End-to-End Pareto Set Prediction with Graph Neural Networks for Multi-objective Facility Location

The facility location problems (FLPs) are a typical class of NP-hard combinatorial optimization problems, which widely seen in the supply chain and logistics. Many mathematical heuristic algorithms have been developed for optimizing FLP. In addition to transportation cost, there usually multiple conflicting objectives realistic applications. It is therefore desirable design that approximate set Pareto solutions efficiently without enormous search cost. this paper, we consider multi-objective problem (MO-FLP) simultaneously minimizes overall cost maximizes system reliability. We develop learning-based approach predicting distribution probability entire given problem. To end, MO-FLP modeled as bipartite graph two neural networks constructed learn implicit representation on nodes edges. network outputs then converted into set, from non-dominated can be sampled non-autoregressively. Experimental results instances different scales show proposed achieves comparable performance used evolutionary algorithm terms solution quality while significantly reducing computational search.