Escaping Local Minima via Topological Phase Space Expansion: The Kuramoto Annealer Heuristic

This work introduces the Topological Kuramoto Annealer (TKA), a geometry-driven heuristic for combinatorial optimization in complex energy landscapes. Unlike traditional methods such as simulated annealing, which rely on stochastic fluctuations to overcome energy barriers, the TKA dynamically modifies the topology of the search space by introducing auxiliary degrees of freedom. This expansion transforms local minima into saddle points, enabling barrier-free traversal. A subsequent Kuramoto-based synchronization protocol reduces relational entropy and projects the system back to its original dimensionality, yielding improved solutions. This framework provides a physically motivated, non-equilibrium approach to optimization, bridging concepts from nonlinear dynamics, synchronization, and algorithmic complexity.