Forecasting Glucose Levels in Patients with Diabetes Mellitus using Semantic Grammatical Evolution and Symbolic Aggregate Approximation

Type 1 Diabetes Mellitus can only be treated injecting insulin and glucagon into the blood stream. This research is motivated by the challenge to accurately predict future blood glucose levels of a diabetic patient so that an automatic system could decide when is necessary the injection of a bolus of insulin to keep blood sugar in the healthy range. In this paper, we have studied different evolutionary strategies based on geometric semantic genetic programming and grammatical evolution. The main contribution of this paper is the use of the symbolic aggregate approximation representation of the glucose time series that allow us to define easily semantic operators. We have developed a new strategy that combines grammatical evolution with the geometric semantic approach and that, thanks to the use of the symbolic representation, improves the previous models of glucose time series. We also present a variation of this technique that employs a univariate marginal distribution algorithm to tune the parameters of the symbolic representation. The experimental results are compared against classical grammatical evolution and geometric semantic hill climbing genetic programming. The baseline is provided by the conventional ARIMA model. Our experimental results show that the symbolic representation improves the performance of the geometric semantic strategy and reduces the number of mistakes that, if in an automatic system, would put patient's health at risk.