A UNIFORM ENHANCEMENT APPROACH FOR OPTIMIZATION ALGORITHMS: SMOOTHING FUNCTION METHOD
Abstract
In this paper, we propose a uniform enhancement approach called smoothing function method, which can cooperate any optimization algorithm and improve its performance. The method has two phases. In the first phase, a smoothing function is constructed by using a properly truncated Fourier series. It can preserve the overall shape of the original objective function but eliminate many of its local optimal points, thus it can well approach the objective function. Then, the optimal solution of the smoothing function is searched by an optimization algorithm (e.g. traditional algorithm or evolutionary algorithm) so that the search becomes much easier. In the second phase, we switch to optimize the original function for some iterations by using the best solution(s) obtained in phase 1 as an initial point (population). Thereafter, the smoothing function is updated in order to approximate the original function more accurately.
These two phases are repeated until the best solutions obtained in several successively second phases cannot be improved obviously. In this manner, any optimization algorithm will become much easier in searching optimal solution. Finally, we use the proposed approach to enhance two typical optimization algorithms: Powell direct algorithm and a simple genetic algorithm. The simulation results on ten challenging benchmarks indicate the proposed approach can effectively improve the performance of these two algorithms.
