Application of Signomial Programming to Aircraft Design

Abstract

Due to the coupled nature of aircraft design, it is important to consider all major subsystems when optimizing a configuration. This is difficult when each individual subsystem model can be arbitrarily complex. By restricting an optimization problem to have a certain mathematical structure, significantly more effective and tractable solution techniques can be used. Geometric programming, one such technique, guarantees finding a globally optimal solution. Although it has been shown that geometric programming can be used to solve some aircraft design problems, the required formulation can prove too restrictive for certain relationships. Signomial programming is a relaxation of geometric programming that offers enhanced expressiveness. Although they do not guarantee global optimality, solution methods for signomial programs are disciplined and effective. In this work, signomial programming models are proposed for optimal sizing of the wing, tail, fuselage, and landing gear of a commercial aircraft. These models are combined together to produce a system-level optimization model. Signomial programming’s formulation allows it to handle some key constraints in aircraft design, and therefore an improvement in fidelity over geometric programming models is achieved. A primary contribution of this work is to demonstrate signomial programming as a viable tool for multidisciplinary aircraft design optimization.