Justin Pearson

JAIR Journal 2025 Journal Article

Invariant Graph Propagation in Constraint-Based Local Search

• Frej Knutar Lewander
• Pierre Flener
• Justin Pearson

In constraint-based local search, an assignment to the search variables is improved upon by an iterative procedure that replaces the current assignment with a similar assignment. The latter is selected by a heuristic that assesses the qualities of a subset of all similar assignments, where the quality of such assignments is determined via a process called invariant graph propagation. Since, typically, many similar assignments are considered in every iteration, invariant graph propagation must be as efficient as possible. Since invariant graph propagation is independent of the selection heuristic, any comparison between different invariant graph propagation styles under different selection heuristics can be misleading. In this paper, we describe and compare both theoretically and empirically the throughput of several invariant graph propagation styles, and give criteria when one style or another is to be used.

AIJ Journal 2016 Journal Article

A parametric propagator for pairs of Sum constraints with a discrete convexity property

• Jean-Noël Monette
• Nicolas Beldiceanu
• Pierre Flener
• Justin Pearson

LOPSTR Conference 2016 Conference Paper

MiniZinc with Strings

• Roberto Amadini
• Pierre Flener
• Justin Pearson
• Joseph D. Scott
• Peter J. Stuckey
• Guido Tack

Abstract Strings are extensively used in modern programming languages and constraints over strings of unknown length occur in a wide range of real-world applications such as software analysis and verification, testing, model checking, and web security. Nevertheless, practically no constraint programming solver natively supports string constraints. We introduce string variables and a suitable set of string constraints as builtin features of the MiniZinc modelling language. Furthermore, we define an interpreter for converting a MiniZinc model with strings into a FlatZinc instance relying only on integer variables. This conversion is obtained via rewrite rules, and does not require any extension of the existing FlatZinc specification. This provides a user-friendly interface for modelling combinatorial problems with strings, and enables both string and non-string solvers to actually solve such problems.

AAAI Conference 2014 Conference Paper

A Propagator Design Framework for Constraints over Sequences

• Jean-Noel Monette
• Pierre Flener
• Justin Pearson

Constraints over variable sequences are ubiquitous and many of their propagators have been inspired by dynamic programming (DP). We propose a conceptual framework for designing such propagators: pruning rules, in a functional notation, are refined upon the application of transformation operators to a DP-style formulation of a constraint; a representation of the (tuple) variable domains is picked; and a control of the pruning rules is picked.

AAAI Conference 2014 Conference Paper

Propagating Regular Counting Constraints

• Nicolas Beldiceanu
• Pierre Flener
• Justin Pearson
• Pascal Van Hentenryck

Constraints over finite sequences of variables are ubiquitous in sequencing and timetabling. This led to general modelling techniques and generic propagators, often based on deterministic finite automata (DFA) and their extensions. We consider counter-DFAs (cDFA), which provide concise models for regular counting constraints, that is constraints over the number of times a regular-language pattern occurs in a sequence. We show how to enforce domain consistency in polynomial time for at-most and at-least regular counting constraints based on the frequent case of a cDFA with only accepting states and a single counter that can be increased by transitions. We also show that the satisfaction of exact regular counting constraints is NP-hard and that an incomplete propagator for exact regular counting constraints is faster and provides more pruning than the existing propagator from (Beldiceanu, Carlsson, and Petit 2004). Finally, by avoiding the unrolling of the cDFA used by COSTREGULAR, the space complexity reduces from O(n · |Σ| · |Q|) to O(n · (|Σ| + |Q|)), where Σ is the alphabet and Q the state set of the cDFA.

KER Journal 2012 Journal Article

Constraint programming for air traffic management: a survey

• Cyril Allignol
• Nicolas Barnier
• Pierre Flener
• Justin Pearson

Abstract Air traffic management (ATM) under its current paradigm is reaching its structural limits considering the continuously growing demand. The need for a decrease in traffic workload opens numerous problems for optimization, from capacity balancing to conflict solving, using many different degrees of freedom, such as re-routing, flight-level changes, or ground-holding schemes. These problems are usually of a large dimension (there are 30 000 daily flights in Europe in the year 2012) and highly combinatorial, hence challenging for current problem solving technologies. We give brief tutorials on ATM and constraint programming (CP), and survey the literature on deploying CP technology for modelling and solving combinatorial problems that occur in an ATM context.

KER Journal 2012 Journal Article

Constraint programming for air traffic management: preface

• Pierre Flener
• Justin Pearson
• Marc Bourgois

ECAI Conference 2008 Conference Paper

Solving Necklace Constraint Problems

• Pierre Flener
• Justin Pearson

Some constraint problems have a combinatorial structure where the constraints allow the sequence of variables to be rotated (necklaces), if not also the domain values to be permuted (unlabelled necklaces), without getting an essentially different solution. We bring together the fields of combinatorial enumeration, where efficient algorithms have been designed for (special cases of) some of these combinatorial objects, and constraint programming, where the requisite symmetry breaking has at best been done statically so far. We design the first search procedure and identify the first symmetry-breaking constraints for the general case of unlabelled necklaces. Further, we compare dynamic and static symmetry breaking on real-life scheduling problems featuring (unlabelled) necklaces.

LOPSTR Conference 2003 Conference Paper

Introducing esra, a Relational Language for Modelling Combinatorial Problems

• Pierre Flener
• Justin Pearson
• Magnus Ågren 0002

Abstract Current-generation constraint programming languages are considered by many, especially in industry, to be too low-level, difficult, and large. We argue that solver-independent, high-level relational constraint modelling leads to a simpler and smaller language, to more concise, intuitive, and analysable models, as well as to more efficient and effective model formulation, maintenance, reformulation, and verification. All this can be achieved without sacrificing the possibility of efficient solving, so that even time-pressed or less competent modellers can be well assisted. Towards this, we propose the esra relational constraint modelling language, showcase its elegance on some well-known problems, and outline a compilation philosophy for such languages.