# Assessing the Added Value of Sentinel-1 PolSAR Data for Crop Classification
## 3 Methods
### Genetic Algorithm  
In our research, we implemented a custom GA in order to derive the most informative optical and polarimetric features for the crop classification problem at hand. A GA is an evolutionary, metaheuristic optimization method, conceived by [PERSON] (1992) [118], and inspired by [PERSON]'s theory of biological evolution [119]. GAs are part of the family of population-based algorithms [120]. Based on the theoretical background of this method, problem features are called genes, which are initially organised in a random way into different subsets of the total feature space, named chromosomes [121]. These feature subsets represent candidate solutions for the optimization problem at hand [122]. A GA is practically an iterative process of evaluating chromosomes' quality using a fitness function and of improving chromosomes' fitness through selection, crossover, and mutation processes, by which eventually an optimal feature subset is derived [86; 123]. GA implementation requires the definition of a large set of hyperparameters by the user, which significantly affect its effectiveness [123]. Population size, as well as crossover and mutation probabilities, are considered GA as the most important parameters and selecting them properly, taking into account the nature of the specific optimization problem at hand [124], is crucial for GA performance [119]. In our research, population size was set to 100 chromosomes, being a common choice in the literature [125] and ensuring satisfactory exploratory ability of the solution space with a reasonable computational cost [126]. Crossover probability was set to 0.9, considered an appropriate value for allowing the proper exploitation of the current population's genetic material and the formation of better chromosomes [84]. Concerning the mutation process, we defined two mutation probabilities, one related to the probability of a chromosome being subjected to mutation and another related to the probability of a particular gene being mutated, following [PERSON]'s methodology [84]. The first one was set to the relatively low value of 0.2 for improving population diversity, while preventing the GA to turn into a random \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Crop Type** & **Class Code** & **Number of Fields** & **Total Area (ha)** \\ \hline soft wheat & 1 & 5461 & 10,922 \\ barley & 5 & 3609 & 7218 \\ oats & 8 & 1172 & 2344 \\ rapeseed & 35 & 708 & 1416 \\ shrub grass & 65 & 326 & 652 \\ sunflower & 33 & 285 & 570 \\ maize & 4 & 223 & 446 \\ broad beans & 41 & 210 & 420 \\ vineyards & 102 & 208 & 416 \\ cherry trees & 110 & 127 & 254 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Main characteristics of each crop type. search method [86; 121]. The second one was calculated by the ratio \(\frac{1}{N}\), where N symbolises the chromosome length [84]. Regarding the design of chromosomes, each gene was coded as a string, referring to one of the 818 multi-temporal features of the study. Each one of the first-generation chromosomes, representing a feature subset, was randomly initialised with a number of unique genes. In our attempt to determine an optimal chromosome length (number of genes), we examined how this parameter affects the highest weighted average f1 score obtained at GA's convergence, as well as the mean computational time required for each iteration. In further detail, 12 GA implementations were performed, testing multiple values of the chromosome length parameter, ranging from 10 to 120 with a step size of 10 genes. The results of these experiments are presented schematically in Figure 5.  
According to Figure 5a, as the chromosome length increases from 10 to 70 genes, the maximum weighted average f1 score achieved by the GA at convergence sharply and gradually improves by 6.5%. However, implementing the GA with a chromosome length of more than 70 genes, does not contribute to a significant further improvement of GA's performance, as the maximum weighted average f1 score obtained reaches a plateau of approximately 93.5%.