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arXiv · 2510.14317

Column Generation with Domain-Independent Dynamic Programming

Ryo Kuroiwa·Edward Lam
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Abstract

Column generation and branch-and-price (B&P) are leading mathematical optimization methods for large-scale exact optimization, iterating between solving a master problem and a pricing problem. Due to the difficulty of discrete optimization, high-performance column generation often relies on a custom pricing algorithm built specifically to exploit the problem's structure. This bespoke nature of the pricing solver makes column generation a problem-specific method and hinders the use of generic implementations across a wide range of problems. We show that domain-independent dynamic programming (DIDP), a model-based paradigm for dynamic programming, can be used as a generic pricing solver. We develop new modeling features and a solving algorithm for DIDP to achieve better performance in typical pricing problems. We demonstrate that in four problem classes, our implementations of B&P, with pricing by DIDP, empirically outperform an existing automated B&P solver and B&P with pricing by mixed-integer programming or constraint programming.

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Ryo Kuroiwa, Edward Lam. 2025-10-16. Column Generation with Domain-Independent Dynamic Programming. https://doi.org/10.4230/lipics.cp.2026.37

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