This paper proposes an integer multiobjective mean-CVaR portfolio optimization model with variable cardinality constraint and rebalancing and two different methods of decision-maker used to guide and select, according to the decision maker preferences, a solution comes from the non-dominated portfolios generated by a proposed evolutionary algorithm. The decision-making methods were used to approximate investor behavior according to three functions, chosen to represent different investor profiles (conservative, moderate and aggressive). The proposed methods are compared with those found in the literature. Additionally, computational simulations are performed using assets from the Brazilian stock exchange for the period between January 2011 and December 2015. The strategy is that each beginning of the month: the previous portfolio is sold, the optimization is performed, and the decision-making method selects the new portfolio to be purchased. Results of the simulations consider monthly maximum drawdown and cumulative return during the entire study period and show that the optimization model is robust, considering the three simulated profiles. The methods always present cumulative returns above safe investments for the analyzed period, and the aggressive profile obtained bigger gains with greater risk.