Geometric Programming for Aircraft Design Optimization

Abstract

Formulating conceptual-stage aircraft design problems as geometric programs, which are a specific type of convex optimization problem, is proposed. Recent advances in convex optimization offer significant advantages over the general nonlinear optimization methods typically used in aircraft design. Modern geometric program solvers are extremely fast (even on large problems), require no initial guesses or tuning of solver parameters, and guarantee globally optimal solutions. These benefits come at a price: all objective and constraint functions, the mathematical models that describe aircraft design relations, must be expressed within the restricted functional forms of geometric programs. Perhaps surprisingly, this restricted set of functional forms appears again and again in prevailing physics-based models for aircraft systems. Moreover, it is shown that, for various models that cannot be manipulated algebraically into the forms required by geometric programs, compact geometric program models that accurately approximate the original models can often be fit. The speed and reliability of geometric program solution methods makes them a promising approach for conceptual-stage aircraft design problems.