Resultant Gradient Flow Method for Multiple Objective Programming Based on Efficient Computing

Abstract

The process of blending gas transmission contains multiple kinds of influence factors that are related with the achievement of maximal overall profit for a refinery gas company. It is, therefore, a multiple objective optimization problems. To maximize overall profit, we proposes a multiple objective resultant gradient descent method (RGDM) to solve fractional, nonlinear, and multiple objective programming problems. Resultant gradient descent requires a proper direction of multiple objective functions. The proper direction in this paper is computed by gradient flow to approach to the global maximum values. Gradient flow is one of the forms of geometric flow, which is widely used in linear programming, least-squares approximation, optimization, and differential equation. It is the first time to be used in mathematical programming. Resultant gradient flow is calculated in linear programming, and the extremum can directly affect the extremum of the our multiple objective functions. Such steps can indirectly simplify the non-linear objective function by separate the single objective functions so that we can use the gradient flow method to solve the multi-objective problem of non-linear programming. It also embodies the stability and efficiency of the proposed gradient flow.