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In this paper we investigate the benefits of applying a multi-objective approach for solving a symbolic regression problem by means of Grammatical Evolution. In particular, we extend previous work, obtaining mathematical expressions to model glucose levels in the blood of diabetic patients. Here we use a multi-objective Grammatical Evolution approach based on the NSGA-II algorithm, considering the root-mean-square error and an ad-hoc fitness function as objectives. This ad-hoc function is based on the Clarke Error Grid analysis, which is useful for showing the potential danger of mispredictions in diabetic patients. In this work, we use two datasets to analyse two different scenarios:  What-if  and  Agnostic , the most common in daily clinical practice. In the  What-if  scenario, where future events are evaluated, results show that the multi-objective approach improves previous results in terms of Clarke Error Grid analysis by reducing the number of dangerous mispredictions. In the  Agnostic  situation, with no available information about future events, results suggest that we can obtain good predictions with only information from the previous hour for both Grammatical Evolution and Multi-Objective Grammatical Evolution.

Blood glucose prediction using multi-objective grammatical evolution: analysis of the “agnostic” and “what-if” scenarios