# Evolutionary Statistical System Based on Novelty Search:
## 2 Related Works
### ESSIM-EA and ESSIM-DE Frameworks  
This section summarizes the operation of the more recently developed systems, ESSIM-EA and ESSIM-DE, which are both based on ESS and are also included in our comparison against our new method in Section 4. ESSIM-EA stands for _Evolutionary Statistical System with Island Model based on evolutionary algorithms_, while ESSIM-DE is _ESSIM based on Differential Evolution_. Both systems fit into the category of DDM-MOS, since they employ a method for selecting multiple  
Figure 3: Generation of the prediction. **sc. **: scenario; **FS**: fire simulator. ; **SS**: Statistical Stage; **Kign\({}_{n}\)**: _Key Ignition Value_ computed for instant \(t_{n}\); **PS**: Prediction Stage; **PFL\({}_{n+1}\)**: predicted fire line for \(t_{n+1}\). solutions from the space of possible scenarios and producing an overlapped result in order to perform the prediction of fire propagation. ESSIM-EA and ESSIM-DE are summarized in Figure 4, reproduced and modified from [11] (Published under a Creative Commons Attribution-NonCommercial-No Derivatives License (CC BY NC ND). See [[https://creativecommons.org/licenses/by-nc-nd/4.0/](https://creativecommons.org/licenses/by-nc-nd/4.0/)]([https://creativecommons.org/licenses/by-nc-nd/4.0/](https://creativecommons.org/licenses/by-nc-nd/4.0/)), accessed on 13 October 2022). The four main stages in these systems are the same as in ESS: Optimization Stage (**OS**), Statistical Stage (**SS**), Calibration Stage (**CS**), and Prediction Stage (**PS**). Because both ESSIM systems use a hierarchical scheme of processes, these stages are subdivided to carry out the different processes in the hierarchy. The Master/Worker hierarchy of ESS is augmented with a more complex hierarchy that consists of one Monitor, which handles multiple Masters, and, in turn, each Master manages a number of Workers. Essentially, the system uses a number of islands where each island implements a Master/Worker scheme; the Monitor then acts as the Master process for the Masters of the islands. On each island, the Master/Worker process operates as described in Section 2.1 for ESS: the Master distributes scenarios among the Workers for performing the simulations in the **OS**. Figure 4: Evolutionary Statistical System with Island Model. **RFL\({}_{4}\)**: Real Fire Line at time \(t_{i}\); **PV\({}_{\{\textbf{1}\_n\}}\)**: parameter vectors (scenarios); **FS**: fire simulator; **PEA\({}_{\textbf{F}}\)**: Parallel Evolutionary Algorithm (fitness evaluation); **OS-Master\({}_{\{a,b,\ldots\}}\)**: Optimization Stage in Masters \(a,b\), etc. ; **OS-Worker\({}_{\{1,n\}}^{\{a,b,\ldots\}}\)**: Optimization Stage in Workers \(1\) to \(n\) belonging to one Master in \(\{a,b,\ldots\}\); **PEA**: Parallel Evolutionary Algorithm; **SS**: Statistical Stage in Master; **SK**: Search for \(K_{igni}\); **K\({}_{\textbf{Sign}}\)**: _Key Ignition Value_; **FF**: Fitness Function; **CS-Master**: Calibration Stage in Master; **CS-Monitor**: Calibration Stage in Monitor; **PS**: Prediction Stage; **PFL\({}_{\textbf{i}+1}\)**: Predicted Fire Line for instant \(t_{i+1}\); **SS\({}_{\textbf{SM}}\)**: Statistical Stage in Monitor; **pm\({}_{\textbf{a}}\)**: probability map sent from \(Master_{a}\) to Monitor; \(\{\textbf{pm},\textbf{K}\}\)**: best probability map and associated \(K_{ign}\). The process begins with the Monitor, which sends the initial information to each island to carry out the different stages. The Master process of each island performs the **OS**: it controls the evolution of its population and the migration process. On each island during each iteration of the evolutionary algorithm, the Master sends individuals to the Worker processes, which are in charge of their evaluation. For more details on the operation of the island model, see [11]. After the evolutionary process, the **SS** takes place in which the Master performs the computation of the probability matrix that is required for the **CS** and **PS**.