Simulated Annealing Algorithm Code Implementation

This section presents the code implementation of the Simulated Annealing Algorithm (SAA) for solving the 0-1 knapsack problem. The simulated annealing algorithm is a stochastic search technique that mimics the metal cooling process to find optimal solutions. For the 0-1 knapsack problem, the objective is to select items to maximize total value while ensuring the total weight does not exceed the knapsack's capacity. The code implementation follows these key steps: 1. Initialization: Generates random initial solutions representing item selections 2. Temperature scheduling: Implements a cooling scheme that gradually reduces the temperature parameter 3. Neighborhood search: Creates new solutions by flipping item selection states (0 to 1 or 1 to 0) 4. Acceptance probability: Uses the Metropolis criterion to probabilistically accept worse solutions to escape local optima 5. Termination: Stops when temperature approaches zero or reaches maximum iterations Key functions include: - Energy calculation: Evaluates solution quality using value maximization and weight constraint handling - State transition: Implements random perturbation mechanism for solution space exploration - Cooling schedule: Controls the exploration-exploitation balance through temperature decay The algorithm continuously modifies item selections and arrangements to find improved solutions. Through simulated annealing, we achieve better optimization results for the 0-1 knapsack problem by balancing global exploration and local refinement, ultimately returning the best-found solution when the algorithm converges.