集成调度数据集

1 配送 121TTT

1.1 配送集成ADSAS1

简介：生产与配送集成调度是近些年来热门的研究领域。大多数学者认为 (Potts, 1980)是该领域的开篇之作。随着该领域专家学者的不断拓展和深入，集成调度的相关研究得到了空前的发展。各方面的理论和方法也不断被提出，可参照综述文献 (Chen, 2010),(Moons et al., 2017), (Kumar et al., 2020)进行系统的梳理。

根据问题特征我们对如下数据集进行简要描述：

• 生产调度：(作业车间调度、流水车间调度（流水线、置换、混流）、分布式车间调度、柔性调度、模糊调度、动态调度 等)
• 配送调度：(运输问题、车辆路径问题（容量限制、时间窗约束、多行程等））
  我们所提出的数据集所应用的模型涉及：
  流水线生产 & 车辆路径问题（考虑容量限制、时间窗约束、多行程）&模糊旅途时间

  1.1 配送集成ADSAS1

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  1.1 配送集成ADSAS1

  $$\begin{equation} \textcolor{red} {w_{k+1}=w_k-a_k \tilde{g}\left(w_k, \eta_k\right) ,k=1,2,3,\dots} \end{equation}$$

  1.1 配送集成ADSAS1

  This simple example can illustrate why the RM algorithm converges.

  1.4配送集成

• When $w_k>w^$, we have $g\left(w_k\right)>0$. Then, $w_{k+1}=w_k-a_k g\left(w_k\right)<w_k$. If $a_k g\left(w_k\right)$ is sufficiently small, we have $w^<w_{k+1}<w_k$. As a result, $w_{k+1}$ is closer to $w^*$ than $w_k$.
• When $w_kw_k$. If $\left|a_k g\left(w_k\right)\right|$ is sufficiently small, we have $w^>w_{k+1}>w_k$. As a result, $w_{k+1}$ is closer to $w^$ than $w_k$.

$$\begin{aligned} \tilde{g}(w, \eta) & = w-x \\ & =w-x+\mathbb{E}[X] -\mathbb{E}[X] \\ & =(w-\mathbb{E}[X]) + (\mathbb{E}[X]-x)\\ & =g(w)+\eta \end{aligned}$$ $$\begin{equation} w_{k+1} = w_k-\alpha_k \textcolor{blue} {\nabla_w f\left(w_k, x_k\right)}, \end{equation}$$

where $x_k$ is the sample collected at time step $k$. It relies on stochastic samples ${x_k}$

1. Compared to the gradient descent algorithm: Replace the true gradient $\mathbb{E}\left[\nabla_w f\left(w_k, X\right)\right]$ by the stochastic gradient $\nabla_w f\left(w_k, x_k\right)$.

2. Compared to the batch gradient descent method: let $n=1$.

3. From GD to SGD: The stochastic gradient $\nabla_w f\left(w_k, x_k\right)$ can be viewed as a noisy measurement of the true gradient $\mathbb{E}\left[\nabla_w f(w, X)\right]$:

$$\nabla_w f\left(w_k, x_k\right)=\mathbb{E}\left[\nabla_w f(w, X)\right]+\underbrace{\nabla_w f\left(w_k, x_k\right)-\mathbb{E}\left[\nabla_w f(w, X)\right]}_\eta .$$ $$\begin{aligned} \mathbb{E}(\eta) & =\mathbb{E}(\nabla_w f\left(w_k, x_k\right)-\mathbb{E}\left[\nabla_w f(w, X)\right])\\ & =\mathbb{E}_{x_k}[\nabla_w f\left(w_k, x_k\right)]-\mathbb{E}_X\left[\nabla_w f(w, X)\right]=0 \end{aligned}$$

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