NCO4CVRP: Neural Combinatorial Optimization for the Capacitated Vehicle Routing Problem

2026-04-17

AI Summary

This work proposes an enhanced inference framework for the Capacitated Vehicle Routing Problem (CVRP) that integrates Simulated Annealing with Randomized Reconstruction (SA-RRC) and beam search to improve solution quality and generalization of neural combinatorial optimization models. By systematically combining SA-RRC to escape local optima and beam search to broaden solution space exploration, and further incorporating strategies such as Softmax sampling, Gumbel-Softmax, Epsilon-Greedy selection, and geometric data augmentation, the method significantly reduces optimality gaps across multiple CVRP benchmarks. Experimental results demonstrate that the combination of beam search and SA-RRC yields the best performance, confirming the effectiveness and robustness of the proposed approach during inference.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Computer Vision: Learning & Optimization for CV
• Constraint Satisfaction and Optimization: Search

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Economics, Online Markets and Human Computation: LLM based quality controls for crowd work

Abstract

Neural Combinatorial Optimization (NCO) has emerged as a powerful framework for solving combinatorial optimization problems by integrating deep learning-based models. This work focuses on improving existing inference techniques to enhance solution quality and generalization. Specifically, we modify the Random Re-Construct (RRC) approach of the Light Encoder Heavy Decoder (LEHD) model by incorporating Simulated Annealing (SA). Unlike the conventional RRC, which greedily replaces suboptimal segments, our SA-based modification introduces a probabilistic acceptance mechanism that allows the model to escape local optima and explore a more diverse solution space. Additionally, we enhance the Policy Optimization with Multiple Optima (POMO) approach by integrating Beam Search, enabling systematic exploration of multiple promising solutions while maintaining diversity in the search space. We further investigate different inference strategies, including Softmax Sampling, Greedy, Gumbel-Softmax, and Epsilon-Greedy, analyzing their impact on solution quality. Furthermore, we explore instance augmentation techniques, such as horizontal and vertical flipping and rotation-based augmentations, to improve model generalization across different CVRP instances. Our extensive experiments demonstrate that these modifications significantly reduce the optimality gap across various Capacitated Vehicle Routing Problem (CVRP) benchmarks, with Beam Search and SA-based RRC consistently yielding superior performance. By refining inference techniques and leveraging enhanced search strategies, our work contributes to the broader applicability of NCO models in real-world combinatorial optimization tasks.

Problem

• Neural Combinatorial Optimization
• Capacitated Vehicle Routing Problem
• Inference Techniques
• Solution Quality
• Generalization

Innovation

• Neural Combinatorial Optimization
• Simulated Annealing
• Beam Search
• Capacitated Vehicle Routing Problem
• Inference Enhancement