Manuscript draft to JOSH

JOSH/DAgger.tex

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+\begin{algorithm}[t]
+    \caption{DAgger: Dataset Aggregation for JSP}
+    \label{pseudo:DAgger}
+    \begin{algorithmic}[1]
+        \Require $T\geq1$
+        \Procedure{DAgger}{$\pi_\star,\Phi^\text{OPT},T$}
+        \State $\Phi^{\text{IL}0} \gets \Phi^{\text{OPT}}$ \Comment{initialize 
+        dataset}
+        \State $\hat{\pi}_0 \gets$ \Call{Train}{$\Phi^{\text{IL}0}$}
+        \Comment{initial model, equivalent to \cref{sec:expertPolicy}}
+        \For{i}{1}{T} \Comment{at each imitation learning iteration}
+        \State Let $\pi_i = \beta_i\pi_\star + (1-\beta_i)\hat{\pi}_{i-1}$
+        \Comment{\cref{eq:il}}
+        \State Sample $K$-step tracks using $\pi_i$
+        \Comment{cf. \Call{ActiveIL}{$i,\hat{\pi}_{i-1},\pi_\star$}}
+        \State $\Phi^{\text{IL}i} = \{(s,\pi_\star(s))\}$ 
+        \Comment{visited states for $\pi_i$ and actions by $\pi_\star$}
+        \State $\Phi^{\text{DA}i} \gets \Phi^{\text{DA}i-1} \cup 
+        \Phi^{\text{IL}i}$ 
+        \Comment{aggregate datasets, cf. \cref{eq:DAgger}}
+        \State $\hat{\pi}_{i+1} \gets$ \Call{Train}{$\Phi^{\text{DA}i}$}
+        \Comment{preference model from \cref{eq:jssp:linweights}}
+        \EndFor
+        \State \Return best $\hat{\pi}_i$ on validation \Comment{best 
+        preference model}
+        \EndProcedure
+    \end{algorithmic}
+\end{algorithm}

JOSH/constructJSP.tex

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+\begin{algorithm}[t]
+    \caption{Pseudo code for constructing a JSP sequence using a 
+    deterministic scheduling policy rule, $\pi$, 
+    for a fixed construction heuristic, $\Upsilon$.} 
+    \label{pseudo:constructJSP}
+    \begin{algorithmic}[1]
+        \Procedure{ScheduleJSP}{$\pi,\Upsilon$}
+        \State $\vchi \gets \emptyset$  
+        \Comment{initial current dispatching sequence}
+        \For{k}{1}{K=n\cdot m} 
+        \Comment{at each dispatch iteration}
+        \ForAll{$J_j\in \mathcal{L}^{(k)}\subset \mathcal{J}$} 
+        \Comment{inspect job-list}
+        \State $\vphi^j \gets \vphi\circ\Upsilon\left(\vchi^j\right)$ 
+        \label{pseudo:constructJSP:phi}
+        \Comment{temporal features for $J_j$}
+        \State $I_j^{\pi} \gets \pi\left(\vphi^j\right)$ 
+        \Comment{priority for $J_j$}
+        \EndFor
+        \State $j^* \gets \argmax_{j\in \mathcal{L}^{(k)}}\{I_j^{\pi}\}$ 
+        \Comment{choose highest priority}
+        \State $\chi_k \gets J_{j^*}$ 
+        \Comment{dispatch $j^*$}
+        \EndFor
+        \State \Return $C_{\max}^{\pi} \gets \Upsilon(\vchi)$ 
+        \Comment{makespan and final schedule}
+        \EndProcedure
+    \end{algorithmic}
+\end{algorithm}

JOSH/data-sim.tex

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+{\renewcommand{\arraystretch}{1.5}
+	\begin{tabular}{lcccl}\toprule 
+		name & size ($n\times m$) & $N_{\text{train}}$ & $N_{\text{test}}$ & note\\
+		\midrule
+		\jrnd{10}{10}  & $10\times10$ & 300 & 200 & random        \\
+		\jrndn{10}{10} & $10\times10$ & 300 & 200 & random-narrow \\ 
+		\frnd{10}{10}  & $10\times10$ & 300 & 200 & random        \\ 
+		\bottomrule
+	\end{tabular}
+}

JOSH/features-description.tex

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+\centering
+\scriptsize
+\begin{tabular}{cll} %p{0.45\textwidth}|p{0.4\textwidth}|}
+	\toprule
+	$\vphi$ & Feature description & Mathematical formulation \\ 
+	%\hline \multicolumn{4}{c}{\textbf{Local features}} \\
+	\midrule
+	\multicolumn{3}{c}{\textbf{job related}}\\
+	\phiproc & job processing time & $p_{ja}$ \\
+	\phistartTime & job start-time & $x_s(j,a)$ \\
+	\phiendTime & job end-time & $x_e(j,a)$ \\
+	\phiarrivalTime & job arrival time & $x_e(j,a-1)$\\
+	\phiwait & time job had to wait & $x_s(j,a)-x_e(j,a-1)$ \\
+	\phijobTotProcTime & total processing time for job & 
+ $\sum_{a\in \mathcal{M}}p_{ja}$ \\
+	\phijobWrm & total work remaining for job & 
+	$\sum_{a'\in\mathcal{M}\setminus \mathcal{M}_{j}}p_{ja'}$ \\
+	\phijobOps & number of assigned operations for job & 
+	$|\mathcal{M}_j|$ \\
+	\midrule
+	\multicolumn{3}{c}{\textbf{machine related}}\\
+	\phimacFree & when machine is next free & 
+ $\max_{j'\in \mathcal{J}_a} \{x_e(j',a)\}$ \\
+	\phimacTotProcTime & total processing time for machine & 
+ $\sum_{j\in \mathcal{J}}p_{ja}$ \\
+	\phimacWrm & total work remaining for machine & 
+	$\sum_{j'\in\mathcal{J}\setminus \mathcal{J}_{a}}p_{j'a}$ \\
+	\phimacOps & number of assigned operations for machine & 
+	$|\mathcal{J}_a|$ \\
+	\phireducedSlack & change in idle time by assignment & 
+ $\Delta s(a,j)$ \\
+	\phimacSlack & total idle time for machine & 
+ $\sum_{j'\in \mathcal{J}_a}s(a,j')$ \\
+	\phiallSlack & total idle time for all machines & $\sum_{a'\in 
+	\mathcal{M}}\sum_{j'\in \mathcal{J}_{a'}}s(a',j')$ \\
+	\phimakespan & current makespan &
+ $\max_{(j',a')\in \mathcal{J} \times \mathcal{M}_{j'}}\{x_f(j',a')\}$ \\
+	\bottomrule
+\end{tabular}