Towards Constraint-Based Adaptive Hypergraph Learning for Solving Vehicle Routing: An End-to-End Solution

• URL: http://arxiv.org/abs/2503.10421v1
• Date: Thu, 13 Mar 2025 14:42:44 GMT
• Title: Towards Constraint-Based Adaptive Hypergraph Learning for Solving Vehicle Routing: An End-to-End Solution
• Authors: Zhenwei Wang, Ruibin Bai, Tiehua Zhang,
• Abstract summary: Vehicle routing problems are characterized by vast solution spaces and intricate constraints.<n>This study introduces a novel end-to-end framework that combines constraint-oriented hypergraphs with reinforcement learning.
• Score: 4.965709007367529
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: The application of learning based methods to vehicle routing problems has emerged as a pivotal area of research in combinatorial optimization. These problems are characterized by vast solution spaces and intricate constraints, making traditional approaches such as exact mathematical models or heuristic methods prone to high computational overhead or reliant on the design of complex heuristic operators to achieve optimal or near optimal solutions. Meanwhile, although some recent learning-based methods can produce good performance for VRP with straightforward constraint scenarios, they often fail to effectively handle hard constraints that are common in practice. This study introduces a novel end-to-end framework that combines constraint-oriented hypergraphs with reinforcement learning to address vehicle routing problems. A central innovation of this work is the development of a constraint-oriented dynamic hyperedge reconstruction strategy within an encoder, which significantly enhances hypergraph representation learning. Additionally, the decoder leverages a double-pointer attention mechanism to iteratively generate solutions. The proposed model is trained by incorporating asynchronous parameter updates informed by hypergraph constraints and optimizing a dual loss function comprising constraint loss and policy gradient loss. The experiment results on benchmark datasets demonstrate that the proposed approach not only eliminates the need for sophisticated heuristic operators but also achieves substantial improvements in solution quality.

Related papers

• Single-loop Algorithms for Stochastic Non-convex Optimization with Weakly-Convex Constraints [49.76332265680669]
  This paper examines a crucial subset of problems where both the objective and constraint functions are weakly convex. Existing methods often face limitations, including slow convergence rates or reliance on double-loop designs. We introduce a novel single-loop penalty-based algorithm to overcome these challenges.
  arXiv  Detail & Related papers  (2025-04-21T17:15:48Z)
• qNBO: quasi-Newton Meets Bilevel Optimization [26.0555315825777]
  Bilevel optimization, addressing challenges in hierarchical learning tasks, has gained significant interest in machine learning. We introduce a general framework to address these computational challenges in a coordinated manner. Specifically, we leverage quasi-Newton algorithms to accelerate the resolution of the lower-level problem while efficiently approximating the inverse Hessian-vector product.
  arXiv  Detail & Related papers  (2025-02-03T05:36:45Z)
• Optimization by Parallel Quasi-Quantum Annealing with Gradient-Based Sampling [0.0]
  This study proposes a different approach that integrates gradient-based update through continuous relaxation, combined with Quasi-Quantum Annealing (QQA) Numerical experiments demonstrate that our method is a competitive general-purpose solver, achieving performance comparable to iSCO and learning-based solvers.
  arXiv  Detail & Related papers  (2024-09-02T12:55:27Z)
• A Primal-Dual-Assisted Penalty Approach to Bilevel Optimization with Coupled Constraints [66.61399765513383]
  We develop a BLOCC algorithm to tackle BiLevel Optimization problems with Coupled Constraints. We demonstrate its effectiveness on two well-known real-world applications.
  arXiv  Detail & Related papers  (2024-06-14T15:59:36Z)
• GASE: Graph Attention Sampling with Edges Fusion for Solving Vehicle Routing Problems [6.084414764415137]
  We propose an adaptive Graph Attention Sampling with the Edges Fusion framework to solve vehicle routing problems. Our proposed model outperforms the existing methods by 2.08%-6.23% and shows stronger generalization ability.
  arXiv  Detail & Related papers  (2024-05-21T03:33:07Z)
• Learning Constrained Optimization with Deep Augmented Lagrangian Methods [54.22290715244502]
  A machine learning (ML) model is trained to emulate a constrained optimization solver. This paper proposes an alternative approach, in which the ML model is trained to predict dual solution estimates directly. It enables an end-to-end training scheme is which the dual objective is as a loss function, and solution estimates toward primal feasibility, emulating a Dual Ascent method.
  arXiv  Detail & Related papers  (2024-03-06T04:43:22Z)
• DiffuSolve: Diffusion-based Solver for Non-convex Trajectory Optimization [9.28162057044835]
  Optimal trajectory local is computationally expensive for nonlinear and high-dimensional dynamical systems. In this paper we introduce Diffu-based general model for non-dimensional optima problems. We also present Diff+, a novel constrained diffusion model with an additional loss in that further reduces the problem violations.
  arXiv  Detail & Related papers  (2024-02-22T03:52:17Z)
• An Optimization-based Deep Equilibrium Model for Hyperspectral Image Deconvolution with Convergence Guarantees [71.57324258813675]
  We propose a novel methodology for addressing the hyperspectral image deconvolution problem. A new optimization problem is formulated, leveraging a learnable regularizer in the form of a neural network. The derived iterative solver is then expressed as a fixed-point calculation problem within the Deep Equilibrium framework.
  arXiv  Detail & Related papers  (2023-06-10T08:25:16Z)
• Backpropagation of Unrolled Solvers with Folded Optimization [55.04219793298687]
  The integration of constrained optimization models as components in deep networks has led to promising advances on many specialized learning tasks. One typical strategy is algorithm unrolling, which relies on automatic differentiation through the operations of an iterative solver. This paper provides theoretical insights into the backward pass of unrolled optimization, leading to a system for generating efficiently solvable analytical models of backpropagation.
  arXiv  Detail & Related papers  (2023-01-28T01:50:42Z)
• Unsupervised Learning for Combinatorial Optimization with Principled Objective Relaxation [19.582494782591386]
  This work proposes an unsupervised learning framework for optimization (CO) problems. Our key contribution is the observation that if the relaxed objective satisfies entry-wise concavity, a low optimization loss guarantees the quality of the final integral solutions. In particular, this observation can guide the design of objective models in applications where the objectives are not given explicitly while requiring being modeled in prior.
  arXiv  Detail & Related papers  (2022-07-13T06:44:17Z)
• Neural Improvement Heuristics for Graph Combinatorial Optimization Problems [49.85111302670361]
  We introduce a novel Neural Improvement (NI) model capable of handling graph-based problems where information is encoded in the nodes, edges, or both. The presented model serves as a fundamental component for hill-climbing-based algorithms that guide the selection of neighborhood operations for each.
  arXiv  Detail & Related papers  (2022-06-01T10:35:29Z)
• Combining Deep Learning and Optimization for Security-Constrained Optimal Power Flow [94.24763814458686]
  Security-constrained optimal power flow (SCOPF) is fundamental in power systems. Modeling of APR within the SCOPF problem results in complex large-scale mixed-integer programs. This paper proposes a novel approach that combines deep learning and robust optimization techniques.
  arXiv  Detail & Related papers  (2020-07-14T12:38:21Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.