Integration of neural solver and problem-specific solver through bilevel approach: a case study of min-max capacitated vehicle routing problem

Akihiro Yoshida, Nozomi Hata, Hiroki Ishikura, Keiichiro Yamamura, Katsuki Fujisawa

Keywords: self-supervised learning, combinatorial optimization, optimal transport, vehicle routing problem, neural combinatorial solver

TL;DR: We propose a framework that integrates machine learning, optimal transport, and a problem-specific solver to obtain high-quality solutions quickly for large-scale combinatorial optimization problems.

Abstract:

In real-world operations with combinatorial structures like vehicle routing problems, similar optimization problems have to be solved repeatedly with slight parameter variations.
A key challenge in such scenarios is achieving both high solution quality and fast computation time, while traditional methods like heuristics or branch-and-bound struggle to achieve both simultaneously.
In contrast, problem-specific solvers can effectively balance solution quality and computation speed for specific problems.
However, since real-world problems have more complex structures, they can handle only subproblems.
To enhance the applicability of the problem-specific solvers, we propose a framework that integrates a problem-specific solver and a neural solver.
Our framework decomposes the optimization problem into subproblems so that some of which can be solved by problem-specific solvers, such as the traveling salesperson problem.
For the remaining portions of the problem, we utilize the similarities of the problems and design a neural solver.
By integrating two solvers, we can utilize the strengths of the problem-specific solver in balancing solution accuracy and computation speed, as well as the neural solver’s ability to infer a solution from the similarity of optimization problems.
Based on the case study with the min-max capacitated vehicle routing problem, we demonstrate that it outperforms the state-of-the-art solver regarding both high solution quality and short computation time.

Primary Area: unsupervised, self-supervised, semi-supervised, and supervised representation learning

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Submission Number: 9680