Towards Efficient Constraint Handling in Neural Solvers for Routing Problems
arXiv:2602.16012v1 Announce Type: new Abstract: Neural solvers have achieved impressive progress in addressing simple routing problems, particularly excelling in computational efficiency. However, their advantages under complex constraints remain nascent, for which current constraint-handling schemes via feasibility masking or implicit feasibility awareness can be inefficient or inapplicable for hard constraints. In this paper, we present Construct-and-Refine (CaR), the first general and efficient constraint-handling framework for neural routing solvers based on explicit learning-based feasibility refinement. Unlike prior construction-search hybrids that target reducing optimality gaps through heavy improvements yet still struggle with hard constraints, CaR achieves efficient constraint handling by designing a joint training framework that guides the construction module to generate diverse and high-quality solutions well-suited for a lightweight improvement process, e.g., 10 steps ver
arXiv:2602.16012v1 Announce Type: new Abstract: Neural solvers have achieved impressive progress in addressing simple routing problems, particularly excelling in computational efficiency. However, their advantages under complex constraints remain nascent, for which current constraint-handling schemes via feasibility masking or implicit feasibility awareness can be inefficient or inapplicable for hard constraints. In this paper, we present Construct-and-Refine (CaR), the first general and efficient constraint-handling framework for neural routing solvers based on explicit learning-based feasibility refinement. Unlike prior construction-search hybrids that target reducing optimality gaps through heavy improvements yet still struggle with hard constraints, CaR achieves efficient constraint handling by designing a joint training framework that guides the construction module to generate diverse and high-quality solutions well-suited for a lightweight improvement process, e.g., 10 steps versus 5k steps in prior work. Moreover, CaR presents the first use of construction-improvement-shared representation, enabling potential knowledge sharing across paradigms by unifying the encoder, especially in more complex constrained scenarios. We evaluate CaR on typical hard routing constraints to showcase its broader applicability. Results demonstrate that CaR achieves superior feasibility, solution quality, and efficiency compared to both classical and neural state-of-the-art solvers.
Executive Summary
This article presents Construct-and-Refine (CaR), a novel framework for efficiently handling complex constraints in neural solvers for routing problems. CaR achieves this through a joint training framework that guides the construction module to generate diverse and high-quality solutions, suitable for a lightweight improvement process. The framework also employs a construction-improvement-shared representation, enabling knowledge sharing across paradigms. The authors evaluate CaR on typical hard routing constraints and demonstrate its superiority in feasibility, solution quality, and efficiency compared to classical and neural state-of-the-art solvers. This contribution has the potential to significantly impact the field of routing problems and neural solvers, particularly in complex constrained scenarios.
Key Points
- ▸ CaR presents a general and efficient constraint-handling framework for neural routing solvers
- ▸ The framework employs a joint training approach to guide solution construction and refinement
- ▸ CaR achieves superior performance in feasibility, solution quality, and efficiency compared to existing methods
Merits
Strength
CaR's joint training framework enables the generation of diverse and high-quality solutions, suitable for lightweight improvement processes.
Strength
The framework's construction-improvement-shared representation facilitates knowledge sharing across paradigms, particularly in complex constrained scenarios.
Demerits
Limitation
The article primarily focuses on routing problems and may not demonstrate generalizability to other problem domains.
Limitation
The computational efficiency of CaR may be sensitive to the choice of hyperparameters and may require further tuning for specific problem instances.
Expert Commentary
While CaR presents a significant advancement in constraint handling for neural solvers, its generalizability and applicability to other problem domains remain to be explored. Furthermore, the article's focus on routing problems may limit its broader impact. Nevertheless, the framework's potential to facilitate knowledge sharing across paradigms and its computational efficiency make it an exciting development in the field. As the authors note, CaR's contribution has significant implications for the field of neural solvers and routing problems, particularly in complex constrained scenarios. The development of CaR highlights the potential of AI-powered optimization techniques in addressing real-world routing problems and may inform policy decisions regarding the adoption of these methods.
Recommendations
- ✓ Future research should focus on exploring CaR's generalizability to other problem domains and its applicability in various industries and domains.
- ✓ The authors should investigate the sensitivity of CaR's computational efficiency to hyperparameter choices and explore methods for tuning these parameters for specific problem instances.
