This paper presents a combinatorial multiobjective optimization methodology to address diversification of investment in portfolios consistent with the market practices, using a downside risk measure. To cope with this feature, parallel versions of two evolutionary algorithms are considered, based on NSGA-II and DEMO. Simulations are shown with portfolios comprised of stocks that participated in the theoretical portfolio of Ibovespa in 2015. In-sample analysis considers graphical analysis, performance measures for diversity solutions and objective space coverage. Out-of-sample analysis is performed comparing the behavior of lower risk and higher return portfolios in relation to measures of risk and return, for several cardinalities.
