Symmetry Detection for Quadratically Constrained Quadratic Programs Using Binary Layered Graphs

TL;DR

This paper introduces a graph-theoretic method using Binary Layered Graphs and nauty software to detect symmetry in quadratically constrained quadratic programming problems, aiming to improve optimization efficiency.

Contribution

It develops a novel approach for symmetry detection in QCQPs by transforming adjacency matrices into Binary Layered Graphs and analyzing them with nauty.

Findings

Effective symmetry detection in QCQPs

Reduction of search tree size in optimization

Enhanced performance of branch-and-bound algorithms

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.