Pruning Isomorphic Structural Sub-problems in Configuration

TL;DR

This paper introduces a formalism-independent algorithm to detect and break symmetries in configuration problems, reducing redundant searches by identifying isomorphic sub-problems efficiently.

Contribution

It presents a novel algorithm for testing configuration canonicity that can be integrated into any configurator without model modifications.

Findings

The canonicity test effectively detects isomorphic configurations.

The approach improves configuration efficiency by reducing symmetry-related redundancies.

The algorithm's cost and efficiency are quantitatively analyzed.

Abstract

Configuring consists in simulating the realization of a complex product from a catalog of component parts, using known relations between types, and picking values for object attributes. This highly combinatorial problem in the field of constraint programming has been addressed with a variety of approaches since the foundation system R1(McDermott82). An inherent difficulty in solving configuration problems is the existence of many isomorphisms among interpretations. We describe a formalism independent approach to improve the detection of isomorphisms by configurators, which does not require to adapt the problem model. To achieve this, we exploit the properties of a characteristic subset of configuration problems, called the structural sub-problem, which canonical solutions can be produced or tested at a limited cost. In this paper we present an algorithm for testing the canonicity of configurations, that can be added as a symmetry breaking constraint to any configurator. The cost and efficiency of this canonicity test are given.