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arxiv: 2604.16581 · v1 · submitted 2026-04-17 · 💻 cs.LG · cs.AI

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NCO4CVRP: Neural Combinatorial Optimization for the Capacitated Vehicle Routing Problem

Mahir Labib Dihan , Md. Ashrafur Rahman Khan , Wasif Jalal , Md. Roqunuzzaman Sojib , Mashroor Hasan Bhuiyan
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Pith reviewed 2026-05-10 08:50 UTC · model grok-4.3

classification 💻 cs.LG cs.AI
keywords optimizationcombinatorialsearchinferencemodelsolutiontechniquesacross
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The pith

Adding simulated annealing to random reconstruction and beam search to POMO in neural CVRP solvers reduces optimality gaps on standard benchmarks.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The work starts from two prior neural models that learn to build routes for trucks with capacity limits. One model uses a light encoder and heavy decoder; the other uses multiple starting points for policy learning. The authors change how these models pick final routes at test time. Instead of always taking the best immediate fix, they let the model sometimes accept a slightly worse fix with a probability that decreases over time, like cooling metal in simulated annealing. They also let the model keep several good partial routes at once and expand them systematically with beam search. They try different ways to sample next steps, such as softmax, greedy, or epsilon-greedy, and they flip or rotate the input maps to make the model more robust. Experiments on common CVRP test sets show smaller gaps to the best known solutions when these search tricks are used together.

Core claim

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.

Load-bearing premise

That the probabilistic acceptance in SA-RRC and the beam expansion in POMO produce genuinely better generalization rather than merely fitting the chosen benchmark distributions and augmentation set.

Figures

Figures reproduced from arXiv: 2604.16581 by Mahir Labib Dihan, Mashroor Hasan Bhuiyan, Md. Ashrafur Rahman Khan, Md. Roqunuzzaman Sojib, Wasif Jalal.

Figure 1
Figure 1. Figure 1: The structure of our proposed LEHD model, which has a single-layer light encoder and [PITH_FULL_IMAGE:figures/full_fig_p011_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Experiments using different temperatures [PITH_FULL_IMAGE:figures/full_fig_p018_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Experiments using different values of epsilon [PITH_FULL_IMAGE:figures/full_fig_p019_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Comparison of different inference techniques and augmentation types. [PITH_FULL_IMAGE:figures/full_fig_p022_4.png] view at source ↗
read the original 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.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The central claim rests on the assumption that the base LEHD and POMO models already capture useful CVRP structure and that the added search procedures improve upon them without introducing new biases. Because only the abstract is available, a complete ledger of fitted parameters cannot be extracted; the work implicitly depends on many neural-network weights and several inference hyperparameters whose values are not stated.

free parameters (2)
  • Beam width
    Controls how many partial solutions are kept during decoding; value chosen to trade off quality and compute time.
  • Simulated annealing temperature schedule
    Determines probability of accepting worse routes; schedule parameters are tuned for the reported benchmarks.
axioms (1)
  • domain assumption The LEHD and POMO architectures provide a strong starting point whose inference can be improved by classical search heuristics.
    Invoked when the authors state they modify existing models rather than train new ones from scratch.

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Reference graph

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