Weak Symmetries in Problem Formulations

In this article we will present some problems that have weak symmetries. In contrast to a proper symmetry, a weak symmetry acts only on a subset of the variables and preserves the feasibility state only with respect to a subset of the constraints. Therefore, breaking weak symmetries with standard techniques would lead to a loss of solutions. This article presents also a modelling technique which is based on additional variables called SymVar – Symmetry Variable. These variables enable us to achieve symmetry breaking on the symmetric variables of the problem without losing solutions. By using this technique we are able to break the weak symmetry without losing solutions. We will show for three problems how SymVars are applied such that the weak symmetries can be broken.