Application of the steepest descent approximate linear programming on cyclic cleaning scheduling of boiler

Traditional approximate linear programming may exclude the optimal solution out of the boundary condition, which is caused by the subjective choices of initial feasible point, step restriction and reduction coefficient. In this paper, a method called steepest descent-approximate linear programming is presented which redefines the judgment conditions and the way of boundary adjustment based on the purposeful search and rapid convergence from steepest descent method, where the boundary directions are adjusted together by the nonlinear constraint satisfaction degree and the current objective function. Besides absorbing the original advantages of easy implementation and convenient solution from traditional approximate linear programming, the new method can not only eliminate the negative impact which is caused by subjective choices of step restriction and reduction coefficient, but also solve a nonlinear programming problem which only contains linear constraints. The method has been applied in a real thermal power plant, for which a mathematical model for the solution of the cyclic cleaning scheduling problem of boiler system with decaying performance is built and optimized. Moreover, the usefulness of the method shows it achieves remarkable energy saving compared with the original approaches.