Mathematical modeling in the financial area is of great scientific and practical interest because the study of economic systems such as bourses, banks, insurance and investment companies is important for both the participants in these systems and for the state. The study of the above mentioned higher economic systems is a complex task insofar as they operate under conditions of uncertainty caused by the probability nature of the processes in them, large dimensionality and complexity of the systems themselves, as well as the influence of the human factor. Both prerequisites - for the rationality of the decision-maker and for the information about the law on the distribution of the future asset price - in real life are far from being fulfilled. A state-of-the-art survey of different evolutionary techniques used to solve multiple objective portfolio optimization problems is provided. Some basic concepts of this type of algorithms are considered in brief. The Markowitz mean variance optimization model in its single objective and multiple objective variants is described. Different constraint types are briefly presented. Several developments based on this model are discussed and analyzed.