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In this article, a novel general class of optimality criteria is defined and proposed to solve multi-objective optimization problems by using evolutionary algorithms. These criteria, named p-optimality criteria, allow to value (assess) the relative importance of those solutions with outstanding performance in very few objectives and poor performance in all others, regarding those solutions with an equilibrium (balance) among all the objectives. The optimality criteria avoid to interrelate the relative values of the different objectives, respecting the integrity of each one in a rational way. As an example, a simple multi-objective approach based on the p-optimality criteria and genetic algorithms is designed, where solutions used to generate new solutions are selected according to the proposed optimality criteria. It is implemented and applied on several benchmark test problems, and its performance is compared to that of the NSGAII method, in order to analyze the contribution and potential of these new optimality criteria.