Multi Objective Geometric Programming with Interval Coefficients: A Parametric Approach

Abstract

When we talk of optimization in industry we need to pay attention in searching for very powerful and flexible optimization techniques. One of such techniques which has attracted the interest of many researchers in the last few decades is called geometric programming that provides a powerful tool for solving nonlinear problems. As we know in the real world, many applications of geometric programming are engineering design problems. Generally, engineering design problems deal with multi-objective functions, in which their objectives are often in conflicts with each other. This paper considers a solution method when the cost, the constraint coefficients, and the right-hand sides in the multi-objective geometric programming problems are imprecise and represented as interval values. This problem is reduced with the method of weighted sum to a single objective function and further by applying interval-valued function, we solve the problem by geometric programming technique. The ability of calculating the bounds of the objective value developed in this paper might help lead to more realistic modeling efforts in engineering optimization areas. Finally a numerical example is given to illustrate the methodology of solution and efficiency of the present approach.