The Power of Log Transformation: A Comparison of Geometric and Signomial Programming with General Nonlinear Programming Techniques for Aircraft Design Optimization

摘要

Geometric and signomial programming are emerging as promising methods for aircraft design optimization, having both been demonstrated to reliably and quickly find optimal solutions to aircraft design problems. To better understand how they perform compared with more conventional alternatives, this work presents a direct comparison with a general nonlinear programming approach. The crux of geometric programming, and by extension signomial programming, is in the formulation and the logarithmic transformation that makes the problem convex. Starting with the same problem formulation we assess the difference in speed and effectiveness achieved by performing the transformation. Two relatively small aircraft design problems, one a geometric program, the other a signomial program, are solved using the interior point and sequential quadratic programming alogrithms implemented in MATLAB's fmincon function, both with and without performing the log transformation first. Results show that performing the log transformation consistently yields the same optimal solution, independent of initial guess, whereas applying a general nonlinear programming technique directly to the un-transformed problem, at best, takes significantly longer and, at worst, terminates at an infeasible solution. The results also show that the general approach is highly sensitive to the initial guess whereas geometric and signomial programming approaches are not.