A new multi-objective evolutionary optimization algorithm is presented based on the competitive optimization algorithm (COOA) to solve multi-objective optimization problems (MOPs). Based on nature-inspired competition, the competitive optimization algorithm acts between animals such as birds, cats, bees, ants, etc. The present study entails main contributions as follows: First, a novel method is presented to prune the external archive and at the same time keep the diversity of the Pareto front (PF). Second, a hybrid approach of powerful mechanisms such as opposition-based learning and chaotic maps is used to maintain the diversity in the search space of the initial population. Third, a novel method is provided to transform a multi-objective optimization problem into a single-objective optimization problem. A comparison of the result of the simulation for the proposed algorithm was made with some well-known optimization algorithms. The comparisons show that the proposed approach can be a better candidate to solve MOPs.