The combination stretching function technique with simulated annealing algorithm for global optimization

A stretching function technique is combined with the simulated annealing (SA) algorithm for the global optimization problems. In the presented algorithm, the obtained local optimum information by SA search is used to build a stretching function. To speed up the convergence of SA, SA is executed iteratively on the stretching function constructed with respect to the previously found local minima instead of on the original objective function. Furthermore, a new next trial point generation scheme in SA is designed to increase the diversity of the trial points to make the introduced technique more effective. In the numerical experiments, we first investigate and compare the effectiveness and efficiency of the combination of the stretching technique with a newly designed SA (SSA), with particle swarm optimization and with differential evolution algorithm, respectively, on eight typical test functions in terms of the average number of the function evaluations and its standard deviation, and the success rate. Second, we systematically compare the numerical results of SSA with the traditional SA with elitist and SA with new generation scheme on 37 benchmark problems. The numerical results show that the hybrid method is effective for global optimization.