LLM guided search improves adaptive solutions for route planning problems
SPO: Discovering Adaptive Large Neighborhood Search Operators via Stackelberg Program Optimization
Artificial Intelligence
Summary
Finding the best routes to visit many places, like for delivery trucks or salespeople, is a hard problem. The paper presents a new approach where two parts—breaking down a route and fixing it—learn to work together smartly based on the current problem state. This method uses advanced language models to discover adaptable strategies that improve over time. Tests show it beats other strong methods and works well even on bigger, tougher problems.
What this means in practice
- •For logistics planners: Enhance routing and delivery schedules by using adaptive operators that adjust dynamically to changing route conditions.
- •For software engineers: Develop optimization tools that use learned destroy-repair strategies for large-scale combinatorial problems like vehicle routing.
Authors
Xinyi Ke, Kai Li, Junliang Xing, Yifan Zhang, Jian Cheng
Abstract
Large neighborhood search (LNS) relies critically on destroy and repair operators, whose effectiveness depends on both adaptation to the evolving LNS state and interaction between the two roles. We introduce Stackelberg Program Optimization (SPO), an LLM-based framework for discovering adaptive executable destroy-repair programs. SPO conditions operator decisions on a compact LNS state, allowing state-dependent behavior to emerge through program discovery, and organizes destroy-repair discovery as a Stackelberg interaction over program space that reflects their asymmetric dependency. Role-specific credits evaluate destroy programs as leaders and repair programs as conditional follower responses, guiding a coupled optimization process that combines LLM generator learning with population-based evolutionary search over programs. Experiments on the traveling salesperson problem and capacitated vehicle routing problem show that SPO outperforms strong baselines across a broad range of settings and generalizes beyond the discovery scale to larger instances and benchmark sets. Behavioral analyses further demonstrate state-dependent operator behavior and coupled destroy-repair improvement during discovery.