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Symmetry in mathematical programming may lead to a multiplicity of solutions.In nonconvex optimisation, it can negatively affect the performance of thebranch-and-bound algorithm. Symmetry may induce large search trees withmultiple equivalent solutions, i.e. with the same optimal value. Dealing withsymmetry requires detecting and classifying it first. This work developsmethods for detecting groups of symmetry in the formulation of quadraticallyconstrained quadratic optimisation problems via adjacency matrices. Using graphtheory, we transform these matrices into Binary Layered Graphs (BLG) and enterthem into the software package nauty. Nauty generates important symmetricproperties of the original problem.

Symmetry Detection for Quadratically Constrained Quadratic Programs Using Binary Layered Graphs