## 1 Introduction  
In solving the problem of uncertainty, the Expected Utility Theory describes the rational people how to determine the optimal decisions and then take action when faced with the uncertainty of risk and return. The Expect Utility Theory assumes that the individual is risk aversion, that is, its utility function is concave. In modern economics, how to choose the optimal portfolio is one of its central problems. Based on the relationship between the risk of assets and the return on assets, [PERSON] [1] solve the portfolio optimization problem through mathematic statistic method and propose the Mean-Variance model. The Mean-Variance model measures the expected revenue at the required rate of return, and measures the risk size with the variance of required rate of return. However, the model gets poor applications because of its harsh assumptions. To supply a gap, [PERSON] [2] propose the Stochastic Dominance theory and apply it into portfolio optimization problem. The Stochastic Dominance theory takes the risk appetite into consideration, which has been widely used in the financial field. Thereinto, second order stochastic dominance (SSD) is a branch of Stochastic Dominance theory. [PERSON] and [PERSON] [3,4] introduce the second order stochastic dominance into portfolio optimization model. They also take the portfolio selection theory as a constraint and apply it to the risk repugnance asset optimization problem. While the second order stochastic dominance constraint requires that the investable assets should be compared with each other. When the number of investable assets is large, the calculation requirements becomes very harsh. [PERSON] and [PERSON] (2016) propose a new duality theory for this problem and optimize the model by cutting plane methods. [PERSON] and [PERSON] (2016) and [PERSON], [PERSON] and [PERSON] (2017) also use the cutting plane methods to solve the portfolio optimization problem. The cutting plane method has a great efficiency in portfolio optimization problem, while this method is too restrictive. Besides, the probability space is discrete, which greatly limits the application of this method. [PERSON] and [PERSON] (2016) introduce a subsidiary variable into SSD model and transform it into a linear programming model. However, the number of variables in the model depends on the number of investable assets, which increases the pressure of calculation. [PERSON], [PERSON] and [PERSON] (2017) penalize SSD constraints to the objective under [PERSON]'s constraint qualification and apply the SA method and LF method to solve the penalized problem. [PERSON] (2017) apply the Sample Average Approximation method into SSD model, which introduces new variables into the model. Besides, [PERSON], [PERSON] and [PERSON] (2018) present an empirical study which analyses the effectiveness in the context of enhanced indexation. Inspired by Biogeography (2018), [PERSON] (2018) propose the Biogeography-based optimization (BBO) which is a sort of bionic optimization algorithm consists of three operators: migration operator, mutation operator and elimination operator. As a swarm intelligence optimization algorithm, the Biogeography-based optimization has advantages of good ability of robustness, easy to implement and the process of algorithm is relatively simple. Besides, the mutation operator helps to increase the diversity of solutions. Because the BBO algorithm does not depend on a particular problem, it is widely used in various fields, such as pathology test (2018; 2019), distributed generation (2019), intelligent identification (2018; 2019; 2019) and other fields recently. While BBO algorithm also has some disadvantages, including easy to fall into the local optimization, poor exploration ability, strong randomness and lacking theoretical basis. In this paper, to increase the exploration ability of algorithm, we propose the \(\epsilon\)BBO algorithm based on the DE algorithm. We improve the mutation operator to prevent the algorithm falling into the local optimization.