Quantum-Inspired Evolutionary Algorithms for Traveling Salesman Optimization

This paper introduces a novel hybrid evolutionary approach to the Traveling Salesman Problem (TSP), integrating adaptive mutation strategies with quantum-inspired harmonic perturbations. Our method achieves a final route distance of 7.4202 on a 50-city instance, surpassing traditional heuristics and competing with state-of-the-art solvers. We formalize the mathematical foundations, analyze computational efficiency, and benchmark results against existing techniques. Future work explores scalability, reinforcement learning hybrids, and potential quantum computing integration.