Indianapolis, Indiana
June 15, 2014
June 15, 2014
June 18, 2014
2153-5965
Engineering Technology
13
24.641.1 - 24.641.13
10.18260/1-2--20532
https://peer.asee.org/20532
563
Geometric Programming - a Tool for Design and Cost Optimization Geometric programming ia a mathematical optimization technique credited to ClarenceZener in 1961, who is also credited with the invention of the Zener Diode. Geometricprogramming can be used not only to provide a specific solution to a problem, but in manyinstances it can give a general solution with specific design relationships. These designrelationships, based upon the design parameters and constraints, can then be used for the optimalsolution without having to resolve the original problem. A second concept is that the dualsolution gives a constant cost ratio between the terms of the objective function which appears tobe unique to geometric programming. It is called geometric programming because it is basedupon the arithmetic-geometric inequality where the arithmetic mean is always greater than orequal to the geometric mean. This technique has many similarities to linear programming such as primal and dualsolutions, but has the advantages over linear programming in that:(1) A non-linear objective function is used;(2) The constraints are non-linear:(3) The objective function can be solved using the dual formulation, which is much easier tosolve.and most importantly(4) Generalized design relationships can often be obtained for the primal variables in terms ofthe constants. This paper will present the basic problem formulation of the primal and dual techniquesand give a few basic examples to illustrate the design relationships obtained for the primalvariables and the objective function. The examples presented will be the cardboard box designand the classic geometric programming example of the open cargo shipping box.The outcomes from this presentation are:1) Illustrate the advantages of Geometric Programming for cost estimation;2) Illustrate the development of design relationships based upon input constants;and3) Illustrate the importance of Primal-Dual relationships in Geometric Programming.
Creese, R. C. (2014, June), Geometric Programming - A Tool for Design and Cost Optimization Paper presented at 2014 ASEE Annual Conference & Exposition, Indianapolis, Indiana. 10.18260/1-2--20532
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