Implementing Cumulative Functions with Generalized Cumulative Constraints

2025-08-03

AI Summary

Existing open-source constraint solvers lack support for jointly modeling conditional time intervals and cumulative functions, and relevant implementation documentation is absent. Method: We propose the generalized cumulative global constraint—the first to fully support cumulative function modeling with conditional time intervals in an open-source framework—and design a novel schedule-based propagation algorithm that integrates conditional interval handling into modern solver architectures. Contribution/Results: The approach significantly improves constraint propagation efficiency and is specifically optimized for producer-consumer scheduling scenarios. Empirical evaluation demonstrates performance on par with leading commercial solvers across multiple benchmark problem classes, while scaling efficiently to large-scale instances. This work bridges a critical gap between expressive modeling capabilities and practical solver performance in cumulative resource scheduling.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Planning, Routing, and Scheduling: Temporal Planning
• Search and Optimization: Mixed Discrete/Continuous Search

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines

Abstract

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 time-table filtering algorithm 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 problems.

Problem

• Implementing cumulative functions in open-source solvers
• Modeling scheduling with conditional time intervals
• Developing scalable algorithms for producer-consumer problems

Innovation

• Uses Generalized Cumulative global constraint
• Introduces time-table filtering algorithm
• Scales effectively to large problems