Many practical optimisation problems are too large and too rugged for exact methods. For high-dimensional, non-convex problems (non-convex meaning the landscape can have many dips in which a search can get stuck), a common recourse is a metaheuristic. This is a general-purpose search strategy that does not guarantee the best answer but tends to find good ones, often by moving a population of candidate solutions across the landscape. In a 2026 paper in Scientific Reports, Keyin Chen and Yuanlin Liu of Jiaying University argue that such algorithms usually have no theory behind one of their central choices, and they borrow one from physics.

That choice is the balance between exploration and exploitation. A search that roams for too long wastes effort, and one that settles too early can lock onto a mediocre valley. According to the authors, most metaheuristics are designed by analogy with a biological or physical process. They manage this trade-off with schedules, which are rules for how the search should change its behaviour over a run, and those schedules are chosen heuristically rather than derived from any underlying theory.

Their algorithm, Symmetry-Breaking Swarm Optimization (SBSO), draws on Landau's theory of phase transitions. A second-order phase transition is a continuous change of state, such as a magnet losing its magnetisation as it is heated past a critical temperature. Landau theory describes such changes through an order parameter, a quantity that is zero in the disordered, symmetric phase and becomes non-zero once the system orders. The Landau–Ginzburg version lets that parameter vary from place to place, which makes it a field. As the temperature falls through the critical point, the symmetric state becomes unstable and the system settles into one of several equivalent ordered states. Physicists call this spontaneous symmetry breaking.

In SBSO, each search agent carries one component of such an order-parameter field. The field relaxes downhill along the gradient of a Landau–Ginzburg free energy, the quantity a physical system would minimise, while a computational temperature is lowered through the critical point. Once the field breaks symmetry, the local value of the order parameter at each agent schedules that agent's search operator. The exploration–exploitation balance is therefore not a timetable written in by the designer. It is the consequence of a transition the algorithm passes through. The authors also describe a vector version with one field component per coordinate of the problem, so that search intensity can adapt coordinate by coordinate on problems whose variables behave differently. When a quantity they call the differentiation strength is set to zero, this version reduces exactly to the scalar algorithm.

The authors tested SBSO against eleven other optimisers from four families, with every method held to the same evaluation budget. On a classical suite of test functions it ranked fourth of twelve. The authors note that this suite contains separable unimodal problems, which are single-valley functions whose variables can be optimised independently. Such problems favour methods that collapse the population onto a point. The second test used five blocks of shifted and rotated problems from the IEEE CEC benchmarks. In these, the test functions are moved and turned so that the optimum is not conveniently placed and the variables interact. There, SBSO ranked second of twelve and was consistently the runner-up.

To find out where the gains come from, the authors ran controlled ablations, which are experiments that change or remove one ingredient at a time. They report that the benefit traces to the phase transition itself rather than to any individual search operator. A check of this kind is meant to separate a design principle doing real work from a well-chosen move that happens to sit inside it.

The abstract leaves much unstated. It does not name the eleven rival methods or their four families. It does not identify the methods that finished ahead of SBSO, and it does not give the size of the evaluation budget. The comparisons the abstract reports are all on benchmark suites, and SBSO does not come out on top in either suite. Its claim is narrower: the exploration–exploitation balance can be derived from physical theory instead of tuned by hand, the results are competitive, and the ablations suggest that the derived transition is what helps.