Simulated Annealing Algorithm

The Simulated Annealing algorithm is an optimization technique inspired by the physical process of annealing in metallurgy, widely used for solving complex global optimization problems. It mimics the thermal motion of molecules during the cooling of high-temperature materials, introducing stochastic behavior during the search process to avoid trapping in local optima.

### Core Algorithm Concept Initial Temperature Setting: The system starts at a high temperature where the algorithm has a higher probability of accepting worse solutions, facilitating escape from local optima. Iterative Search: As temperature gradually decreases, the algorithm probabilistically accepts solutions inferior to the current one to prevent premature convergence. Cooling Schedule: Temperature reduces according to a predefined strategy (e.g., exponential decay), eventually stabilizing near the global optimum.

### Key Parameters Temperature Schedule: Dictates how the algorithm cools, directly impacting convergence speed and solution quality. Implementation often uses a geometric cooling function like `T_new = α * T_old` where α is the cooling rate. Acceptance Criterion: Typically based on the Metropolis criterion, allowing acceptance of worse solutions at high temperatures to enhance global exploration. Code implementation compares `exp(-ΔE/T) > rand()` where ΔE is energy difference. Termination Condition: Stops when temperature falls below a threshold or no improvement occurs after consecutive iterations.

### MATLAB Implementation Features MATLAB code typically includes clear temperature control and state generation logic, allowing easy parameter adjustment for experimentation. The algorithm handles both continuous and discrete optimization problems, such as TSP (Traveling Salesman Problem) or function extremum searching. Key functions often involve: - `anneal()` for main optimization loop - `energy()` for objective function calculation - `neighbor()` for generating candidate solutions

The algorithm's strength lies in its robustness and adaptability to complex problems, though careful parameter tuning is essential to balance efficiency and solution accuracy.