# Optimization of CART Models Using Metaheuristics for Predicting Peach Firmness
## 1 Introduction  
The food production process of the farming systems can be improved using the vast amounts of measured data in combination with machine learning algorithms. With the application of machine learning in the field of agriculture, more sustainable food production can be obtained, increasing global food security and reducing food waste. Determining the correct fruit harvest time is critical for reducing food waste along the food supply chain [1]. Fruit quality evaluation is important to accurately predict the harvest date and extend the fruit shelf life. To accurately determine the quality of the fruit, physical and chemical quality detection methods exist, such as the detection of firmness, soluble solids concentration, and tittatable acidity [2]. Manual fruit quality evaluation methods such as appearance screening by the operator are being replaced by automated evaluation systems based on machine vision, image processing technology, and other emerging technologies, which could improve the efficiency of the farming systems [2]. Some of the new technologies for predicting and identifying properties of various fruit are backpropagation neural networks [2], convolutional neural networks [3], discriminant analysis [4], and simple linear regression [5]. Previous work [1] investigated the possibilities of optimizing regression trees using nature-inspired metaheuristic algorithms. The work described in this paper extends [1]by introducing new machine learning models and metaheuristics used for regression tree optimization. The desire to solve any problem in an optimal way is very common; hence, optimization techniques are extensively applied in the fields of science and engineering. Optimization techniques aim to find the best solution to a particular problem out of a set of possible options. Optimization problems usually consist of an objective function and constraints with either discrete or continuous variables [6]. With the larger search space, the complexity of the optimization problems increases, where real-world optimization problems are often NP (non-deterministic polynomial-time) problems that can be solved with non-deterministic algorithms, which are computationally very demanding [6]. In the fields of computer science and mathematical optimization, a metaheuristic is defined as a higher-level process that can satisfactorily solve an optimization problem, especially when given limited computing power or incomplete information [7]. Since metaheuristics make few assumptions about the optimization problem being solved, they can be applied to a variety of different optimization problems. Numerous metaheuristics employ stochastic optimization, whereby the solution obtained relies on a set of randomly generated variables [7]. The advantage of using metaheuristics is that they provide fast and cost-effective solutions to complex problems. However, they cannot ensure global optimality, unlike numerical optimization algorithms. By balancing between the exploration and exploitation phases, the metaheuristic algorithms aim to find the optimal solution to a given problem. Due to their stochastic character and the No Free Lunch (NFL) theorem, the optimal performance on one problem does not guarantee similar results on another problem by using the same metaheuristic algorithm [6]. This is the reason for the large number of currently existing algorithms, as well as the proposal of new ones. Considering the NFL theorem, additional metaheuristics are introduced in this research compared to [1] to try to improve the peach firmness prediction accuracy of the regression tree model. The idea of this study is to build a precise machine learning model for estimating peach firmness. The starting point for this research is the work described in [1], in which multiple linear regression and classification and regression tree models were developed with the same goal in mind. This research supplements [1] by introducing new machine learning models.