# Towards a Vectorial Approach to Predict Beef Farm Performance
## 5 Conclusions  
Exploring the vectorial approach required, as already stated, a different input data structure. To this purpose, the farms considered in the pool of instances were the same as in [16]. However, since the results showed that GP exploited only certain variables, the number of predictors was reduced to 18. In this way, possible noise due to extra variables, which were not very informative, was avoided. The main goal was to inspect the ability of Vectorial Genetic Programming (VE-GP) with respect to ST-GP to predict the target. The recently developed VE-GP algorithm could produce better results, by achieving a better fitness on both the learning and test sets. VE-GP proved to be more stable, evolving a population through more generations without showing overfitting, while Standard Genetic Programming (ST-GP), was affected by overfitting already in the early generations under analogous experimental settings. VE-GP still favored model investigation by giving access to the formula and hence to the features implicitly selected, providing meaningful information about the tackled issue. Better results were obtained by encapsulating fewer variables in each extracted candidate model, detecting almost all the information among specific features. The algorithm improved the target forecast, proving to outperform not only ST-GP, but also other techniques used in the field of ML. The algorithm, in particular, was compared to Long Short-Term Memory Recurrent Neural Network (LSTM), suitable for handling vectorial predictors. Even though performing similar to the LSTM and Generalized Linear Models (GLMNET), the latter exploiting the standard data panel representation, VE-GP was the only method entailing a greater ability in generalization over unseen data. The introduction of vectorial variables produced a significant improvement over the accuracy of the result. Evolution was also much more stable, and the ability of the algorithm to handle any type of variable, both scalar and vectorial, makes it quite a flexible tool. These considerations open the possibility of providing more complex datasets, containing different types of sequential features. The possibility of managing vectorial variables, whose values can be of different types and have no fixed length among the whole dataset, push the analysis beyond the basic research conducted at this point. On the one side, both categorical and continuous variables can be treated simultaneously, without specifying it explicitly to the algorithm: The latter is indeed able to process them during the evolution without hints given by the user. On the other hand, when dealing with vectors, some data may be not available. Thus, the vector variables may have different lengths, even being scalars when the latter is equal to one. VE-GP is suitable to manage all kinds of features dynamically, combining them in the prediction of the target. Evolutionary algorithms can be applied to zootechnical data, achieving performing models able to learn from all the available data. In this case study, the breeding variables in the report extracted at the end of the year were used. In one case, they were managed for only one year; in the other four, the average values, corresponding to four years, were used, proving to be more suitable for reducing the prediction and generalization errors. Instead of limiting the analysis to the year-end average, it might be more useful to incorporate the data collected from each farm visit into a vector representation. As a result, all variations, even small ones, would be available, and the algorithm could identify temporal patterns that were not visible by directly processing the average value for the whole year. Conceptualization, F.A. and M.G. ; methodology, F.A., L.V., and M.G. ; validation, L.V. and M.G. ; formal analysis, F.A. ; investigation, F.A. ; resources, F.A. ; data curation, F.A. ; writing--original draft preparation, F.A. ; writing--review and editing, F.A. and M.G. ; visualization, F.A. ; supervision, L.V. and M.G. ; project administration, M.G.