中文摘要：

针对伊藤算法在求解离散组合优化问题时效率较低、收敛性较差等缺陷,本文提出的改进伊藤算法引入了协同扩散过程的漂移系数,采用局部搜索能力强的爬山法确定波动系数,将漂移和波动同步进行,当找到可行解之后再进行一定程度的波动.为了验证算法的有效性,将改进后的伊藤算法用于求解带软时间窗的车辆路径问题.仿真结果表明,改进后的算法效率更高,收敛速度更快,算法稳定性和健壮性也更好.此外,本文还根据马尔科夫链移向吸引元的性质及其各状态之间的转换关系,探讨了构造伊藤随机微分方程的马尔科夫链近似模拟算法及其收敛性证明.

英文摘要：

In order to overcome the shortcoming of the efficiency of the Ito algorithm for the discrete combinatorial optimization problems,an improved Ito algorithm based on collaborative diffusion coefficient and Hill climbing was proposed in this paper. To be consistent with the principle of Brownian motion, the drift and wave should be moved simultaneously, when it found a feasible solution, which continued to be a degree of renewed volatility. Experimental results show that the improved Ito algorithm for solving vehicle muting problem with a soft time window is valid, with the convergence speed, robustness and stability, especially Ito algorithm combines the ability of local search algorithms after climbing method performance has been greatly improved. Finally, according the nature of Markov chain to move to its attractive element and the transformation of the relationship between each state, the Markov chain approximation simulation algorithm which structures the Ito stochastic differential equation and its convergence was proved in this paper.