The Improvement And Application Of Approximate Linear Programming Algorithm

Approximate linear programming (ALP) is a useful method for solving nonlinear programming (NLP) problems of all nonlinear programming methods. It mainly uses the first order Taylor expansion to obtain a linear programming problem which nearly has the same solution and the problem turns into solving a linear problem. But there are many defects in its implementation. Firstly, the judgmental condition and the way of adjusting boundaries for variables while the iteration point does not satisfy one or more constrains or it does not make the objective function better. Secondly, the judgmental condition of the optimal solution has no theoretical proof. Thirdly, new iterates’obtaining depends on other linear programming algorithms. Lastly, the initial point and step restriction and reduction coefficient in application are selected subjectively. All of those factors will have a great influence in accuracy and convergence.The paper improves the ALP mainly by the following three aspects and proposes a new method named approximation linear filter programming (ALFP) based on research and analysis of approximation linear programming:1) using the steepest search thought to obtain new iterates rather than depend on other linear programming methods;2) introducing evaluation function to ensure that every iteration point has a good spatiality and directionality and introducing idea of linear filter to strengthen the convergence and reliability for ALFP;3) introducing definition of move-in vector and move-out vector to overcome defects of subjective selections of step restriction and reduction coefficient and refining boundary adjustment. Take the ALFP to test numbers of NLP problems, the results indicate that the ALFP has high accuracy and good convergence.In order to examine the practical application of the ALFP, this paper establishes cyclic scheduling cleaning model of boiler system and benzene-toluene flash separation process model respectively. The results show that the ALFP has more economical efficiency and practical significance while compared with the available results.