Simulated Annealing (SA) Algorithm

In this article, we explore the Simulated Annealing (SA) algorithm, a probabilistic heuristic optimization technique inspired by the annealing process in metallurgy. SA algorithm serves as a powerful tool for solving complex real-world optimization problems by simulating the physical process of heating and controlled cooling of materials. The core implementation involves defining an objective function (energy function) and performing stochastic searches through state space via random walks. A key characteristic is the temperature parameter that gradually decreases according to a cooling schedule, allowing the algorithm to escape local optima while progressively converging toward global solutions. Typical implementations include Metropolis acceptance criteria where worse solutions may be temporarily accepted with probability exp(-ΔE/T), where ΔE represents energy change and T is current temperature. SA has demonstrated effectiveness in combinatorial optimization, parameter estimation, physical system modeling, and computer vision applications. Code implementations typically involve initialization routines, neighbor state generation functions, and temperature decay mechanisms using geometric cooling schedules like T_{k+1} = α·T_k with α∈(0,1).