Geometric programming with fuzzy parameters in engineering optimization Original Research Article

Geometric programming provides a powerful tool for solving a variety of engineering optimization problems. Many applications of geometric programming are engineering design problems in which some of the problem parameters are estimates of actual values. When the parameters in the problem are imprecise, the calculated objective value should be imprecise as well. This paper develops a procedure to derive the fuzzy objective value of the fuzzy posynomial geometric programming problem when the exponents of decision variables in the objective function, the cost and the constraint coefficients, and the right-hand sides are fuzzy numbers. The idea is based on Zadeh’s extension principle to transform the fuzzy geometric programming problem into a pair of two-level of mathematical programs. Based on duality algorithm and a simple algorithm, the pair of two-level mathematical programs is transformed into a pair of conventional geometric programs. The upper bound and lower bound of the objective value are obtained by solving the pair of geometric programs. From different values of α, the membership function of the objective value is constructed. Two examples are used to illustrate that the whole idea proposed in this paper.