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...

TO SYMMETRIC VARIATIONAL PROBLEMS Giuseppe Gaeta Department of Mathematical Sciences Loughborough University of Technology Loughborough LE11 3TU (England) [email protected] Summary By combining the Michel's geometric theory of symmetry breaking and classical result from variational analysis, we obtain a lower bound on critical points with given symmetry H G of a potential symmetric under G. The...

We discuss excitations in nonrelativistic field theories with spontaneous breaking of a continuous global symmetry. It is known that in such systems there are two types of Goldstone bosons (Type A and Type B) whose dispersion law is generically linear or quadratic, respectively. We show that Type B Goldstone bosons may have gapped partners which we call almost-Goldstone bosons. With some nondeg...