CROSS cyclic resource-constrained scheduling solver

• Published in: Artificial intelligence Vol. 206; pp. 25 - 52
• Main Authors: Bonfietti, Alessio, Lombardi, Michele, Benini, Luca, Milano, Michela
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier B.V 01.01.2014; Elsevier
• Subjects: Applied sciences; Computer science; control theory; systems; Constraint programming; Cumulative constraint; Cyclic scheduling problem; Exact sciences and technology; Filtering algorithm; Mathematical programming; Operational research and scientific management; Operational research. Management science; Programming languages; Scheduling, sequencing; Software; Cyclic scheduling problem; Cumulative constraint; Filtering algorithm; Constraint programming; Production system; Compiler; Compilation; Filtering; Constraint satisfaction; Scheduling; Modeling; Precedence constraint; Cyclic system; Constrained optimization; Boarded computer; Flexible manufacturing system; Filter; Resource constraint; Non linear model; Modular arithmetic; Ordering; Problem solving; Resource management; Chemical system
• ISSN: 0004-3702; 1872-7921
• DOI: 10.1016/j.artint.2013.09.006

Cyclic scheduling problems consist in ordering a set of activities executed indefinitely over time in a periodic fashion, subject to precedence and resource constraints. This class of problems has many applications in manufacturing, embedded systems and compiler design, production and chemical systems. This paper proposes a Constraint Programming approach for cyclic scheduling problems, based on modular arithmetic: in particular, we introduce a modular precedence constraint and a global cumulative constraint along with their filtering algorithms. We discuss two possible formulations. The first one (referred to as CROSS) models a pure cyclic scheduling problem and makes use of both our novel constraints. The second formulation (referred to as CROSS⁎) introduces a restrictive assumption to enable the use of classical resources constraints, but may incur a loss of solution quality. Many traditional approaches to cyclic scheduling operate by fixing the period value and then solving a linear problem in a generate-and-test fashion. Conversely, our technique is based on a non-linear model and tackles the problem as a whole: the period value is inferred from the scheduling decisions. Our approach has been tested on a number of non-trivial synthetic instances and on a set of realistic industrial instances. The method proved to effective in finding high quality solutions in a very short amount of time.