This paper deals with the multiobjective definition of video compression and its optimization. The opti-mization will be done using NSGA-II, a welltested and highly accurate algorithm with a high conver-gence speed developed for solving multiobjective problems. Video compression is defined as a problem including two competing objectives. We try to find a set of optimal, so-called Pareto-optimal solutions, instead of a single optimal solution. The two competing objectives are quality and compression ratio maximization. The optimization will be achieved using a new patent pending codec, called MIJ2K, also outlined in this paper. Video will be compressed with the MIJ2K codec applied to some classical vid-eos used for performance measurement, selected from the Xiph.org Foundation repository. The result of the optimization will be a set of near-optimal encoder parameters. We also present the convergence of NSGA-II with different encoder parameters and discuss the suitability of MOEAs as opposed to classical search-based techniques in this field.