Portfolio optimization context has shed only a little light on the dependence structure among the financial returns along with the fat-tailed distribution associated with them. This study tries to find a remedy for this shortcoming by exploiting stable distributions as the marginal distributions together with the dependence structure based on copula function. We formulate the portfolio optimization problem as a multi-objective mixed integer programming. Value-at-Risk (VaR) is specified as the risk measure due to its intuitive appeal and importance in financial regulations. In order to enhance the model's applicability, we take into account cardinality and quantity constraints in the model. Imposing such practical constraints has resulted in a non-continuous feasible region. Hence, we propose two variants of multi-objective particle swarm optimization (MOPSO) algorithms to tackle this issue. Finally, a comparative study among the proposed MOPSOs, NSGAII and SPEA2 algorithms is made to demonstrate which algorithm is outperformed. The empirical results reveal that one of the proposed MOPSOs is superior over the other salient algorithms in terms of performance metrics.