Hepatocellular carcinoma (HCC) is the most common liver cancer in adults. Many different factors make it difficult to diagnose in humans.. In this paper, a novel diagnostics approach based on machine learning techniques is presented. Logistic regression is one of the most classic machine learning models used to solve the problem of binary classification. In typical implementations, logistic regression coefficients are optimized using iterative methods. Additionally, parameters such as solver, C - a regularization parameter or the number of iterations of the algorithm operation should be selected. In our research, we propose a combination of logistic regression with genetic algorithms. We present three experiments showing the fusion of those methods. In the first experiment, we genetically select the logistic regression parameters, while the second experiment extends this approach by including a genetic selection of features. The third experiment presents a novel approach to train the logistic regression model - the genetic selection of coefficients (weights). Our models are tested for the survival prediction of hepatocellular carcinoma based on patient data collected at Coimbra's Hospital and Universitary Center (CHUC), Portugal. The model we proposed achieved a classification accuracy of 94.55% and an f1-score of 93.56%. Our algorithm shows that machine learning techniques optimized by the proposed concept can bring a new and accurate approach in HCC diagnosis with high accuracy.