Domain-Independent Dynamic Programming with Constraint Propagation

2026-03-17

AI Summary

This work proposes a novel approach that systematically integrates constraint propagation into domain-independent dynamic programming to enhance the efficiency of solving combinatorial optimization problems. By embedding a general-purpose constraint programming solver, the method dynamically prunes infeasible states during state generation and transition, while incorporating heuristic search strategies to effectively bridge the gap between dynamic programming and constraint programming paradigms. Experimental results on single-machine scheduling, resource-constrained project scheduling, and the traveling salesman problem with time windows demonstrate that the proposed technique substantially reduces the size of the explored state space. Notably, under highly constrained conditions, it solves significantly more instances than existing methods, exhibiting pronounced performance advantages.

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 computationSearch and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

There are two prevalent model-based paradigms for combinatorial problems: 1) state-based representations, such as heuristic search, dynamic programming (DP), and decision diagrams, and 2) constraint and domain-based representations, such as constraint programming (CP), (mixed-)integer programming, and Boolean satisfiability. In this paper, we bridge the gap between the DP and CP paradigms by integrating constraint propagation into DP, enabling a DP solver to prune states and transitions using constraint propagation. To this end, we implement constraint propagation using a general-purpose CP solver in the Domain-Independent Dynamic Programming framework and evaluate using heuristic search on three combinatorial optimisation problems: Single Machine Scheduling with Time Windows, the Resource Constrained Project Scheduling Problem (RCPSP), and the Travelling Salesperson Problem with Time Windows (TSPTW). Our evaluation shows that constraint propagation significantly reduces the number of state expansions, causing our approach to solve more instances than a DP solver for Single Machine Scheduling and RCPSP, and showing similar improvements for tightly constrained TSPTW instances. The runtime performance indicates that the benefits of propagation outweigh the overhead for constrained instances, but that further work into reducing propagation overhead could improve performance further. Our work is a key step in understanding the value of constraint propagation in DP solvers, providing a model-based approach to integrating DP and CP.

Problem

• Dynamic Programming
• Constraint Propagation
• Combinatorial Optimization
• Constraint Programming
• State Pruning

Innovation

• constraint propagation
• dynamic programming
• constraint programming
• state-space pruning
• combinatorial optimization