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Domain-Independent Dynamic Programming with Constraint Propagation

Imko Marijnissen, J. Christopher Beck, Emir Demirović, Ryo Kuroiwa

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.

Domain-Independent Dynamic Programming with Constraint Propagation

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.
Paper Structure (34 sections, 20 equations, 13 figures, 2 algorithms)

This paper contains 34 sections, 20 equations, 13 figures, 2 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Domain-Independent Dynamic Programming
  4. Heuristic Search
  5. Constraint Programming
  6. Related Work
  7. DIDP with Constraint Propagation
  8. Framework
  9. $\bm{1|r_i, \delta_i|\sum w_i T_i}$
  10. DP Model
  11. Constraint Propagation
  12. RCPSP
  13. DP Model
  14. Constraint Propagation
  15. TSPTW
  16. ...and 19 more sections

Figures (13)

  • Figure 1: An overview of the interactions in our framework.
  • Figure 2: Number of $1|r_i, \delta_i|\sum w_i T_i$ instances solved compared to the number of state expansions and time.
  • Figure 3: Number of $1|r_i, \delta_i|\sum w_i T_i$ instances solved over $\phi$. The marked parts are instances proven infeasible and unmarked parts are instances proven optimal. Our approach solves the most instances when they are tightly constrained.
  • Figure 4: Number of RCPSP instances solved compared to the number of state expansions and time.
  • Figure 5: Number of TSPTW instances solved compared to the number of state expansions and time.
  • ...and 8 more figures