UNB Researcher Takes a Geometric Axe to Optimization's Symmetry Problem

Optimization solvers have a wasteful habit: when a problem looks the same from several angles, they happily solve every mirrored copy of the answer instead of one.

Geometric Quadratic Separators for Symmetric Integer Programs, a poster from Canadian Institute for Cybersecurity researcher Seyedeh Maryam Abbasnia, takes a geometric approach to that problem — and it will be on display at the PST Cybersecurity Summit 2026 in Fredericton on Aug. 20.

The problem: symmetry breeds redundant search

Many real-world planning problems — scheduling, routing, resource allocation — are Integer Linear Programming (ILP) problems, where solvers search for the best integer-valued solution. When a problem has cyclic symmetry (rotations or permutations that map one feasible solution onto an equivalent one), solvers can spend enormous effort re-exploring equivalent solutions, one mirror image at a time.

The approach: cut through the symmetry

The research introduces a quadratic separator based on invariant subspaces — a geometric construction that slices through the search space so that symmetric copies collapse into one region. The framework pairs geometric reasoning with modern optimization solvers, giving a new way to reduce redundant search in symmetric problems.

It's the kind of foundational mathematics that quietly underpins applied work: better symmetry handling means solvers spend their time on new solutions rather than re-discovering the same one, which pays off anywhere scheduling and logistics meet the institute's broader security and AI research.

Sources

• Canadian Institute for Cybersecurity: Research Spotlight post — project summary, author, and approach