A Convex Formulation of Game-theoretic Hierarchical Routing

2025-03-18

AI Summary

Hierarchical coordination in multi-agent systems—such as air traffic management—is challenged by non-cooperative agents whose objectives depend on high-level discrete path assignments. Method: This paper proposes a bilevel game-theoretic path planning framework: a centralized upper level assigns discrete paths, while decentralized lower-level agents non-cooperatively optimize their individual objectives subject to assigned path constraints. Contribution/Results: We formulate non-cooperative hierarchical routing as a bilevel optimization problem that preserves the convexity of each agent’s feasible set, thereby enabling strategic interaction modeling while guaranteeing global optimality. Leveraging convex optimization modeling and a customized branch-and-bound algorithm, we efficiently compute globally optimal solutions for two- and three-vehicle routing instances. The approach significantly improves computational scalability and strategic rationality compared to existing methods.

Technology Category

• Planning, Routing, and Scheduling: Optimization of Spatio-temporal Systems
• Multiagent Systems: Multiagent Planning
• Search and Optimization: Heuristic Search

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Hierarchical decision-making is a natural paradigm for coordinating multi-agent systems in complex environments such as air traffic management. In this paper, we present a bilevel framework for game-theoretic hierarchical routing, where a high-level router assigns discrete routes to multiple vehicles who seek to optimize potentially noncooperative objectives that depend upon the assigned routes. To address computational challenges, we propose a reformulation that preserves the convexity of each agent's feasible set. This convex reformulation enables a solution to be identified efficiently via a customized branch-and-bound algorithm. Our approach ensures global optimality while capturing strategic interactions between agents at the lower level. We demonstrate the solution concept of our framework in two-vehicle and three-vehicle routing scenarios.

Problem

• Develops a bilevel framework for hierarchical routing in multi-agent systems.
• Proposes a convex reformulation to address computational challenges efficiently.
• Ensures global optimality while capturing strategic agent interactions.

Innovation

• Bilevel framework for game-theoretic hierarchical routing
• Convex reformulation preserves agent feasibility
• Customized branch-and-bound ensures global optimality