Genetic Algorithms for Solving a Class of Constrained Nonlinear Integer Programs (original) (raw)
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The purpose of this research is to determine an optimal batch size for a product, and purchasing policy of associated raw materials. The mathematical model for this problem is a constrained nonlinear integer program. Considering the complexity of solving such model, we investigate the use of genetic algorithms (GAs) for solving this model. We develop genetic algorithm code with three different penalty functions usually used for constraint optimizations. The model is also solved using an existing commercial optimization package to compare the solution. The detail computational experiences are presented.
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Due to their large variety of applications, complex optimisation problems induced a great effort to develop efficient solution techniques, dealing with both continuous and discrete variables involved in non-linear functions. But among the diversity of those optimisation methods, the choice of the relevant technique for the treatment of a given problem keeps being a thorny issue. Within the Process Engineering context, batch plant design problems provide a good framework to test the performances of various optimisation methods : on the one hand, two Mathematical Programming techniques-DICOPT++ and SBB, implemented in the GAMS environment-and, on the other hand, one stochastic method, i.e. a genetic algorithm. Seven examples, showing an increasing complexity, were solved with these three techniques. The result comparison enables to evaluate their efficiency in order to highlight the most appropriate method for a given problem instance. It was proved that the best performing method is SBB, even if the GA also provides interesting solutions, in terms of quality as well as of computational time.
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In order to make the Economic Production Quantity (EPQ) model more applicable to real-world production and inventory control problems, in this paper we expand this model by assuming that some imperfect items of different product types being produced such as reworks are allowed. In addition, we may have more than one product and supplier along with warehouse space and budget limitation. We show that the model of the problem is a constrained non-linear integer program and propose a genetic algorithm to solve it. Moreover, a design of experiments is employed to calibrate the parameters of the algorithm for different problem sizes. In the end, a numerical example is presented to demonstrate the application of the proposed methodology.
GENETIC ALGORITHM: APPLICATIONS TO LINEAR AND INTEGER PROGRAMMING PROBLEMS
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. .
International Journal of the Physical Sciences, 2012
In order to make the economic production quantity (EPQ) model more applicable to real-world production and inventory control problems, in this paper, we expand this model by assuming that some imperfect items of different product types are being produced such that reworks are allowed. In addition, we may have more than one product and supplier along with warehouse space and budget limitation. We show that the model of the problem is a constrained non-linear integer program and propose a genetic algorithm (GA) to solve it. Moreover, design of experiments is employed to calibrate the parameters of the algorithm for different problem sizes. At the end, a numerical example is presented to demonstrate the application of the proposed methodology.