GENETIC ALGORITHM: APPLICATIONS TO LINEAR AND INTEGER PROGRAMMING PROBLEMS (original) (raw)

Linear programming problem has powerful capabilities that enable businesses to reduce costs, improve profitability, use resources effectively, reduce risks and provide benefits in many other key dimensions. Integer programming problem is a special case of linear programming problem because this optimization technique provides optimal integer solution of the programming problem. This technique plays important role in business and industry problems. In this paper, we have discussed linear and integer programming problems and their various applications. Apart from regular methods of solving these problems, we have studied a heuristic search approach Genetic Algorithm in optimization. Keywords: Linear programming problems, integer programming problems, methods for optimizing LPP and IPP, Genetic algorithm, applications of LPP and IPP, genetic algorithm for solving linear and integer programming problems. Introduction Linear programming is one of the most important optimization techniques which are developed in the field of operation research. It is a method or mathematical technique to find the best outcome (such as maximum profit or lowest cost) of linear function. A linear programming problem, maximizing or minimizing a linear function, can be of several decision variables subjected to linear constraints where constraints can be either inequalities or equalities. A linear programming problem consists of three components:  Decision variable  Objective function  Constraints General form: Suppose x1, x2,-, xn are n variables. Find the values of n decision variables which maximize or minimize the objective function z = c1x1 + c2x2 +-+cnxn where all cj are constants. j = 1, 2,-n. and satisfy m constraints a11x1 + a12x2 +-+ a1jxj +-+ a1nxn (≤ or ≥ or =) b1 a21x1 + a22x2 +-+ a2jxj +-+ a2nxn (≤ or ≥ or =) b2. .