# Evolutionary Statistical System Based on Novelty Search:
## 1 Introduction
In order to produce acceptable results in a feasible time, other methods introduced the idea of performing a search over this space in order to reduce the sample space considered for the simulations. One of the frameworks that follow this strategy is the _Evolutionary Statistical System_ (ESS) [10], which embeds an evolutionary algorithm for the optimization of scenarios in order to find the best candidates for predicting future propagation. Recently, other proposals based on ESS have been developed: ESSIM-EA [11, 12] and ESSIM-DE [13]. These systems use Parallel Evolutionary Algorithms (PEAs) with an Island Model hierarchy: a _Genetic Algorithm_[14, 15], and _Differential Evolution_[16], respectively. The optimization performed by these methods was able to outperform previous approaches, but it presented several limitations. The three frameworks mentioned use evolutionary algorithms that are based on a process that iteratively modifies a \"population\" of scenarios by evaluating them according to a fitness function. In this case, the fitness function compares the simulation with the real fire progress. For problems with high degrees of uncertainty, the fitness function may present features that hinder the search process and might prevent the optimization from reaching the best solutions [17]. Another limitation that becomes relevant in this work is that the state-of-the-art methods ESS, ESSIM-EA, and ESSIM-DE use techniques that were designed with the objective of converging to a single solution, which might negate the benefits of using multiple solutions if the results to be overlapped are too similar to each other. In this work, we propose and evaluate a new method for the optimization of scenarios. Our method avoids the issues of previous works by using a different criterion for guiding the search: the _Novelty Search_ (NS) paradigm [18; 19; 20]. NS is an alternative approach that ignores the objective as a guide for exploration and instead rewards candidate solutions that exhibit novel (different from previously discovered) behaviors in order to maximize exploration and avoid local optima and other issues related to objective-based algorithms. In an early work [21], we presented the preliminary design of a new framework based on ESS that incorporated the Novelty Search paradigm as the search strategy for the optimization of scenarios. This article is an extended work whose main contributions are the experimental results and their corresponding discussion. These results comprise two sets of experiments: one for the calibration of our method and another for the comparison of our method against other state-of-the-art methods. In addition, we have made some corrections in the pseudocode, reflecting the final implementation that was evaluated in the experiments. Our experimental results support the idea that the application of a novelty-based metaheuristic to the fire propagation prediction problem can obtain comparable or better results in quality with respect to existing methods. Furthermore, the execution times of our method are better than its competitors in most cases. To the best of our knowledge, this is the first application of NS as a parallel genetic algorithm and also the first application of NS in the area of propagation phenomena. In the next section, we guide the reader throughout previous works related to our present contribution; firstly, in the area of DDM-MOS, with a detailed explanation of existing systems (Sections 2.1 and 2.2), and secondly, in the field of NS (Section 2.3), where we explain the paradigm and its contributions in general terms. Then, in Section 3, we present a detailed description of the current contribution and provide a pseudocode of the optimization algorithm. Section 4 presents the experimental methods, results, and discussion. Finally, in Section 5, we detail our main conclusions and describe possible lines of future work. In addition, Appendix A presents a static calibration experiment performed on our method. Figure 1: Taxonomy of wildfire spread prediction methods.