# Evolutionary Statistical System Based on Novelty Search:
## 2 Related Works
### ESS Framework  
The systems referred to in this paper fit into the DDM-MOS category, given that they perform multiple simulations, each based on a different scenario, and rely on a number of simulations in order to yield a fire spread prediction. Previous approaches showed limitations, either caused by the use of a single simulation for the predictions or by the complexity of considering a large space of possibilities, which includes redundant or unfeasible scenarios. To overcome these limitations, the _Evolutionary Statistical System_ (ESS) was developed. Its core idea is to produce a reduced selection of results with the aid of an evolutionary algorithm that searches over the space of all possible scenarios. The objective is to reduce the complexity of the computations while considering a sample of scenarios that may produce better prediction results. In order to understand the scheme of the method proposed in this paper and of its other, more recent competitors, it is necessary to have a general comprehension of how ESS works, since they all share a similar framework. A general scheme of the operation of ESS can be seen in Figure 2 (reproduced and modified with permission from [11]). ESS takes advantage of parallelization with the objective of reducing computation times. This is achieved by implementing a _Master/Worker_ parallel hierarchy for carrying out the optimization of scenarios. During the fire, the whole prediction process is repeated for different discrete time instants. These instants are called _prediction steps_, and in each of them, four main stages take place: Optimization Stage (divided into Master and Workers, respectively: **OS-Master** and **OS-Worker**), Statistical Stage (**SS**), Calibration Stage (**CS**), and Prediction Stage (**PS**). Figure 2: Evolutionary Statistical System. **RFL\({}_{i}\)**: real fire line of instant \(t_{i}\); **OS-Master**: Optimization Stage in Master; **OS-Worker\({}_{\{1..n\}}\)**: Optimization Stage in Workers 1 to \(n\); **FS**: fire simulator; **PEA**: Parallel Evolutionary Algorithms; **PEA\({}_{F}\)**: Parallel Evolutionary Algorithm (fitness evaluation); **PV\({}_{\{1..n\}}\)**: parameter vectors (scenarios); **CS**: Calibration Stage; **SS**: Statistical Stage; **SK\({}_{\textbf{ign}}\)**: Key Ignition Value search; **FF**: fitness function; **K\({}_{\textbf{ign}_{i}}\)**: Key Ignition Value for \(t_{i}\); **PS**: Prediction Stage; **PFL\({}_{\textbf{i+1}}\)**: predicted fire line of instant \(t_{i+1}\). At each prediction step, the process aims to estimate the growth of the fire line from \(t_{i}\) to \(t_{i+1}\). For every step, a new optimization starts with the **OS**. This involves a search through the space of scenarios guided by a fitness function. The process is a classic evolutionary algorithm that starts with the initialization of the population, performs the evolution of the population (selection, reproduction, and replacement), and then finishes when a termination condition is reached. This parallel evolutionary process is divided into the Master and Workers, shown in Figure 2 as **OS-Master** and **OS-Worker**, respectively. The **OS-Master** block involves the initialization and modification of the population of scenarios, represented by a set of parameter vectors \(\textbf{PV}_{\{1...n\}}\). The Master distributes these scenarios to the Workers processes (shown as \(PV_{1}\) to \(PV_{n}\)). The Workers evaluate each scenario that they receive by sending it as input to a fire behavior simulator **FS**. In the **FS** block, the information from the Real Fire Line at the previous instant, \(RFL_{i-1}\), is used together with the scenario to produce a simulated map for that scenario. Then, this simulated map and the information from \(RFL_{i}\) are passed into the block \(PEA_{F}\). As represented in the figure, two inputs from the fire line are needed at the **OS-Worker** (i.e., \(RFL_{i-1}\) and \(RFL_{i}\)): the first one to produce the simulations, and the second one to evaluate the fitness of those simulations.