Sequence Variables: A Constraint Programming Computational Domain for Routing and Sequencing

Constraint Programming (CP) offers an intuitive, declarative framework for modeling Vehicle Routing Problems (VRP), yet classical CP models based on successor variables cannot always deal with optional visits or insertion based heuristics. To address these limitations, this paper formalizes sequence variables within CP. Unlike the classical successor models, this computational domain handle optional visits and support insertion heuristics, including insertion-based Large Neighborhood Search. We provide a clear definition of their domain, update operations, and introduce consistency levels for constraints on this domain. An implementation is described with the underlying data structures required for integrating sequence variables into existing trail-based CP solvers. Furthermore, global constraints specifically designed for sequence variables and vehicle routing are introduced. Finally, the effectiveness of sequence variables is demonstrated by simplifying problem modeling and achieving competitive computational performance on the Dial-a-Ride Problem.