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arxiv: 2605.23569 · v1 · pith:HBO2QRFHnew · submitted 2026-05-22 · 💻 cs.AI

CP or DP? Why Not Both: A Case Study in the Partial Shop Scheduling Problem

Emma Legrand , Roger Kameugne , Pierre Schaus This is my paper

Pith reviewed 2026-05-25 04:18 UTC · model grok-4.3

classification 💻 cs.AI
keywords dynamic programmingconstraint programminghybrid solverpartial shop schedulinglarge neighborhood searchprecedence constraintsscheduling problem
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The pith

Dynamic programming can call constraint programming as a subroutine to solve the partial shop scheduling problem with flexible precedences.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper shows how to combine dynamic programming and constraint programming for the Partial Shop Scheduling Problem by using DP as the main search method and invoking CP for global constraint propagation. The hybrid method allows for anytime algorithms like column search and easily incorporates arbitrary precedence constraints between operations. It also enables a large neighborhood search scheme that reuses the DP model across restarts with partial-order schedules imposed.

Core claim

The paper establishes that DP and CP can be integrated such that DP provides the primary search framework while CP filtering algorithms serve as subroutines, resulting in a flexible solver for PSSP that handles any precedence graph and supports LNS, although not yet competitive with pure CP solvers.

What carries the argument

The hybrid integration where CP is used as a subroutine inside the DP search framework for global constraint propagation on PSSP states.

If this is right

  • The model accommodates anytime DP strategies such as anytime column search instead of strict layer-wise operation.
  • Arbitrary precedence constraints are handled straightforwardly due to CP modeling flexibility.
  • The DP model can be reused in a Large Neighborhood Search scheme with partial-order schedules imposed across restarts.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • This integration approach could be tested on other combinatorial problems where efficient CP propagators already exist.
  • Performance gains might appear in instances with complex precedences where pure DP struggles with state representation.

Load-bearing premise

Efficient CP filtering algorithms for the PSSP exist and can be invoked inside DP searches without their cost dominating the runtime.

What would settle it

Running the hybrid solver on PSSP instances and observing that the total time exceeds that of the original pure DP method due to subroutine overhead would falsify the viability claim.

read the original abstract

Dynamic Programming (DP) and Constraint Programming (CP) are well-established paradigms for solving combinatorial optimization problems. Usually, these two approaches are used separately. This paper aims to show that the two can be combined effectively and elegantly, with DP serving as the primary search framework and CP used as a subroutine to leverage global constraint propagation. This paper presents such an approach for the Partial Shop Scheduling Problem (PSSP), for which a pure DP method has previously been proposed, and efficient CP filtering algorithms are available. The PSSP is a general scheduling problem where each job consists of a set of operations with arbitrary precedence constraints. The approach is flexible enough to accommodate anytime DP strategies, such as anytime column search, whereas the original DP algorithm operated in a strictly layer-wise manner. Moreover, the flexibility of the CP modeling makes it straightforward to incorporate arbitrary precedence constraints. As a result, the model naturally handles any precedence graph and even enables the design of a Large Neighborhood Search (LNS) scheme, in which the DP model is reused, and partial-order schedules are imposed across restarts to improve the incumbent solution. While not competitive with state-of-the-art pure CP solvers for this specific problem, our primary contribution is demonstrating the viability of this hybrid integration.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

2 major / 0 minor

Summary. The paper claims that Dynamic Programming (DP) and Constraint Programming (CP) can be combined effectively for the Partial Shop Scheduling Problem (PSSP) by using DP as the primary search framework and CP as a subroutine to leverage global constraint propagation. It presents a hybrid approach that supports anytime strategies such as column search, naturally accommodates arbitrary precedence constraints, and enables a Large Neighborhood Search (LNS) scheme by reusing the DP model with partial-order schedules across restarts. The manuscript explicitly states that the hybrid is not competitive with state-of-the-art pure CP solvers and positions its primary contribution as demonstrating the viability and flexibility of this DP-primary + CP-subroutine integration.

Significance. If the integration can be realized as described, the work provides a concrete case study of hybridizing DP search with CP propagation in a general scheduling setting with arbitrary precedences. This offers a template for leveraging complementary strengths of the two paradigms without requiring major reformulation of either, and the LNS extension illustrates reuse potential. The paper's modest positioning as a viability demonstration (rather than a performance claim) is a strength.

major comments (2)
  1. [Abstract and approach description] The central claim of an 'effective and elegant' combination rests on the embedding of the CP subroutine inside the DP search, yet the manuscript provides no description of how the CP filtering is actually invoked (e.g., state representation passed to the subroutine, how global constraints are maintained across DP transitions, or the interface between the two). This implementation detail is load-bearing for the viability demonstration.
  2. [Abstract and experimental section] No performance numbers, runtime results, or comparison tables are supplied, even to illustrate basic feasibility (e.g., that propagation overhead does not dominate). While the paper does not claim superiority over pure CP, the absence of any empirical grounding makes it impossible to assess whether the hybrid 'works' in practice as asserted.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments. We address each major comment below and will revise the manuscript to strengthen the presentation of the hybrid approach.

read point-by-point responses

  1. Referee: [Abstract and approach description] The central claim of an 'effective and elegant' combination rests on the embedding of the CP subroutine inside the DP search, yet the manuscript provides no description of how the CP filtering is actually invoked (e.g., state representation passed to the subroutine, how global constraints are maintained across DP transitions, or the interface between the two). This implementation detail is load-bearing for the viability demonstration.

    Authors: We agree that the current description of the integration is insufficient. In the revised manuscript we will add a dedicated subsection (with pseudocode) that specifies the state representation passed to the CP subroutine, the exact invocation points inside DP transitions, and the mechanism for maintaining global constraints across transitions. revision: yes

  2. Referee: [Abstract and experimental section] No performance numbers, runtime results, or comparison tables are supplied, even to illustrate basic feasibility (e.g., that propagation overhead does not dominate). While the paper does not claim superiority over pure CP, the absence of any empirical grounding makes it impossible to assess whether the hybrid 'works' in practice as asserted.

    Authors: While the paper positions its contribution as a viability demonstration rather than a performance claim, we accept that basic empirical evidence is needed to show the hybrid can be realized without prohibitive overhead. The revision will include a short experimental subsection with runtime results on small instances that quantify CP propagation cost relative to pure DP, without any competitiveness claims. revision: yes

Circularity Check

0 steps flagged

No significant circularity; hybrid integration is an existence demonstration

full rationale

The paper presents a case study demonstrating the viability of a hybrid DP-primary + CP-subroutine architecture for the PSSP. No equations, fitted parameters, or derived predictions appear in the argument. The central claim reduces to an implementation showing that existing CP filtering algorithms can be invoked inside a DP search framework without major reformulation, which is self-contained as an algorithmic construction rather than a reduction to its own inputs. No self-citation load-bearing steps, uniqueness theorems, or ansatzes are invoked to justify the result. The contribution is explicitly modest and does not claim superiority or derive quantities by construction.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The approach rests on the existence and efficiency of prior CP filtering algorithms for PSSP and on the correctness of standard DP state transitions; no new entities or fitted constants are introduced.

axioms (2)
  • domain assumption CP global constraints for PSSP admit efficient filtering algorithms that can be called as black-box subroutines
    Abstract states efficient CP filtering algorithms are available and are used inside DP
  • domain assumption DP state transitions remain valid when partial-order information is added by CP propagation
    The hybrid reuses the original DP model while imposing extra precedence constraints

pith-pipeline@v0.9.0 · 5755 in / 1320 out tokens · 17802 ms · 2026-05-25T04:18:31.749775+00:00 · methodology

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Reference graph

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