Automatic text summarization is a topic of great interest in many fields of knowledge. Particularly, query-oriented extractive multi-document text summarization methods have increased their importance recently, since they can automatically generate a summary according to a query given by the user. One way to address this problem is by multi-objective optimization approaches. In this paper, a memetic algorithm, specifically a Multi-Objective Shuffled Frog-Leaping Algorithm (MOSFLA) has been developed, implemented, and applied to solve the query-oriented extractive multi-document text summarization problem. Experiments have been conducted with datasets from Text Analysis Conference (TAC), and the obtained results have been evaluated with Recall-Oriented Understudy for Gisting Evaluation (ROUGE) metrics. The results have shown that the proposed approach has achieved important improvements with respect to the works of scientific literature. Specifically, 25.41%, 7.13%, and 30.22% of percentage improvements in ROUGE-1, ROUGE-2, and ROUGE-SU4 scores have been respectively reached. In addition, MOSFLA has been applied to medicine texts from the Topically Diverse Query Focus Summarization (TD-QFS) dataset as a case study.