Lagrangian Relaxation Score-based Generation for Mixed Integer linear Programming
arXiv:2603.24033v1 Announce Type: new Abstract: Predict-and-search (PaS) methods have shown promise for accelerating mixed-integer linear programming (MILP) solving. However, existing approaches typically assume variable independence and rely on deterministic single-point predictions, which limits solution diversityand often necessitates extensive downstream search for high-quality solutions. In this paper, we propose \textbf{SRG}, a generative framework based on Lagrangian relaxation-guided stochastic differential equations (SDEs), with theoretical guarantees on solution quality. SRG leverages convolutional kernels to capture inter-variable dependencies while integrating Lagrangian relaxation to guide the sampling process toward feasible and near-optimal regions. Rather than producing a single estimate, SRG generates diverse, high-quality solution candidates that collectively define compact and effective trust-region subproblems for standard MILP solvers. Across multiple public bench
arXiv:2603.24033v1 Announce Type: new Abstract: Predict-and-search (PaS) methods have shown promise for accelerating mixed-integer linear programming (MILP) solving. However, existing approaches typically assume variable independence and rely on deterministic single-point predictions, which limits solution diversityand often necessitates extensive downstream search for high-quality solutions. In this paper, we propose \textbf{SRG}, a generative framework based on Lagrangian relaxation-guided stochastic differential equations (SDEs), with theoretical guarantees on solution quality. SRG leverages convolutional kernels to capture inter-variable dependencies while integrating Lagrangian relaxation to guide the sampling process toward feasible and near-optimal regions. Rather than producing a single estimate, SRG generates diverse, high-quality solution candidates that collectively define compact and effective trust-region subproblems for standard MILP solvers. Across multiple public benchmarks, SRG consistently outperforms existing machine learning baselines in solution quality. Moreover, SRG demonstrates strong zero-shot transferability: on unseen cross-scale/problem instances, it achieves competitive optimality with state-of-the-art exact solvers while significantly reducing computational overhead through faster search and superior solution quality.
Executive Summary
The article proposes a novel generative framework, SRG, based on Lagrangian relaxation-guided stochastic differential equations (SDEs) for mixed-integer linear programming (MILP) solving. SRG leverages convolutional kernels to capture inter-variable dependencies and guides the sampling process toward feasible and near-optimal regions. The framework generates diverse, high-quality solution candidates and demonstrates strong zero-shot transferability. Empirical results show SRG's superiority over existing machine learning baselines in solution quality and its ability to achieve competitive optimality with state-of-the-art exact solvers while reducing computational overhead. This work has significant implications for solving large-scale MILP problems efficiently and effectively.
Key Points
- ▸ SRG leverages Lagrangian relaxation-guided SDEs for MILP solving
- ▸ SRG captures inter-variable dependencies using convolutional kernels
- ▸ SRG generates diverse, high-quality solution candidates
- ▸ SRG demonstrates strong zero-shot transferability
Merits
Strength in solution quality
SRG consistently outperforms existing machine learning baselines in solution quality, making it a valuable addition to the field of MILP solving.
Efficient computation
SRG reduces computational overhead through faster search and superior solution quality, making it a promising approach for large-scale MILP problems.
Zero-shot transferability
SRG achieves competitive optimality with state-of-the-art exact solvers on unseen cross-scale/problem instances, demonstrating its strong zero-shot transferability.
Demerits
Complexity of implementation
The proposed framework may be complex to implement, requiring expertise in machine learning and MILP solving.
Limited scalability
The effectiveness of SRG may be limited to smaller-scale MILP problems, and its performance may degrade for larger problems.
Expert Commentary
The proposed framework, SRG, represents a significant advancement in the field of MILP solving. By leveraging Lagrangian relaxation-guided SDEs and convolutional kernels, SRG effectively captures inter-variable dependencies and generates diverse, high-quality solution candidates. The empirical results demonstrate SRG's superiority over existing machine learning baselines and its ability to achieve competitive optimality with state-of-the-art exact solvers. However, the complexity of implementation and limited scalability of SRG are notable concerns. As the field continues to evolve, it will be essential to address these limitations and explore ways to further improve the efficiency and effectiveness of SRG.
Recommendations
- ✓ Future research should focus on developing more efficient and scalable implementations of SRG.
- ✓ Investigating the application of SRG to real-world problems and evaluating its practical impact is essential.
Sources
Original: arXiv - cs.LG
