PyCSP3-Scheduling: A Scheduling Extension for PyCSP3

In this document, we introduce PyCSP$3$, a Python library that allows us to write models of combinatorial constrained problems in a declarative manner. Currently, with PyCSP$3$, you can write models of constraint satisfaction and optimization problems. More specifically, you can build CSP (Constraint Satisfaction Problem) and COP (Constraint Optimization Problem) models. Importantly, there is a complete separation between the modeling and solving phases: you write a model, you compile it (while providing some data) in order to generate an XCSP$3$ instance (file), and you solve that problem instance by means of a constraint solver. You can also directly pilot the solving procedure in PyCSP$3$, possibly conducting an incremental solving strategy. In this document, you will find all that you need to know about PyCSP$3$, with more than 50 illustrative models.

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.

This paper introduces SCHEDBench, a natural-language benchmark for evaluating combinatorial scheduling constraint faithfulness under surface-form variation. Grounded in canonical scheduling instances and solver-derived feasibility and optimality, SCHEDBench assesses whether large language models (LLMs) generate schedules with the same constraint-feasible behavior across varied natural-language (NL) surface forms. SCHEDBench spans 1,132 instances across job-shop scheduling problems (JSP), single and multi-mode resource-constrained project scheduling problems (RCPSP), nurse rostering/scheduling, and curriculum timetabling problems of varying difficulty. Instances are templated into natural language problems using domain-specific templates, themed entities, lexical-syntactic template rephrasing, and constraint-level surface-form variation, with reference solutions verified for feasibility and objective optimality. Across thirteen frontier and open-weight LLMs, we find that models are not reliably invariant to semantically equivalent renderings of the same scheduling problem. Surface-form variation reduces feasibility and induces above-noise shifts in per-instance hard-constraint violations on matched instances. Among the tested isolated axes, constraint reordering yields the clearest above-noise sensitivity.