Multi-Objective Geometric Programming Problem Being Cost Coefficients as Continous Function with Weighted Mean Method

‐ Geometric programming problems occur frequently in engineering design and management. In multi‐ objective optimization, the trade‐off information between different objective functions is probably the most important piece of information in a solution process to reach the most preferred solution. In this paper we have discussed the basic concepts and principles of multiple objective optimization problems and developed a solution procedure to solve this optimization problem where the cost coefficients are continuous functions using weighted method to obtain the non‐inferior solutions.1. INTRODUCTION Geometric programming (GP) derives its name from its intimate connection with geometrical concepts because the method based on geometric inequality and their properties that relate sums and products of positive numbers. Its attractive structural properties as well as its elegant theoretical basis have led to a number of interesting applications and the development of numerous useful results. The integrated circuit design, engineering design project management and inventory management are examples. Geometric programming problems (GPPs) are smooth non-linear programs in which the objective and each constraint function is a posynomials i.e. a linear combination of terms with each term a product of variables raised to real powers and each constraint function must be < 1.The decision variables x j are restricted to be positive, to ensure that terms involving variables raised to fractional powers are defined. If all the linear combination coefficients are positive, the functions are called posynomials and the problem is easily transformed to a convex program in new variables y j = lnx j. Otherwise the general posynomial problem is non-convex. Most of these GP applications are posynomial type with zero or few degrees of difficulty. The degree of difficulty is defined as the number of terms minus the number of variables minus one, and is equal to the dimension of the dual problem. When the degree of difficulty is zero, there is a unique dual feasible solution. If the degree of difficulty is positive, then the dual feasible region must be searched to maximize the dual objective, while if the degree of difficulty is negative, the dual constraints may be inconsistent. For detailed discussions of various algorithms and computational aspects for both posynomial and signomial GP refers to Beightler [2], Duffin [7], Ecker [8] and Phillips [15]. Generally, an engineering design problem has multiple objective functions that are usually non-commensurable and in conflict. An ideal solution is that which is optimal with respect to all …