Abstract: There are many shortages for the optimization of multidimensional continuous function, such as the low convergence speed and the poor accuracy. In order to improve the global optimization performance of multidimensional continuous function, this paper proposes the parameters optimization of the Modified Staged Continuous Tabu Search algorithm（MSCTS） based on multidimensional normal distribution. MSCTS is based on Staged Continuous Tabu Search algorithm（SCTS）, which includes three stages and has different starting points, selection range of neighborhoods and searching step size at different stages. To get the best accuracy and high convergence speed, the multidimensional normal distribution function is used to give the direction of neighborhoods selection. The results of experiments show that the reduction ratio of solution space in second stage has great impact on the accuracy and convergence speed, and the best reduction ratio is 0.5. At the same time, to improve the accuracy, the step size is shrinking at the third stage. The results of experiments show the best shrinking ratio is 0.1. Compared with SCTS algorithm, especially to solve multidimensional continuous function, MSCTS algorithm, after parameters optimization, can obtain nearly 5 times higher convergence speed and raises 10 orders of magnitude on the accuracy. Therefore, MSCTS algorithm is more suitable for solving multidimensional continuous function optimization.

Key words: Tabu search algorithm, parameter optimization, neighborhoods, multidimensional normal distribution, convergence speed

摘要： 针对多维连续函数全局优化中存在的算法收敛速度低和求解精度差的问题，在基于多维正态分布的分段禁忌优化算法的基础上，进行参数优化设置，对多维连续函数进行高精度快速优化。基于多维正态分布的分段禁忌优化算法以分阶段禁忌算法为基础，对于每一阶段设置不同的初始值、邻域选取范围和搜索步长。为获取精度高的全局最优解和较快的收敛速度，利用多维正态分布函数来指导邻域点的选取。试验表明：解精度和收敛速度受第二阶段解空间的缩小比例影响较大，当缩小比例为0.5时，对大部分测试函数会获得较高的解精度。同时为进一步提高解的精度，在算法的第三阶段进行变步长搜索，测试试验表明当步长缩小比例取0.1时，算法的运行速度较快。将经过参数优化设置后的改进的算法（MSCTS）与分段禁忌算法（SCTS）进行对比测试，试验结果表明，对多维连续函数寻优问题，利用MSCTS算法寻优，其收敛速度可达到5倍以上，同时结果精度提高10个数量级以上。因此MSCTS算法非常适合多维连续函数优化问题。

关键词: 禁忌搜索算法, 参数优化, 邻域, 多维正态分布, 收敛速度