Papers by Author: Hong Wei Jiao

Abstract: Multiplicative problems are a kind of difficult global optimization problems known to be NP-hard. At the same time, these problems have some important applications in engineering, system, finance, economics, and other fields. In this paper, an optimization method is proposed to globally solve a class of multiplicative problems with coefficients. Firstly, by utilizing equivalent transformation and linearization method, a linear relaxation programming problem is established. Secondly, by using branch and bound technique, a determined algorithm is proposed for solving equivalent problem. Finally, the proposed algorithm is convergent to the global optimal solution of original problem by means of the subsequent solutions of a series of linear programming problems.

Abstract: In this paper a feasible method is proposed for solving a class of mathematical problems in manufacturing system and production system. By utilizing linearization technique the relaxation programming problem about the original problem is constructed. The proposed branch and bound algorithm is convergent to the global minimum of original problem through the successive refinement linear relaxation of the feasible region of objective function and solutions of a series of relaxation linear programming problem. And large number of experiments results show feasibility of presented method.

Abstract: In this paper, we develop an algorithm to globally solve a kind of mathematical problem. Firstly, by utilizing equivalent problem and linear relaxation method, a linear relaxation programming of original problem is established. Secondly, by using branch and bound technique, a determined global optimization algorithm is proposed for solving equivalent problem. Finally, the convergence of the proposed algorithm is proven and numerical examples showed that the presented algorithm is feasible to solve the kind of mathematical problems.

Abstract: In this technical note, we develop an approach to globally solve a class of optimization problems in system engineering based on the recent paper ([1]). Actually the problem we investigated is more general, since we extend numerators and denominators of linear ratios to generalized polynomial functions. And we give a new linear relaxation method for obtaining the lower bound of problems. Our approach is easy to be implemented, since it need not additional special program to the upper and lower bound for numerator and denominator of each generalized polynomial ratio.

Abstract: In this paper, a new computational method is proposed for solving a class of optimization problems which have broad applications in production system and system engineering. Firstly, by exploiting structure of the problem, linear relaxation programming of the original problem is constructed. By using simplex method we can solve a sequence of linear relaxation programming, the proposed algorithm is convergent to the global minimum of original problem through the successive refinement of the feasible region of a series of linear programming problems. In finally, numerical experiments are given to show the feasible of the proposed method.

Abstract: In this paper, we proposed an algorithm to globally solve a class of mathematical problems in mechanical system. Firstly, by utilizing equivalent problem and linear relaxation technique, a linear relaxation programming of original mathematical problem is established. Secondly, by using branch and bound theory, a feasible algorithm is proposed for globally solving original problem. Finally, the convergence of the proposed algorithm is proven, and numerical experiments showed that the presented algorithm is feasible.

Abstract: In this paper, we develop an algorithm to globally solve a class of mathematical models in system engineering. Firstly, by utilizing equivalent problem and linear relaxation method, a linear relaxation programming of original problem is established. Secondly, by using branch and bound technique, a determined branch and bound algorithm is proposed for globally solving original problem. Finally, the convergence of the proposed algorithm is given and numerical examples showed that the presented algorithm is feasible.