In this paper we address symmetry on combinatorial problems by following the approach of imposing additional symmetry-breaking constraints. Differently from other works in the literature, we attack the problem at the specification level. In fact, sometimes symmetries on specifications can be very easily detected, and symmetry-breaking formulae generated. We give formal definitions of symmetries...

Many constraint problems exhibit dominance relations which can be exploited for dramatic reductions in search space. Dominance relations are a generalization of symmetry and conditional symmetry. However, unlike symmetry breaking which is relatively well studied, dominance breaking techniques are not very well understood and are not commonly applied. In this paper, we present formal definitions...

This paper introduces six ways for handling a chain of lexicographic ordering constraint between the origins of identical orthotopes (e.g., rectangles, boxes, hyper-rectangles) subject to the fact that they should not pairwise overlap. While the first two ways deal with the integration of a chain of lexicographic ordering constraint within a generic geometric constraint kernel, the four latter ...

Symmetry is an important feature of many constraint programs. We show that any problem symmetry acting on a set of symmetry breaking constraints can be used to break symmetry. Different symmetries pick out different solutions in each symmetry class. This simple but powerful idea can be used in a number of different ways. We describe one application within model restarts, a search technique desi...

We introduce a new global constraint which combines together the lexicographic ordering constraint with some sum constraints. Lexicographic ordering constraints are frequently used to break symmetry, whilst sum constraints occur in many problems involving capacity or partitioning. Our results show that this global constraint is useful when there is a very large space to explore, such as when th...

We show that in theories with radiatively induced electro-weak symmetry breaking the EDMs obey a simple approximate scaling under the transformation m0 → λm0, m 1 2 → λm 1 2 in the large μ region. In the scaling region the knowledge of a single point in the MSSM parameter space where the cancellation in the EDMs occur allows one to generate a trajectory in the m0 −m 1 2 plane where the cancella...

Solution symmetries in integer linear programs often yield long Branch-and-Bound based solution processes. We propose a method for finding elements of the permutation group of solution symmetries, and two different types of symmetry-breaking constraints to eliminate these symmetries at the modelling level. We discuss some preliminary computational results.

The paper proposes a dynamic method, Recursive Symmetry Breaking During Search (ReSBDS), for efficient partial symmetry breaking. We first demonstrate how Partial Symmetry Breaking During Search (ParSBDS) misses important pruning opportunities when given only a subset of symmetries to break. The investigation pinpoints the culprit and in turn suggests rectification. The main idea is to add extr...

für Naturforschung in cooperation with the Max Planck Society for the Advancement of Science under a Creative Commons Attribution 4.0 International License. Dieses Werk wurde im Jahr 2013 vom Verlag Zeitschrift für Naturforschung in Zusammenarbeit mit der Max-Planck-Gesellschaft zur Förderung der Wissenschaften e.V. digitalisiert und unter folgender Lizenz veröffentlicht: Creative Commons Namen...