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.

Many edge-selection problems, such as the Traveling Salesman Problem and Orienteering Problem, are NP-hard, making them expensive to solve with exact methods and challenging to address with hand-crafted heuristics. Learning-based approaches provide an efficient alternative, while self-supervised methods avoid costly solution labels. However, existing approaches often still rely on heavy post-processing or narrow problem-specific designs. We propose a reusable self-supervised framework for edge-selection optimization that learns directly from unlabeled instances. The framework uses differentiable surrogate objectives and feasibility-driven penalties to encourage the model to learn feasibility-aware solution structure during training. To support efficient inference, we introduce a lightweight graph architecture centered on a cost-attention convolution, where edge costs and feasibility information directly shape message passing. Experiments on three problem families demonstrate strong solution quality and efficient inference across diverse edge-selection settings.

Multi-agent path finding is the problem of navigating a set of agents from their starting locations to their target locations while avoiding collisions. A leading method for optimal multi-agent path finding is branch-and-cut-and-price, a framework based on mathematical optimization. The reference implementation, named BCP-MAPF, shows highly competitive results against AI-based search. This paper presents BCP2-MAPF, a new implementation of branch-and-cut-and-price paired with a novel low-level path finder based on time intervals. Experimental results demonstrate that BCP2-MAPF significantly outperforms the other state-of-the-art optimal algorithms BCP-MAPF, Lazy CBS and CBSH2-RTC.

Given a tree, a set of pebbles initially stationed at some nodes of the tree and a set of target nodes, the Unlabeled Pebble Motion on Trees problem (UPMT) asks to find a plan to move the pebbles one-at-a-time from the starting nodes to the target nodes along the edges of the tree while minimizing the number of moves. This paper proposes the first optimal algorithm for UPMT that is asymptotically as fast as possible, as it runs in a time linear in the size of the input (the tree) and the size of the output (the optimal plan).

Machine learning (ML) is ubiquitous in modern life. Since it is being deployed in technologies that affect our privacy and safety, it is often crucial to understand the reasoning behind its decisions, warranting the need for explainable AI. Rule-based models, such as decision trees, decision lists, and decision sets, are conventionally deemed to be the most interpretable. Recent work uses propositional satisfiability (SAT) solving (and its optimization variants) to generate minimum-size decision sets. Motivated by limited practical scalability of these earlier methods, this paper proposes a novel approach to learn minimum-size decision sets by enumerating individual rules of the target decision set independently of each other, and then solving a set cover problem to select a subset of rules. The approach makes use of modern maximum satisfiability and integer linear programming technologies. Experiments on a wide range of publicly available datasets demonstrate the advantage of the new approach over the state of the art in SAT-based decision set learning.

There are currently two broad strategies for optimal Multi-agent Pathfinding (MAPF): (1) search-based methods, which model and solve MAPF directly, and (2) compilation-based solvers, which reduce MAPF to instances of well-known combinatorial problems, and thus, can benefit from advances in solver techniques. In this work, we present an optimal algorithm, BCP, that hybridizes both approaches using Branch-and-Cut-and-Price, a decomposition framework developed for mathematical optimization. We formalize BCP and compare it empirically against CBSH and CBSH-RM, two leading search-based solvers. Conclusive results on standard benchmarks indicate that its performance exceeds the state-of-the-art: solving more instances on smaller grids and scaling reliably to 100 or more agents on larger game maps.