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Abstract In this study, we analyze three portfolio selection strategies for loss-averse investors: semi-variance, conditional value-at-risk, and a combination of both risk measures. Moreover, we propose a novel version of the non-dominated sorting genetic algorithm II and of the strength Pareto evolutionary algorithm 2 to tackle this optimization problem. The effectiveness of these algorithms is compared with two alternatives from the literature from five publicly available datasets. The computational results indicate that the proposed algorithms in this study outperform the others for all the examined performance metrics. Moreover, they are able to approximate the Pareto front even in cases in which all the other approaches fail.