Simulated Annealing with Advanced Adaptive Neighborhood

It was Kirkpatrick et al. who first proposed simulated annealing, SA, as a method for solving combinatorial optimization problems[1]. It is reported that SA is very useful for several types of combinatorial optimization problems[2]. The advantages and the disadvantages of SA are well summarized in [3]. The most remarkable disadvantages are that it needs a lot of time to find the optimum solution and it is very difficult to determine the proper cooling schedule. To determine the proper cooling schedule, many preparatory trials are needed. When the cooling schedule is not proper, the guarantee of finding optimum solution is lost. There are two approaches to shorten the calculation time in SA. One is determining the cooling schedule properly. SA with the proper cooling schedule can provide an optimum solution quickly. This approach is well reported by Ingber[3]. The other approach is to choose a proper neighborhood. For discrete or combinatorial optimization problems, the neighborhood structure is uniquely determined by the generation method of a new solution from the current one and it is difficult to control. However, the neighborhood structure for continuous optimization problems is very simple, and it is easily controlled by the neighborhood range, or the scaling parameter of the search step. In this paper, we propose a new method for controlling the neighborhood range in continuous optimization problems to obtain good solutions in shorter annealing steps. The Corana’s method[4] which controls the neighborhood range is very useful since the method automatically determines the neighborhood range, but the performance of the method in terms of the search ability has not been clear. We investigate the performance of the Corana’s method, and show the necessity of introducing a new adaptive method which controls the neighborhood range and also provides high searching performance.