Implementing Traveling Salesman Problem (TSP) Using Simulated Annealing Algorithm with Code Integration

The provided documentation explores the application of simulated annealing algorithm to solve the classic combinatorial optimization challenge known as the Traveling Salesman Problem (TSP). This NP-hard problem requires finding the shortest possible Hamiltonian cycle visiting each city in a given set exactly once before returning to the origin city. The implementation employs simulated annealing - a probabilistic metaheuristic inspired by metallurgical annealing processes where controlled cooling reduces material defects. Algorithmically, this translates to: - Temperature parameter controlling exploration intensity - Neighbor generation through city swaps (2-opt moves) - Acceptance probability using Boltzmann distribution - Cooling schedule implementation (geometric/linear decay) Key implementation components include: 1. Distance matrix calculation between cities 2. Initial solution generation (random or nearest-neighbor) 3. Energy function representing total route distance 4. Acceptance criterion allowing temporary cost increases 5. Termination conditions (temperature threshold/iteration limit) The algorithm strategically accepts worse solutions during early high-temperature phases to escape local optima, while progressively favoring improvement as temperature decreases. This balance between exploration and exploitation enables effective navigation of complex solution spaces, making it particularly valuable for large-scale TSP instances in logistics, route planning, and circuit design applications.