Problems And Algorithms Of Programming With Interval Coefficients

The phenomenon of uncertainty exist widely in our real life and engineering problems, the regulation theories and algorithms about it have a great significance for the reliability design in the products and systems. Stochastic programming and fuzzy programming are two traditional uncertainty regulation methodologies, but the probability distributing of random parameters or the membership functions of fuzzy parameters are usually unknown, and in most circumstances, we can only obtain the change bounds of the uncertain parameters. So we introduce the programming with coefficients interval, which is a flexible programming and can easily solve some optimization problems in uncertain system. The programming with coefficients interval is a relatively new optimization uncertainty programming method, it reflects the very good convenience and economy in uncertainty modeling. In recent years, the programming with coefficients interval has been attracting more and more attentions at home and abroad, and it is expected to become the third major uncertain optimization methodology after stochastic programming and fuzzy programming. Furthermore, the programming with coefficients interval even shows a larger application potential for practical engineering problems than the other two methods. However, it is still at its preliminary stage for the present programming with coefficients interval research, especially for the nonlinear programming with interval coefficients. So it is very necessary that discussing the models and algorithms about interval programming.In this paper, we give a more systematic and comprehensive study in the linear programming with coefficients interval interval based on the basis of previous studies, and proposed a simple transformation model and algorithm for the quadratic programming with coefficients interval in the nonlinear programming with coefficients interval. The main works of this paper are as follows:(1)Give an overview on the model of linear programming with coefficients interval and its solving method, then introduce a standard model for linear programming with coefficients interval, after that we summarized two kinds of interval optimization algorithms, one is about the satisfaction solution for interval numbers'ordering relation, and the other is about the optimal value in interval upper and lower bounds;(2)After we convert the satisfaction optimization model solution into the interval optimization model for optimal value, two optimization algorithms are been unified, through the improve and supplement for the worst-optimal value in the optimal value interval model, optimizing and improving the optimal value of the interval operator, this enables the linear programming with coefficients interval model and algorithms are more systematic and comprehensive. (3)Studied the class of simple type in nonlinear programming with interval coefficients --quadratic programming with coefficients interval. Use for reference the model of linear programming with coefficients interval and its solving method, we proposed a standard model on quadratic programming with coefficients interval, proofed the reasonable on its decomposition into two deterministic model from the theoretical study,and with the simulation examples showing the feasibility of the solution;(4)Give another new algorithm for single-objective transportation problems in which the parameters about objective function and constraints are all interval numbers, and from the numerical examples in the paper we can see the new algorithm is indeed feasible and practical.