UCPO: A Universal Constrained Combinatorial Optimization Method via Preference Optimization

TL;DR

UCPO is a flexible framework that enhances neural combinatorial solvers by integrating constraint satisfaction through preference learning, enabling efficient and feasible solutions on complex tasks with minimal additional training.

Contribution

UCPO introduces a plug-and-play preference optimization approach that embeds constraints into neural solvers without architectural changes or extensive tuning.

Findings

Achieves near-optimal solutions with only 1% of training budget.

Effectively handles complex constraints in combinatorial problems.

Improves solution feasibility and quality over traditional neural methods.

Abstract

Neural solvers have demonstrated remarkable success in combinatorial optimization, often surpassing traditional heuristics in speed, solution quality, and generalization. However, their efficacy deteriorates significantly when confronted with complex constraints that cannot be effectively managed through simple masking mechanisms. To address this limitation, we introduce Universal Constrained Preference Optimization (UCPO), a novel plug-and-play framework that seamlessly integrates preference learning into existing neural solvers via a specially designed loss function, without requiring architectural modifications. UCPO embeds constraint satisfaction directly into a preference-based objective, eliminating the need for meticulous hyperparameter tuning. Leveraging a lightweight warm-start fine-tuning protocol, UCPO enables pre-trained models to consistently produce near-optimal, feasible solutions on challenging constraint-laden tasks, achieving exceptional performance with as little as 1\% of the original training budget.