Some researchers have framed the extraction of association rules as a multi-objective problem, jointly optimizing several measures to obtain a set with more interesting and accurate rules. In this paper, we propose a new multi-objective evolutionary model which maximizes the comprehensibility, interestingness and performance of the objectives in order to mine a set of quantitative association rules with a good trade-off between interpretability and accuracy. To accomplish this, the model extends the well-known Multi-objective Evolutionary Algorithm Non-dominated Sorting Genetic Algorithm II to perform an evolutionary learning of the intervals of the attributes and a condition selection for each rule. Moreover, this proposal introduces an external population and a restarting process to the evolutionary model in order to store all the nondominated rules found and improve the diversity of the rule set obtained. The results obtained over real-world datasets demonstrate the effectiveness of the proposed approach.