András Z. Salamon

Joan Espasa, Ian P. Gent, Ian Miguel et al.

We report on progress in modelling and solving Puzznic, a video game requiring the player to plan sequences of moves to clear a grid by matching blocks. We focus here on levels with no moving blocks. We compare a planning approach and three constraint programming approaches on a small set of benchmark instances. The planning approach is at present superior to the constraint programming approaches, but we outline proposals for improving the constraint models.

Joan Espasa, Ian Miguel, Peter Nightingale et al.

We study a planning problem based on Plotting, a tile-matching puzzle video game published by Taito in 1989. The objective of this game is to remove a target number of coloured blocks from a grid by sequentially shooting blocks into the grid. Plotting features complex transitions after every shot: various blocks are affected directly, while others can be indirectly affected by gravity. We highlight the challenges of modelling Plotting with PDDL and of solving it with a grounding-based state-of-the-art planner.

Ian Miguel, András Z. Salamon, Christopher Stone

It is well established that formulating an effective constraint model of a problem of interest is crucial to the efficiency with which it can subsequently be solved. Following from the observation that it is difficult, if not impossible, to know a priori which of a set of candidate models will perform best in practice, we envisage a system that explores the space of models through a process of reformulation from an initial model, guided by performance on a set of training instances from the problem class under consideration. We plan to situate this system in a refinement-based approach, where a user writes a constraint specification describing a problem above the level of abstraction at which many modelling decisions are made. In this position paper we set out our plan for an exploratory reformulation system, and discuss progress made so far.

Ian Miguel, András Z. Salamon, Christopher Stone

Formulating an effective constraint model of a parameterised problem class is crucial to the efficiency with which instances of the class can subsequently be solved. It is difficult to know beforehand which of a set of candidate models will perform best in practice. This paper presents a system that employs graph rewriting to reformulate an input model for improved performance automatically. By situating our work in the Essence abstract constraint specification language, we can use the structure in its high level variable types to trigger rewrites directly. We implement our system via rewrite rules expressed in the Graph Programs 2 language, applied to the abstract syntax tree of an input specification. We show how to automatically translate the solution of the reformulated problem into a solution of the original problem for verification and presentation. We demonstrate the efficacy of our system with a detailed case study.

Özgür Akgün, Ian P. Gent, Christopher Jefferson et al.

The performance of a constraint model can often be improved by converting a subproblem into a single table constraint (referred to as tabulation). Finding subproblems to tabulate is traditionally a manual and time-intensive process, even for expert modellers. This paper presents TabID, an entirely automated method to identify promising subproblems for tabulation in constraint programming. We introduce a diverse set of heuristics designed to identify promising candidates for tabulation, aiming to improve solver performance. These heuristics are intended to encapsulate various factors that contribute to useful tabulation. We also present additional checks to limit the potential drawbacks of suboptimal tabulation. We comprehensively evaluate our approach using benchmark problems from existing literature that previously relied on manual identification by constraint programming experts of constraints to tabulate. We demonstrate that our automated identification and tabulation process achieves comparable, and in some cases improved results. We empirically evaluate the efficacy of our approach on a variety of solvers, including standard CP (Minion and Gecode), clause-learning CP (Chuffed and OR-Tools) and SAT solvers (Kissat). Our findings highlight the substantial potential of fully automated tabulation, suggesting its integration into automated model reformulation tools.

Özgür Akgün, Alan M. Frisch, Ian P. Gent et al.

The Essence language allows a user to specify a constraint problem at a level of abstraction above that at which constraint modelling decisions are made. Essence specifications are refined into constraint models using the Conjure automated modelling tool, which employs a suite of refinement rules. However, Essence is a rich language in which there are many equivalent ways to specify a given problem. A user may therefore omit the use of domain attributes or abstract types, resulting in fewer refinement rules being applicable and therefore a reduced set of output models from which to select. This paper addresses the problem of recovering this information automatically to increase the robustness of the quality of the output constraint models in the face of variation in the input Essence specification. We present reformulation rules that can change the type of a decision variable or add attributes that shrink its domain. We demonstrate the efficacy of this approach in terms of the quantity and quality of models Conjure can produce from the transformed specification compared with the original.

Özgür Akgün, Nguyen Dang, Joan Espasa et al.

Many of the core disciplines of artificial intelligence have sets of standard benchmark problems well known and widely used by the community when developing new algorithms. Constraint programming and automated planning are examples of these areas, where the behaviour of a new algorithm is measured by how it performs on these instances. Typically the efficiency of each solving method varies not only between problems, but also between instances of the same problem. Therefore, having a diverse set of instances is crucial to be able to effectively evaluate a new solving method. Current methods for automatic generation of instances for Constraint Programming problems start with a declarative model and search for instances with some desired attributes, such as hardness or size. We first explore the difficulties of adapting this approach to generate instances starting from problem specifications written in PDDL, the de-facto standard language of the automated planning community. We then propose a new approach where the whole planning problem description is modelled using Essence, an abstract modelling language that allows expressing high-level structures without committing to a particular low level representation in PDDL.