Optimization Using The Simulated Annealing Algorithm
Edgar N. Reyes, Dennis I. Merino, Carl W. Steidley · 2020
In this paper we will briefly review the simulated annealing algorithm, an algorithm with applications in optimization and pattern recognition used extensively in artificial intelligence.In earlier papers the authors analyzed a simulation of the annealing of a solid, a dodecahedron in particular.Our use of this algorithm, which is based in the field of combinatorial optimization, reflects properties of Boltzman machines -a neural network characterized by massive parallelism.We will demonstrate two implementations of this algorithm in simulated annealing.Each of the implementations depends upon a neighborhood structure and a transition mechanism.In the first implementation our neighborhood structure is a linear transformation of the vector space of all configurations and the transition probability is deterministic.In this case, we will use techniques from character theory of finite groups to analyze simulated annealing.In the second implementation, a special case of which includes the first implementation, our neighborhood structure is a set-valued function and the transition mechanism is stochastic in nature.In this case, we use techniques from matrix analysis, in particular properties of doubly stochastic matrices, to analyze simulated annealing modeled and based on a class of Boltzman machines.For pattern recognition, we use the simulated annealing algorithm to solve the classic seven-segment display problem.This is a classification problem which we will solve by choosing an appropriate Boltzmann machine.