# Evolutionary Statistical System Based on Novelty Search:
## 2 Related Works
### ESS Framework
Such evaluations are needed for guiding the search and producing an adequate result for the next stage (the **SS**). Therefore, the fitness is obtained by comparing the simulated map with the real state of the fire at the last known instant of time. The Master process receives these evaluations (the simulated maps with their fitness) and uses them to continue with the evolution, i.e., to perform selection, reproduction, and replacement of the population. Although not shown in the figure for clarity, it is important to note that the **OS** is iterative in two ways. Firstly, the Master must divide all scenarios in the population into a number of vectors according to the number of Worker processes; e.g., if there are 200 scenarios and 50 Workers, the Master must send a different **PV** (each containing 50 scenarios \(PV_{\{1...50\}}\)) for evaluation four times in order to complete the 200 evaluations. Secondly, the Master will repeat this process for each generation of the \(PEA\) until a stopping condition is reached. Once the **OS-Master** has finished, the following stages are **CS** and **PS**. These stages involve the computation of the overlapped result. For the **CS**, the general idea is to use a collection of simulated maps resulting from the evolutionary algorithm and produce as output an aggregated map and a threshold value; then, for the **PS**, a final map is produced as a matrix of burned and unburned cells, and this constitutes the prediction for \(t_{n+1}\). In the case of ESS, the collection of simulated maps is equivalent to the evolved population, and the complete **CS** is performed by the Master. This is represented by the **CS** block in Figure 2, which involves several steps. The first step is the Statistical Stage or **SS**. The purpose of this step is to take into consideration a number of solutions for the prediction. For this, the Master aggregates the resulting maps obtained from the evolved population, producing a matrix in which each cell is the sum of cells that are ignited according to each simulated map from the input. These frequencies are interpreted as probabilities of ignition. Although in this case the selection of maps is straightforward, other criteria can be used to consider different simulations with different results regarding the reduction of uncertainty. After obtaining this probability matrix, it will be used for two purposes: on the one hand, it is provided as input for the **PS**; on the other hand, it is used in the next step of the **CS**: the search for the _Key Ignition Value_, or \(K_{ign}\). This is a simple search represented by the block \(SK_{ign}\). These two parts are interrelated: the **PS** at \(t_{n+1}\) depends on the output of the **CS** at \(t_{n}\), which is \(K_{ign_{n}}\). Up to this point, we have a probability map, but the predicted fire line \(PFL\) consists of cells that are marked as either burned or unburned. Then, we need a threshold for establishing which cells of the probability map are going to be considered as ignited. In other words, the threshold establishes how many simulated maps must have each cell as ignited in order for that cell to appear as ignited in the final map. A more detailed diagram of the first use of the matrix is illustrated in Figure 3 (reproduced,modified, and translated with permission from [22]). In the example from this figure, if there are four simulated maps and \(K_{ign}=2\), then for a cell to be predicted as burned in the aggregated map, it must be present as such in at least two of the simulated maps. Note that instead of being the result of one simulation, this final map, \(PFL_{n+1}\) (shown at the right in Figure 3, after the **PS**), aggregates information from the collection of simulated maps obtained as the output of the **OS** (simplified in the l.h.s. of the figure).