Domain-Independent Dynamic Programming

2026-04-11

AI Summary

This paper addresses the tight coupling between modeling and solving in combinatorial optimization by proposing Domain-Independent Dynamic Programming (DIDP), the first general-purpose, declarative, domain-agnostic dynamic programming paradigm. To realize DIDP, we design DyPDL—a dynamic programming description language enabling unified, high-level modeling—and develop seven generic DIDP solvers that integrate state-transition system modeling, heuristic search (A*, IDA*, GBFS), and AI planning principles. Evaluated on 11 benchmark problem classes, DIDP outperforms commercial MIP solvers on 9 classes, CP solvers on 9 classes, and surpasses both simultaneously on 7 classes. Moreover, its overall performance significantly exceeds that of existing general-purpose state-space solvers. The work establishes dynamic programming as a foundational, solver-agnostic modeling framework—bridging classical algorithm design with modern automated reasoning—and demonstrates substantial empirical gains across diverse combinatorial domains.

Technology Category

Constraint Satisfaction and Optimization: Constraint ProgrammingSearch and Optimization: Combinatorial OptimizationPlanning, Routing, and Scheduling: Mixed Discrete/Continuous Planning

Application Category

Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphsEconomics, Online Markets and Human Computation: Research challenges in human and human-AI computationUser Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

For combinatorial optimization problems, model-based paradigms 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 novel model-based paradigm based on dynamic programming (DP). While DP is not new, it has typically been implemented as a problem-specific method. We introduce Dynamic Programming Description Language (DyPDL), a formalism to define DP models based on a state transition system, inspired by artificial intelligence (AI) planning. we show that heuristic search algorithms can be used to solve DyPDL models and propose seven DIDP solvers. We experimentally compare our DIDP solvers with commercial MIP and CP solvers (solving MIP and CP models, respectively) on common benchmark instances of eleven combinatorial optimization problem classes. We show that DIDP outperforms MIP in nine problem classes, CP also in nine problem classes, and both MIP and CP in seven. DIDP also achieves superior performance to existing state-based solvers including domain-independent AI planners.

Problem

• Proposes domain-independent dynamic programming for combinatorial optimization.
• Introduces DyPDL for defining DP models using state transition systems.
• Compares DIDP solvers with MIP and CP solvers on benchmarks.

Innovation

• Domain-independent dynamic programming for optimization
• Dynamic Programming Description Language (DyPDL) introduced
• Heuristic search algorithms solve DyPDL models