Quantum Snowflake Algorithm (QSA): A Snowflake-Inspired, Quantum-Driven Metaheuristic for Large-Scale Continuous and Discrete Optimization with Application to the Traveling Salesman Problem

The Quantum Snowflake Algorithm (QSA) is a novel metaheuristic for both continuous and discrete optimization problems, combining collision-based diversity, quantum-inspired tunneling, superposition-based partial solution sharing, and local refinement steps. The QSA embeds candidate solutions in a continuous auxiliary space, where collision operators ensure that agents—snowflakes—reject each other and remain diverse. This approach is inspired by snowflakes which prevent collisions while retaining unique crystalline patterns. Large leaps to escape deep local minima are simultaneously provided by quantum tunneling, which is particularly useful in highly multimodal environments. Tests on challenging functions like Lévy and HyperSphere showed that the QSA can more reliably obtain very low objective values in continuous domains than conventional swarm or evolutionary approaches. A 200-city Traveling Salesman Problem (TSP) confirmed the excellent tour quality of the QSA for discrete optimization. It drastically reduces the route length compared to Artificial Bee Colony (ABC), Genetic Algorithm (GA), Particle Swarm Optimization (PSO), Simulated Annealing (SA), Quantum Particle Swarm Optimization (QPSO), and Cuckoo Search (CS). These results show that quantum tunneling accelerates escape from local traps, superposition and local search increase exploitation, and collision-based repulsion maintains population diversity. Together, these elements provide a well-rounded search method that is easy to adapt to different problem areas. In order to establish the QSA as a versatile solution framework for a range of large-scale optimization challenges, future research could investigate multi-objective extensions, adaptive parameter control, and more domain-specific hybridisations.