Abstract: A new ε constrained biogeography-based optimization with dynamic migration, εBBO-dm, is proposed to solve constrained optimization problems. In the proposed algorithm, the ε constrained method is utilized to handle the constraints. According to the constraint violation of the colony, the ε level is set to utilize the useful information for the better infeasible individual sufficiently and to improve the search efficiency for the feasible space. Simultaneously, based on the feature of ε constrained method, a new ordering rule based on ε constrained is used to obtain the immigration rate and the emigration rate, which can dynamically balance the relation between the feasible individuals and the infeasible individuals. Additionally, a new dynamic migration strategy is shown to enhance the search ability of the migration mechanism. Eventually, with the purpose of improving the precision of convergence, the piecewise logistic chaotic map is introduced to improve the variation mechanism. Numerical experiments on 13 well-known benchmark test functions show that εBBO-dm is competitive with other optimization algorithms on the accuracy and the speed of convergence, especially when being applied to solve complex single-objective COPs.