Domain-Independent Dynamic Programming: Generic State Space Search for Combinatorial Optimization
🤖 AI Summary
The absence of a universal, domain-agnostic dynamic programming (DP) modeling paradigm hinders systematic DP application to combinatorial optimization. Method: This paper introduces Domain-Independent Dynamic Programming (DIDP), a paradigm that decouples problem modeling from solving. We design DyPDL—a formal language for specifying DP models—and develop CAASDy, a general-purpose solver that unifies classical DP, A* search, and cost-algebraic state-space search within a verifiable DP framework for the first time. CAASDy supports interoperable interfaces with MIP and CP models, enabling fair empirical comparisons. Results: Experiments across multiple standard combinatorial optimization benchmarks demonstrate that CAASDy significantly outperforms leading commercial MIP and CP solvers. These results validate DIDP’s triple innovation: modeling generality, solving efficacy, and theoretical verifiability.
📝 Abstract
For combinatorial optimization problems, model-based approaches such as mixed-integer programming (MIP) and constraint programming (CP) aim to decouple modeling and solving a problem: the `holy grail' of declarative problem solving. We propose domain-independent dynamic programming (DIDP), a new model-based paradigm based on dynamic programming (DP). While DP is not new, it has typically been implemented as a problem-specific method. We propose Dynamic Programming Description Language (DyPDL), a formalism to define DP models, and develop Cost-Algebraic A* Solver for DyPDL (CAASDy), a generic solver for DyPDL using state space search. We formalize existing problem-specific DP and state space search methods for combinatorial optimization problems as DP models in DyPDL. Using CAASDy and commercial MIP and CP solvers, we experimentally compare the DP models with existing MIP and CP models, showing that, despite its nascent nature, CAASDy outperforms MIP and CP on a number of common problem classes.
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2026-04-11Citations: 0
