Solving nonlinear constrained optimization problems: An immune evolutionary based two-phase approach

In this paper, an artificial evolutionary two-phase method that is based upon the immune evolutionary method is proposed to solve nonlinear constrained optimization problems that consist of real variables, integer variables and discrete variables. In the first phase, an immune based algorithm is used to solve the nonlinear constrained optimization problem approximately for all variables. In the second phase, the integer variables and discrete variables are fixed and then a search procedure is proposed to improve the real variable solutions obtained in the first phase. The numerical results for four benchmark problems, including the tube and pressure vessel problem, are reported and compared. As shown, the solutions using the proposed method are all superior to the best solutions for traditional methods detailed in the literature.