模拟退火法临界温度估算及整体最优化新算法

Evaluation of Critical Temperature in Simulated Annealing and New Global Optimization Algorithm

模拟退火法是在模拟固体退火过程的基础上发展起来的一种整体最优化算法。本文在研究模拟退火过程的特征量——临界温度和新的随机搜索算法的基础上，得到一种只需在较小的温度范围内进行退火的新的模拟退火算法。数值试验表明，对于目标函数的局部极小值和整体最小值不接近相等的优化问题，本算法只需较少数量的迭代便能收敛于整体最小解。

Simulated annealing(SA) algorithm is a global optimization algorithm developed from simulating an annealing process in thermophysics.The application of SA is still limited because of its poor efficiency.The key to the efficiency lies in the choice of initial temperature and the random search technique in annealing simulation.The existing study on initial temperature was based on many trial tests for specific problems and the formula derived for estimating initial temperature lacks wide applicability. With localized random search technique, these SA algorithms are difficult to get rid of local minima. After the study on the critical temperature characteristic of annealing process and a random search technique,a new SA algorithm is constructed, in which annealing simulation is carried out within a small temperature range.Numerical tests show that ,if the values of cost function of global minimum and local minima in the problem concerned are not nearly equal, the algorithm converges to the global optimal solution after several iterations.