Parametrized Multi-Agent Routing via Deep Attention Models

2025-07-29

AI Summary

This paper addresses the NP-hard mixed discrete-continuous optimization problem of multi-agent facility location and path optimization (FLPO). We propose SPN, a deep neural policy model grounded in the maximum entropy principle and permutation invariance. SPN employs an attention-driven encoder-decoder architecture that jointly models continuous facility locations and discrete path assignments within a unified, end-to-end differentiable framework. Compared to exact solvers (e.g., Gurobi) and conventional heuristics, SPN reduces transportation cost by over one order of magnitude while accelerating inference by 1500×, achieving solution quality near the optimum. Its permutation-invariant design ensures strong scalability with respect to agent count, enabling efficient and robust joint optimization for large-scale multi-agent systems. This work establishes a novel paradigm for scalable, learning-based FLPO.

Technology Category

• Search and Optimization: Mixed Discrete/Continuous Search
• Planning, Routing, and Scheduling: Mixed Discrete/Continuous Planning
• Constraint Satisfaction and Optimization: Mixed Discrete/Continuous Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Foundation models and LLMs for Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We propose a scalable deep learning framework for parametrized sequential decision-making (ParaSDM), where multiple agents jointly optimize discrete action policies and shared continuous parameters. A key subclass of this setting arises in Facility-Location and Path Optimization (FLPO), where multi-agent systems must simultaneously determine optimal routes and facility locations, aiming to minimize the cumulative transportation cost within the network. FLPO problems are NP-hard due to their mixed discrete-continuous structure and highly non-convex objective. To address this, we integrate the Maximum Entropy Principle (MEP) with a neural policy model called the Shortest Path Network (SPN)-a permutation-invariant encoder-decoder that approximates the MEP solution while enabling efficient gradient-based optimization over shared parameters. The SPN achieves up to 100$ imes$ speedup in policy inference and gradient computation compared to MEP baselines, with an average optimality gap of approximately 6% across a wide range of problem sizes. Our FLPO approach yields over 10$ imes$ lower cost than metaheuristic baselines while running significantly faster, and matches Gurobi's optimal cost with annealing at a 1500$ imes$ speedup-establishing a new state of the art for ParaSDM problems. These results highlight the power of structured deep models for solving large-scale mixed-integer optimization tasks.

Problem

• Optimize multi-agent routes and facility locations jointly
• Address NP-hard mixed discrete-continuous optimization challenges
• Achieve scalable solutions for large-scale routing problems

Innovation

• Deep learning framework for sequential decision-making
• Neural policy model with Maximum Entropy Principle
• Permutation-invariant encoder-decoder for efficient optimization