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.

在本文中，我们研究了应用多目标方法通过语法进化来解决符号回归问题的好处。特别是，我们扩展了以前的工作，获得了数学表达式来模拟糖尿病患者血液中的葡萄糖水平。在这里，我们使用基于 NSGA-II 算法的多目标语法进化方法，将均方根误差和 ad-hoc 适应度函数作为目标。该特别功能基于克拉克误差网格分析，可用于显示糖尿病患者预测错误的潜在危险。在这项工作中，我们使用两个数据集来分析两种不同的场景：假设和不可知论，这是日常临床实践中最常见的。在假设在评估未来事件的场景中，结果表明，多目标方法通过减少危险错误预测的数量来改进之前的克拉克误差网格分析结果。在不可知论的情况下，没有关于未来事件的可用信息，结果表明我们可以仅使用前一小时的信息来获得良好的预测，包括语法进化和多目标语法进化。