A symmetry breaking swarm optimizer derived from the Landau theory of phase transitions

Metaheuristic optimization algorithms are widely used for high-dimensional non-convex problems, yet most are designed by analogy with biological or physical processes and govern their exploration–exploitation balance with heuristic schedules that lack an underlying theory. We introduce Symmetry-Breaking Swarm Optimization (SBSO), in which this balance is not a tuned schedule but a second-order phase transition derived from the Landau-Ginzburg free energy. Each agent carries a component of an order-parameter field that relaxes along the free-energy gradient while a computational temperature is lowered through the critical point; the field then breaks symmetry spontaneously, and the local order parameter schedules the search operator of every agent. A vector generalization with one field component per coordinate searches heterogeneous problems with coordinate-wise adaptive intensity and reduces exactly to the scalar algorithm when the differentiation strength vanishes. Against eleven optimizers from four families under one evaluation budget, SBSO ranks fourth of twelve on a classical suite, where separable unimodal problems favour methods that collapse the population onto a point, and second of twelve on five shifted and rotated IEEE CEC blocks, where it is consistently the runner-up. Controlled ablations attribute the benefit to the phase transition itself rather than to any individual search operator.