Learning to Solve Multi-Objective Routing Problems on Multigraphs

2025-06-27

AI Summary

This paper addresses the multi-objective routing problem in multi-graph environments, where multiple heterogeneous paths—each with distinct attributes—exist between nodes, necessitating joint optimization of conflicting objectives. To overcome limitations of conventional methods in modeling both multi-graph structures and multi-objective trade-offs, we propose the first learning-based end-to-end framework. Our method comprises two core components: (i) an attention-driven autoregressive edge selection mechanism that constructs routes sequentially, and (ii) a learnable graph pruning strategy that compresses the original multi-graph into a single weighted graph to reduce computational complexity. Evaluated on the Traveling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP), our approach significantly outperforms existing baselines. Results demonstrate strong effectiveness, generalizability across diverse routing instances, and scalability to larger problem sizes—establishing its viability for real-world multi-graph routing tasks.

Technology Category

• Planning, Routing, and Scheduling: Learning for Planning and Scheduling
• Search and Optimization: Learning to Search
• Machine Learning: Graph-based Machine Learning

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

Learning-based methods for routing have gained significant attention in recent years, both in single-objective and multi-objective contexts. However, the multigraph setting, where multiple paths with distinct attributes can exist between destinations, has largely been overlooked, despite its high practical relevancy. In this paper, we introduce two neural approaches to address multi-objective routing on multigraphs. Our first approach works directly on the multigraph, by autoregressively selecting edges until a tour is completed. On the other hand, our second model first prunes the multigraph into a simple graph and then builds routes. We validate both models experimentally and find that they demonstrate strong performance across a variety of problems, including the Traveling Salesman Problem (TSP) and Capacitated Vehicle Routing Problem (CVRP).

Problem

• Addresses multi-objective routing on multigraphs
• Overlooked multigraph setting with practical relevance
• Proposes neural approaches for TSP and CVRP

Innovation

• Autoregressive edge selection for multigraph routing
• Multigraph pruning into simple graph first
• Neural approaches for multi-objective routing problems