Simulated Annealing Applications

Abstract

Simulated Annealing (SA) is a method to solve an optimization problem by simulating a stochastic thermal dynamics of a metal cooling process. SA obtains an optimal solution by simulating a physical fact that liquid metal transmutes to be crystal (which has the smallest internal thermal energy) if it is cooled satisfactory slowly from a high temperature state (with large internal thermal energy). In other words, functional minimization corresponds to minimization of internal thermal energy of metal in a melting pot. The idea to solve the optimization problem by using this fact is proposed by Kirkpatric [17]. He demonstrated that the method is successfully applicable to so-called combinatorial optimization problem. In the reference [17], he has introduced several applications (physical design of computers, wiring and traveling salesmen) of SA. In power system applications, many combinatorial optimization problems have been solved by using SA. There are many kinds of combinatorial optimization problems in power systems area: generator maintenance scheduling, unit commitment, VAR planning, network planning, distribution systems reconfiguration etc. It is well known that we have not yet found an established solution algorithm for these problems. Most efficient solution algorithms proposed for the problems can only find approximated optimal solutions, and we cannot find the exact optimal solution for the practical problem. It is well known that SA can find near optimal solutions for these combinatorial optimization problems if we decrease temperature carefully and slowly enough. Moreover, the simulated annealing algorithm is so simple as shown in later sections. Therefore, solutions obtained by using SA are often used as a reference solution to evaluate the performance of newly developed solution algorithms even though it takes huge computational burden.