With the increase in the amount of text information in different real-life applications, automatic text-summarization systems become more predominant in extracting relevant information. In the current study, we formulated the problem of extractive text-summarization as a binary optimization problem, and multi-objective binary differential evolution (DE) based optimization strategy is employed to solve this. The solutions of DE encode a possible subset of sentences to be present in the summary which is then evaluated based on some statistical features (objective functions) namely, the position of the sentence in the document, the similarity of a sentence with the title, length of the sentence, cohesion, readability, and coverage. These objective functions, measuring different aspects of summary, are optimized simultaneously using the search capability of DE. Some newly designed self-organizing map (SOM) based genetic operators are incorporated in the optimization process to improve the convergence. SOM generates a mating pool containing solutions and their neighborhoods. This mating pool takes part in the genetic operation (crossover and mutation) to create new solutions. To measure the similarity or dissimilarity between sentences, different existing measures like normalized Google distance, word mover distance, and cosine similarity are explored. For the purpose of evaluation, two standard summarization datasets namely, DUC2001, and DUC2002 are utilized, and the obtained results are compared with various supervised, unsupervised and optimization strategy based existing summarization techniques using ROUGE measures. Results illustrate the superiority of our approach in terms of convergence rate and ROUGE scores as compared to state-of-the-art methods. We have obtained 45% and 5% improvements over two recent state-of-the-art methods considering ROUGE-2 and ROUGE-1 scores, respectively, for the DUC2001 dataset. While for the DUC2002 dataset, improvements obtained by our approach are 20% and 5%, considering ROUGE-2 and ROUGE-1 scores, respectively. In addition to these standard datasets, CNN news dataset is also utilized to evaluate the efficacy of our proposed approach. It was also shown that the best performance not only depends on the objective functions used but also on the correct choice of similarity/dissimilarity measure between sentences.