# Evolutionary Statistical System Based on Novelty Search:
## 3 Novelty-Based Approach for the Optimization Stage in a Wildfire Prediction System
### Novelty-Based Genetic Algorithm with Multiple Solutions  
Our proposal consists of applying a novelty-based evolutionary metaheuristic as part of the Optimization Stage of a wildfire prediction system. We have selected a classical genetic algorithm (GA) as the metaheuristic, which has been adapted to the NS paradigm. This choice was made for two reasons: on the one hand, for simplicity of implementation and, on the other hand, for comparative purposes, since existing systems are also based on variants of evolutionary algorithms, and two of them (ESS and ESSIM-DE) use a GA as their optimization method. The novelty measure selected is computed as in Equation (1). In this context, \(x\) is a scenario, and we define \(dist\) as the difference between the fitness values of each pair of scenarios:  
\[dist(x,\mu_{i})=|fitness(x)-fitness(\mu_{i})|. \tag{2}\]  
For computing this difference, we used the same fitness function as the one used in the ESS system and its successors: the Jaccard Index [43]. It considers the map of the field as a matrix of square cells (which is the representation used by the simulator):  
\[fitness(A,B)=\frac{|A\cap B|}{|A\cup B|}\, \tag{3}\]  
where \(A\) represents the set of cells in the real map without the subset of burned cells before starting the simulations, and \(B\) represents the set of cells in the simulation map without the subset of burned cells before starting the simulation. (Previously burned cells, which correspond to the initial state of the wildfire in each prediction step, are not considered in order to avoid skewed results.) This formula measures the similarity between prediction and reality and is equal to one when there is a perfect prediction, while a value of zero indicates the worst prediction possible. An example of the computation of this index for ignition maps is represented in Figure 6. Note that the definition of \(dist\) in Equation (2) is trivially a metric in the space of fitness, but it does not provide the same formal guarantees when considering the relationship between these fitness differences and the corresponding scenarios that produced the fitness values. For example, it is possible that two scenarios with the same fitness value (and a distance of 0) are not equal to each other. This is because the similarity between scenarios cannot be measured precisely and because it depends to a great extent on the chosen fire simulator. We present the pseudocode of ESS-NS in Algorithm 1. In previous work [21], we presented the idea of ESS-NS, including the pseudocode for its novelty-based metaheuristic. The present contribution preserves the same general idea with only minor changes to the pseudocode and extends previous work with experiments based on an implementation of such an algorithm. Although the high-level procedure is partially inspired by the algorithm in [33], our version has an important difference, which is the introduction of a collection of solutions, _bestSet_. This collection is updated at each iteration of the GA so that at the conclusion of the main loop of the algorithm the resulting set contains the solutions of highest fitness found _during the entire search_. It should be noted that this set is used as the result set instead of the evolved population set which is used by the previous evolutionary-based systems for both the **CS** and **PS**. In addition, this algorithm uses two stopping conditions (line 6): by number of generations and by a threshold of fitness (both present in ESSIM-EA and ESSIM-DE), and also specifies conventional GA parameters, such as a mutation probability and tournament probability. Mutation works as in classic GAs, while the tournament probability is used for selection, where the algorithm performs a tournament strategy. These parameters are specified as input to the algorithm (the values we used for our experiments are specified in Section 4.1).