SPO: Discovering Adaptive Large Neighborhood Search Operators via Stackelberg Program

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. It comes from a paper posted to arXiv on 28 September 2026. 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. Behavioral analyses further demonstrate state-dependent operator behavior and coupled destroy-repair improvement during discovery.

Why it counts

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.

Sources

Primary source: primary source

What is not known

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