## 1 Introduction  
Since the mean-variance (MV) model is proposed by [PERSON] [1; 2], the portfolio optimization problem has attracted a lot of attention. In MV model, variance is used as the risk measure, and it is assumed that returns are normally or elliptically distributed [3]. However, [PERSON] et al. [4] point out that the return to the world's fourteen major stock market is not normally distributed, which means MV model lacks effectiveness in practical applications. Besides, variance counts both upward and downward deviation, which is contrary to the definition of investment risk. Later, to supply the gap, [PERSON] [5] replaces the risk measure with the semi-variance, which only counts downward deviation. In addition, [PERSON] [6] and [PERSON] [7] introduce the mean absolute deviation (MAD) into portfolio optimization model as risk measure. MAD reduces the sensitivity of risk, while it is difficult to do differential operation. Generally speaking, these risk measures are rather abstract. As a new type of risk measure, value at risk (VaR) is put forward in the mid-90s. Roughly speaking, VaR is a maximum quantile of the random loss in a specified period with some confidence level [8]. However, VaR also has some limitations. For example, [PERSON] et al. [9] point out that VaR is not a coherent measure of risk. Therefore, as an improvement on VaR, conditional value at risk (CVaR) gets widely applications in the field of portfolio optimization. Other than [PERSON] MV model, the stochastic dominance (SD) model is another important model for solving portfolio optimization problem. SD is proposed by [PERSON] [10], then, [PERSON] and [PERSON] [11] introduce SD constraint into portfolio optimization model, which takes the risk appetite into consideration and is more suited to the investors in realistic investment environments. Thereinto, in the SD model, we mainly consider first-order stochastic dominance (FSD) constraint and second-order stochastic dominance (SSD) constraint. Besides, [PERSON] and [PERSON] [12] establish almost stochastic dominance (ASD) rules which formally reveal a preference for most decision makers, but not for all of them. Moreover, [PERSON] and [PERSON] [13] introduce a new second-order stochastic dominance efficiency model called SSD-DP model, which doesn't require a benchmark portfolio. On the basic of MV model and SD model, scholars refine their models by adding a series of objectives or constraints into it. [PERSON] [14] points out that skewness has great importances of financial economics. Then, [PERSON] et al. [15] and [PERSON] et al. [16] study and develop the mean-variance-skewness (MVS) model, which introduce skewness into MV model as one of the objectives. Recently, [PERSON] et al. [17] add \(P/E\) criterion and experts' recommendations on market sectors to the primary MV model as two objectives. Moreover, [PERSON] et al. [18] take sector capitalization constraint into account. Generally speaking, the optimization of MV model and SD model allows these models to be more widely used in realistic investment environments. After adding these objectives to portfolio optimization model, the original single-objective portfolio optimization problem has become a multi-objective optimization problem. Recently, [PERSON] et al. [19] introduce the multi-objective evolutionary algorithms (MOEAs), including non-dominated sorting genetic algorithm II (NSGA-II) and strength pareto evolutionary algorithm II (SPEA-II), into solving mean-semivariance framework model. However, the portfolio optimization entails considering competing and conflicting objectives, it's unlikely that a portfolio can solve the multi-objectives problem simultaneously [20]. Besides, normally multi-objective optimization problem is transformed into a single-objective programming model by using fuzzy programming approach, such as [PERSON] et al. [21]. Therefore, in this paper, we take skewness, kurtosis, CVaR or VaR into SSD framework as constraints, which we called it MCVSK and MVSK model respectively.