【作者】 李楠；

【导师】 李波；

【作者基本信息】 天津大学 ， 物流工程， 2012， 硕士

【摘要】 随机仿真优化问题研究基于仿真的目标优化问题,即用模型仿真的结果来估计实际系统的性能,然后通过优化算法来得到最优解或满意解的过程。随着问题的复杂程度加深,仿真计算量增加的速度十分惊人。如何大幅降低仿真计算量是这类问题的关键所在,因此,探讨研究随机仿真优化问题具有重要的理论意义和应用价值,本文基于模拟预算最优分配算法的思想,对常见的随机仿真优化问题和带随机约束的仿真优化最优子集选择问题进行了一系列的研究。论文在阅读了大量文献的基础上,提出了一种基于模拟预算最优分配的思想来求解随机仿真优化问题。利用数理统计中的Bonferroni不等式估计正确选择的概率,通过对仿真资源的合理分配,使得最优方案被正确选择的概率最大化,从而大大提高了仿真的运行效率。最后仿真试验说明了该方法的高效性。进一步,论文还提出了一种基于改进的模拟预算最优分配的思想来求解带随机约束的仿真优化最优子集选择问题。通过智能控制每个方案的仿真次数,证明了在有限的计算量下,从一系列方案中可选出最优子方案,使得正确选择最优子方案的概率最大化。实践证明,该算法具有普遍性,它可与基于仿真的全局优化算法相结合,来进一步提高解的搜索效率。最后,对随机仿真优化的应用进行了探讨,给出一个与启发式算法的集成化框架,提供了两个应用随机仿真优化方法求解的简单例子并给出了应用模拟预算最优分配方法求解的数值实验。更多还原

【Abstract】 Stochastic simulation optimization (often shortened as simulation optimization) studies the optimization problem of simulation-based objectives, which using the result of the simulation model to estimate the actual performance of the system, and then an optimal or satisfactory solution is found by using the optimization algorithm. With the complexity of the problem at a deeper level, the amount of the computing in simulation is amazing. How to significantly reduce the amount of computing in simulation is the key to such problems, therefore, explore the problem of stochastic simulation optimization has important theoretical significance and application value. This paper introduced an optimal allocation algorithm based on optimal computing budget allocation and conducted a series of studies on the problem of selecting the best design from a discrete numbers of alternatives and the problem of selecting an optimal subset in the presence of stochastic constraints.On the basis of reading a large number of literatures, this paper proposes an idea based on computing budget allocation to solve the stochastic simulation optimization problem. A common approximation procedure used in simulation and statistics literature is adopted to estimates the probability of correct selection, which is based on the Bonferroni inequality. An asymptotic allocation rule is given to maximize the probability of correct selection through rational allocation of simulation resource, and thus greatly improving the efficiency of allocating simulation replications among competing designs. Finally, the simulation result shows the efficiency of the algorithm. Further, this paper provides an alternative approach based on the Optimal Computing Budget Allocation to tackle the problem of selecting an optimal subset in the presence of stochastic constraints. In the limited amount of computation, the top-m out of k designs based on simulated output can be identified and the probability of correct selection can be maximized by intelligent control simulation times of each design. Practice has proved that the algorithm is universal; it can be combined with simulation-based global optimization algorithm to further improve the search efficiency. Finally, the applications of stochastic simulation optimization in supply chain and logistics are discussed, a framework integrated with heuristic algorithm is given, and two examples of stochastic simulation optimization are provided.更多还原