Approximating Linear Programming by Geometric Programming and Its Application to Urban Planning

Abstract

In this study, we approximated linear programming by geometric programming; the developed method converts linear programming to geometric programming. We applied the developed method to Neighbourhood planning, a vital aspect of urban planning, and obtained the optimal cost of Neighbourhood designs. The method demonstrated that geometric programming is a robust non-linear optimization model that can be extended to approximate linear optimization problems. This method has obvious advantages in the sense that it allows every decision variable to contribute to the optimal objective function. This is not the case with the known regular Simplex method and the Interior Point Algorithm of solution to linear programming which assign zeros to some variables when the matrix of the non-basic variables is rectangular or when some of the non-basic variables did not enter the basis. The developed method was used to find the global optimal solution, optimal primal and dual decision variables. The solution was better compared to the linear programming method via Simplex method or Interior Point Algorithm because it achieved the global optimal solution. We observed that in addition to achieving the global optimal solution, we obtained the optimal dual decision variables which was absent in the other methods and all the primal decision variables have value against the other methods that assigned some of the variables with zeroes.