Domain-Independent Dynamic Programming with Constraint Propagation

TL;DR

This paper integrates constraint propagation into dynamic programming to improve solving efficiency for combinatorial problems, bridging the gap between DP and constraint programming paradigms.

Contribution

It introduces a general framework combining DP with constraint propagation, demonstrating significant reductions in state expansions on multiple combinatorial problems.

Findings

Constraint propagation reduces the number of state expansions.

The integrated approach solves more instances than traditional DP.

Propagation benefits are most significant in tightly constrained problems.

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.