# Evolutionary Statistical System Based on Novelty Search:
## 3 Novelty-Based Approach for the Optimization Stage in a Wildfire Prediction System
### New Framework: Ess-Ns  
The framework that has been implemented for the new method is called _Evolutionary Statistical System based on Novelty Search_, or ESS-NS. Its general scheme is illustrated by Figure 5. There are several aspects that are analogous with respect to ESS (compare to Figure 2), such as the Master/Worker hierarchy, where Workers carry out the simulations and fitness evaluations while the Master handles the steps of the evolutionary algorithm; stages other than the Optimization Stage remain unchanged. However, the optimization component has important modifications, particularly in the Master process, and these are highlighted in the figure. As its predecessors, this framework consists of a prediction process with the same stages from Figure 2 (Section 2.1): Optimization Stage (**OS**), Statistical Stage (**SS**), Calibration Stage (**CS**), and Prediction Stage (**PS**). We have used the same propagation simulator, called _fireSim_[4], which is implemented in an open-source and portable library, _fireLib_. This simulator takes the following parameters as input: a terrain ignition map and the set of parameters concerning the environmental conditions and terrain topography. These parameters are described in Table 1. The first row contains the name of the _Rothermel Fuel Model_, which is a taxonomy describing 13 models of fire propagation commonly used by a number of simulators, including _fireSim_. The remaining rows represent environmental aspects, such as wind conditions, humidity, slope, etc. For more information on the parameters modeled by this library, see [42]. The output of this simulator is a map that indicates in each cell the estimated time instant of ignition of each cell. If, according to the simulation, the cell is never reached by the fire, it is set to zero. The order and functioning of the Statistical, Calibration, and Prediction stages, in addition to their assignment to Master and Workers, are the same as those presented in Section 2.1. As for the Optimization Stage, there are two crucial differences from ESS. First, the metaheuristic contained in this stage is also an evolutionary algorithm, but its behavior in this case follows the NS paradigm: the strategy implemented is novelty-based with a genetic algorithm, as shown in the shaded block inside the Master (_PEA: NS-based GA_) in Figure 5. We defer the details of this algorithm to the following section; however, it is important to note here that this novelty-based method requires an additional computation of a score, that is, the _novelty score_, represented by the function \(\rho(x)\) from Equation (1). The second difference is that the output of the optimization algorithm is not the final evolved population, as in previous methods; rather, it is a collection of high fitness individuals which were accumulated during the search, which we call _bestSet_. Although the need for this structure originates from an apparent limitation of NS, that is, its lack of convergence, this mechanism is in fact an advantage of this method, and it is more suitable to this application problem than the previous methods, which are based on single-solution metaheuristics. The difference lies in that our NS design has the ability to record individuals from completely different areas of the search space and include them in the final aggregated matrix. As \begin{table}
\begin{tabular}{l l l l} \hline \hline
\begin{tabular}{l} percent \\ percent \\ percent \\ degrees clockwise from north \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Parameters used by the fireLib library. Figure 5: Evolutionary Statistical System based on Novelty Search.