactive and General Optimizer (LINGO). The examples verify the validity of the models and algorithms, with an average reduction of 6.2% and 3.6% in logistics costs and carbon emissions in the case of demand determination, and at the confidence level of 0.9 under demand uncertainty, both logistics costs and carbon emissions are decreased to varying degrees. This study provides a new research idea for the low-carbon logistics location problem under demand uncertainty, which helps to promote the transformation of the logistics industry to low-carbon and high-efficiency.