To solve a constrained optimization problem, a new strategy is proposed, in which the lexicographical method is used to simultaneously optimize the objective function and the degree of constraint violation. A novel imperialist competitive algorithm (ICA) is presented, in which, cost and normalized cost are redefined to guarantee that the power of all imperialists exceeds zero, and some strategies such as the global search of colonies in assimilation, excellent colonies based revolution, differential evolution of imperialists and a new approach of imperialist competition are applied to improve solution quality. Many experiments are conducted based on two groups of test functions, and the ICA is compared with some algorithms from literature. The computational results show that the ICA with the lexicographical method has promising advantages for solving constrained optimization problems.