Annealing Algorithm for Single-Parameter Optimization

This article introduces an annealing algorithm suitable for single-parameter optimization, which can be applied to solve various problems. The annealing algorithm is an optimization technique based on simulated annealing principles, mimicking the metal annealing process to find optimal solutions. Its core mechanism involves random searching through the solution space while employing a probability-based strategy to accept either better solutions or occasionally worse solutions, gradually reducing the search "temperature" to approach global optima. From an implementation perspective, the algorithm typically requires defining several key components: an objective function to evaluate solution quality, a temperature schedule controlling the cooling process, and a neighbor generation function for exploring nearby solutions. The probability acceptance function often follows the Metropolis criterion, where worse solutions are accepted with probability exp(-ΔE/T), where ΔE represents the energy difference and T denotes the current temperature. This algorithm finds applications across multiple domains including logistics planning, machine learning hyperparameter tuning, and image processing optimization. For single-parameter problems, implementation becomes particularly straightforward - the parameter space can be efficiently navigated using simple neighborhood functions like small perturbations, while temperature scheduling can be implemented through geometric cooling (T_{k+1} = αT_k with α typically between 0.8-0.99). Therefore, the single-parameter annealing algorithm represents a highly practical and powerful optimization tool for various engineering and scientific applications.