离散事件动态系统性能优化的非光滑分析方法

扰动分析（ＩＰＡ）是研究离散事件动态系统性能优化的最有效方法，当系统的性能函数不可微时，该方法不可直接应用．本文利用关键路径的概念，证明了具有有限存储器的随机串行生产线的关键路径以概率１唯一时，系统稳态性能函数可微，而且，当系统的关键路径以正概率不唯一时性能函数的方向导数存在．对于一个给定的样本，当关键路径不唯一时，由关键路径的梯度方向可构造出系统性能函数的下降方向的估计量，进而用非光滑分析方法优化系统性能

PERFORMANCE OPTIMIZATION OF DISCRETE EVENT DYNAMIC SYSTEMS VIA NONSMOOTH OPTIMIZATION

Perturbation analysis is the most efficient method available to study DEDS with differentiable performance functions. However, there exist a broad class of DEDS have nonsmooth performance functions. In this paper, by using the notion of critical path, it is proved that the steady state performance function of stochastic serial production lines is differentiable if the critical path is unique w.p.1. Moreover, it is shown that in the case of the critical path being not unique, the directional derivatives of the performance functions exist. For a given sample point, when the critical paths are not unique, the steepest descent direction of the sample performance function is constructed from the gradients of these critical paths, which is a unbaised estimate of the system performance function. Finally, a nonsmooth optimization algorithm is provided.