Global Optimization Algorithms Of Fractional Programming Problems

Fractional programming problems often exist a number of non-global local optimal solutions, and may be full of challenges to solve them. At the same time, these problems can be widely used in the fields of molecular biology, environmental engineering, econom-ic investment, industrial manufacturing and so on. Therefore, fractional programming problems has attracted the interest of researchers in recent years. This paper propose a branch and bound algorithm for solving the sum of linear ratios fractional programming and an iterative algorithm for a class of generalized fractional programming problems with polynomial constraints respectively. The main contents of this paper are as follows:In Chapter 1, we first give the problem models that will be considered in this paper.Next, we present the application background, theoretical significance and the research status of these issues. Finally, the main work of this paper is introduced briefly.In Chapter 2, a branch and bound algorithm is proposed for globally solving the sum of linear ratios fractional programming. Firstly, the equivalent problem is constructed by introducing new variables, and then by using the relaxation technique, a. linear relaxation prograinming is obtained. Update the upper and lower bounds of the original optimal value by solving a series of linear programming problems, and an approximate optimal solution can be get in the end. Finally, the convergent property of the presented algorithm can be proved, and numerical results are given to show the feasibility of the proposed algorithm.In Chapter 3, we consider a class of generalized fractional programming problems with polynomial constraints. Firstly, the original problem is transformed into its equiva-lent form, and then by using a standardized strategy, the standard geometric programming which is easy to be solved can be gained. By solving a series of standard geometric pro-gramming problems, the approximate optimal solution of the original problem is obtained.Finally, give the iterative algorithm and its convergent analysis, numerical results show that the algorithm is feasible and effective.