## 4 Experimental Results  
In this study, we used j30 (projects with 30 jobs), j60 (projects with 60 jobs), and j90 (projects with 90 jobs), each set containing 480 instances from PSPLIB [69] for analysis. The project instances in PSPLIB have been generated by the standard project generator ProGen [69] by authors of [70]. Tables 1 and 2 contain the summary of the parameters used by the ProGen software to generate the project instances of single-mode RCPSP with renewable resources. \begin{table}
\begin{tabular}{c c c c c c c c} \hline Range & \(d_{j}\) & 1 Q 1 & \(U_{Q}\) & \(K_{Q}\) & \(S_{1}\) & \(S_{j}\) & \(P_{J}\) & \(P_{j}\) \\ \hline Min & 1 & 4 & 1 & 1 & 3 & 1 & 3 & 1 \\ \hline Max & 10 & 4 & 10 & 2 & 3 & 3 & 3 & 3 \\ \hline \end{tabular}
\end{table} 
Table 1: Base parameter setting for ProGen. The base parameters are adjusted individually for each benchmark set, and variable parameters are varied within each benchmark set. As usual, \(d_{j}|\mathbf{Q}|\), \(U_{\mathbf{Q}}\), \(K_{\mathbf{Q}}\), \(S_{1}\), \(S_{j}\), \(P_{j}\), and \(P_{j}\) in Table 1 denote processing time for activity \(j\), total number of unique resources, per-period usage of particular resource, number of different categories of resources consumed, number of start activities, number of successors of an activity \(j\), number of finish activities, and number of predecessors of an activity \(j\), respectively. In Table 2, the abbreviations NC, RF, and RS correspond to network complexity, resource factor, and resource strength, respectively, for resources belonging to category \(k\) within \(K_{\mathbf{Q}}\). NC is quantified as the average number of unique arcs for each node, considering dummy nodes as well. The RF represents the average proportion of resources from category \(k\in K_{\mathbf{Q}}\) that are utilized. It can be seen as an average measure of how much resource is typically used by the activities in a project. Meanwhile, resource strength RS refers to the robustness of the resource constraints for the specified resource category \(k\in K_{\mathbf{Q}}\). It measures the scarcity or abundance of a resource relative to the demand for that resource in a project. If a resource has high strength, it means there is plenty of it available in relation to how much is needed for the project. For each project set, 480 instances were created using the full factorial design of variable parameters with 10 replications (i.e., \(3\times 4\times 4\times 10=480\)). A file named _J9040_9.SM_, corresponds to project set j90, with variable combination 40 and replication number 9 of single-mode. In the experimental design of [70], the authors have used four steps to generate a project in the form of an acyclic directed graph employing a number of fundamental graph theories. The first three steps generate the base project, and the fourth step is repeated until conditions imposed by the combination sought from the parameters in Table 2 are met. For instance, to generate J9001 (i.e., project with 90 jobs and combination 01) the steps are as follows:  
1. Generate a random integer for each of \(S_{1}\) and \(P_{j}\) using the range from Table 1. In our case, a random integer numbers from a closed interval (\(|\,S_{1}|:=rand[3,3]=3\)) for \(S_{1}\) and (\(|\,P_{j}|:=rand[3,3]=3\)) for \(P_{j}\) are generated. Then, \(|\,S_{1}|\) number of nodes are connected by an arc to a dummy node (source) denoted by 1. These \(|\,S_{1}|\) nodes are then numbered from 2 to \(|\,S_{1}|+1\) and are called starting activities. Similarly, \(|P_{j}|\) nodes are connected by an arc to a dummy node (sink) denoted by \((90+1)\) where \(|P_{j}|\) are numbered \((90-|P_{j}|)\) to 90. These nodes are then called finish-activities. 2. A random predecessor node (activity) is assigned starting with the lowest indexed (non-start) node until all the jobs (i.e., \(|S_{1}|+2\) to \((90-|P_{j}|-1)\) are assigned. 3. If any node has no successor, a random node is assigned as the successor to the node.