Toroidal Search Algorithm: A Topology-Inspired Metaheuristic with Applications to ODE Parameterization in Mathematical Oncology

Abstract We present the Toroidal Search Algorithm (TSA), a novel population-based metaheuristic optimization method inspired by the topology of a torus. Conventional metaheuristics frequently suffer from boundary stagnation, a phenomenon that severely degrades performance in bounded and high-dimensional search spaces. TSA addresses this limitation by embedding the search domain into a toroidal geometry, thereby eliminating artificial boundaries and enabling continuous cyclic exploration. Beyond boundary handling, TSA uses winding numbers to capture the history of agent movement across periodic dimensions, which are exploited to adaptively refine local search. A modified sigmoid control function regulates the transition between global and local search. Performance of TSA is evaluated on a collection of unimodal and multimodal benchmark functions at various dimensions. It consistently outperforms established metaheuristics. Notably, TSA demonstrates exceptional robustness to increasing dimensionality, maintaining fast convergence and low variance where competing methods deteriorate. To assess real-world applicability, we apply TSA to an inverse problem from mathematical oncology. With both synthetic and clinical data, TSA reliably recovers physiologically plausible parameters with greater stability and predictive accuracy than competing algorithms. These results demonstrate that TSA is a powerful and robust tool for large-scale global optimization in computational modelling applications. Striking ImageImage generated with Google Gemini. Competing Interest Statement The authors have declared no competing interest.