Solving Nonlinear Equation Systems Using Simulated Annealing Algorithm

This implementation utilizes MATLAB to program a simulated annealing algorithm for solving nonlinear equation systems. Simulated annealing is an optimization algorithm based on the principle of physical annealing, capable of finding optimal solutions for complex nonlinear equation systems. By leveraging MATLAB's powerful computational capabilities and programming environment, we can develop efficient and accurate simulated annealing programs to address this challenge. The algorithm mimics the metal annealing process by gradually reducing the system energy to converge toward optimal solutions. In nonlinear equation system solving, simulated annealing employs random search and progressive optimization to approximate optimal solutions. The MATLAB implementation typically involves defining an objective function that represents the sum of squared residuals of the equations, implementing temperature scheduling using exponential decay (e.g., T = T0 * cooling_rate^iteration), and configuring acceptance probabilities via the Metropolis criterion. Key implementation components include: - Objective function formulation: Converting equation residuals into measurable energy states - Temperature control: Implementing annealing schedules with adjustable cooling rates - State transition: Designing neighborhood search mechanisms for solution exploration - Termination criteria: Setting convergence thresholds or maximum iteration limits The algorithm's stochastic nature allows it to escape local minima, making it particularly effective for multi-modal optimization problems in nonlinear systems. Through proper parameter tuning and MATLAB's vectorized operations, the implementation achieves both computational efficiency and solution accuracy, providing a robust approach for complex nonlinear equation system challenges.