Geometric Programming Problem with Co-Efficients and Exponents Associated with Binary Numbers

TL;DR

This paper introduces a novel geometric programming approach that uses binary numbers to split coefficients and exponents, enabling more realistic modeling in engineering design problems.

Contribution

It develops a new solution procedure for nonlinear programming using GP by splitting parameters with binary numbers, enhancing modeling accuracy.

Findings

Successfully formulated equivalent mathematical programming problems.

Demonstrated the method with two numerical examples.

Utilized standard nonlinear programming software for solutions.

Abstract

Geometric programming (GP) provides a power tool for solving a variety of optimization problems. In the real world, many applications of geometric programming (GP) are engineering design problems in which some of the problem parameters are estimating of actual values. This paper develops a solution procedure to solve nonlinear programming problems using GP technique by splitting the cost coefficients, constraint coefficients and exponents with the help of binary numbers. The equivalent mathematical programming problems are formulated to find their corresponding value of the objective function based on the duality theorem. The ability of calculating the cost coefficients, constraint coefficients and exponents developed in this paper might help lead to more realistic modeling efforts in engineering design areas. Standard nonlinear programming software has been used to solve the proposed optimization problem. Two numerical examples are presented to illustrate the method.