AN AUTOMATED SYSTEM FOR SOLVING MULTIPARAMETRIC PROGRAMMING PROBLEMS

Abstract

An automated system for solving multiparametric programming problems has been developed. The system is designed to solve multiparametric linear and quadratic programming problems. The parameters can exist in the coefficients of objective function as well as in the coefficients of constraint and right-hand sides. Functional dependencies of parameters can be both linear and non-linear. It is assumed that the partial derivatives of the coefficients with parametric dependencies, right-hand sides, as well as the functional dependencies of the solutions which are sought, do exist in respect to all parameters. The system prompts the user to select the class of the problem, the number of variables, the number of parameters and the number of differential images. Then it suggests entering the symbolic notations of the parameters, the interval of change. After that, text fields are created, in which the coefficients of the objective function of the optimization problem, the coefficients of the constraints and the right-hand sides are entered symbolically. For the solution of the problem, the system uses developed models using multidimensional differential transforms. The solutions to the problem are given by change intervals of the parameter, in each of them by the functional dependencies of the objective function and the variables, as well as graphical forms (in the case of one or two parameters). The computational operations are performed in Python 3 programming language using NumPy, SymPy, SciPy and Matplotlib libraries. The modules for calculating differential transforms are integrated in the system. The paper presents the results of solving a two-parameter programming problem by using the developed system which includes 24 intervals of change of the parameter, the functional dependencies of the solutions in each of them. The solutions were presented both in functional and graphical forms.