Symmetry Detection for Quadratically Constrained Quadratic Programs Using Binary Layered Graphs

Abstract

Symmetry in mathematical programming may lead to a multiplicity of solutions. In nonconvex optimisation, it can negatively affect the performance of the branch-and-bound algorithm. Symmetry may induce large search trees with multiple equivalent solutions, i.e. with the same optimal value. Dealing with symmetry requires detecting and classifying it first. This work develops methods for detecting groups of symmetry in the formulation of quadratically constrained quadratic optimisation problems via adjacency matrices. Using graph theory, we transform these matrices into Binary Layered Graphs (BLG) and enter them into the software package nauty. Nauty generates important symmetric properties of the original problem.