On inferring cumulative constraints

PyCSP$^3$ provides a productive way to build constraint models for solving combinatorial constrained problems and export them to XCSP$^3$, preserving a complete separation between modeling and solving. However, it lacks native support for scheduling abstractions such as interval variables, sequence variables, and resource functions. As a result, scheduling models must be encoded with low-level integer variables and manual channeling constraints, even though PyCSP$^3$ already provides global constraints like NoOverlap and Cumulative on integer arrays. We present PyCSP$^3$ Scheduling, a library that adds scheduling abstractions to PyCSP$^3$ through 53 dedicated constraints and 27 expressions, and compiles them down to standard PyCSP$^3$/XCSP$^3$ constraints, maintaining the modeling/solving separation that underpins the PyCSP$^3$ ecosystem. On 261 paired instances across 17 model families (5 runs each), both formulations produce identical objectives on all 72 doubly-proved optimal pairs and nearly half of the families (8/17) remain structurally unchanged after compilation; however, runtime performance diverges across families, with clear gains on some (up to 5.8x) and regressions on others due to the overhead of compilation decompositions. Code and benchmarks are available at: https://github.com/sohaibafifi/pycsp3-scheduling

Modeling scheduling problems with conditional time intervals and cumulative functions has become a common approach when using modern commercial constraint programming solvers. This paradigm enables the modeling of a wide range of scheduling problems, including those involving producers and consumers. However, it is unavailable in existing open-source solvers and practical implementation details remain undocumented. In this work, we present an implementation of this modeling approach using a single, generic global constraint called the Generalized Cumulative. We also introduce a novel timetabling filtering algorithm specifically designed to handle tasks defined on conditional time-intervals. Experimental results demonstrate that this approach, combined with the new filtering algorithm, performs competitively with existing solvers enabling the modeling of producer and consumer scheduling problems and effectively scales to large-scale problems.

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.