A method for detecting symmetries in constraint models and its generalisation

Abstract

The symmetries that appear in many constraint problems can be used to significantly speed up the search for solutions to these problems. While the accurate detection of symmetries in instances of a given constraint problem is possible, current methods tend to be impractical for real-sized instances. On the other hand, methods capable of detecting properties for a problem model -and thus all its instances -are efficient but not accurate enough. This paper presents a new method for inferring symmetries in constraint satisfaction models that combines the high accuracy of instance-based methods with the efficiency of model-based methods; the key insight is that symmetries detected for small instances of the model can be generalised to the model itself. Experimental evaluation shows that this approach is able to find all symmetries in almost all the benchmark problems used. The generality of our method is then illustrated by showing how it can be applied to infer other properties.

Aggregation and Garbage Collection for Online Optimization

“…We distinguish between a problem model, where the input data is described in terms of parameters (i.e., data that will be known before the search starts), and a model instance, where the values of the parameters are added to the model. While an instance can be directly represented as a CSP, a model can be represented as a parameterized CSP [13] P [Data], that is, a family of CSPs P [δ] for every δ ∈ Data. The parameterization also applies to its components (X[Data], D[Data], C[Data]).…”

Automatic Core-Guided Reformulation via Constraint Explanation and Condition Learning

“…This approach gives users expressive and intuitive languages to model their problems, and frees them from knowing how to best map models onto solving algorithms. Further, modelto-model transformation methods exist to improve a model for many/all its instances, rather than just the one being flattened (e.g., (Hentenryck et al 2005;Charnley, Colton, and Miguel 2006;Mears et al 2015;Leo et al 2013)).…”