A Mixed Integer Efficient Global Optimization Framework: Applied to the Simultaneous Aircraft Design, Airline Allocation and Revenue Management Problem

Satadru Roy, Purdue University

Abstract

Traditional approaches to design and optimize a new system, often, use a system-centric objective and do not take into consideration how the operator will use this new system alongside of other existing systems. This "hand-off" between the design of the new system and how the new system operates alongside other systems might lead to a sub-optimal performance with respect to the operator-level objective. In other words, the system that is optimal for its system-level objective might not be best for the system-of-systems level objective of the operator. Among the few available references that describe attempts to address this hand-off, most follow an MDO-motivated subspace decomposition approach of first designing a very good system and then provide this system to the operator who decides the best way to use this new system along with the existing systems. The motivating example in this dissertation presents one such similar problem that includes aircraft design, airline operations and revenue management "subspaces". The research here develops an approach that could simultaneously solve these subspaces posed as a monolithic optimization problem. The monolithic approach makes the problem a Mixed Integer/Discrete Non-Linear Programming (MINLP/MDNLP) problem, which are extremely difficult to solve. The presence of expensive, sophisticated engineering analyses further aggravate the problem. To tackle this challenge problem, the work here presents a new optimization framework that simultaneously solves the subspaces to capture the "synergism" in the problem that the previous decomposition approaches may not have exploited, addresses mixed-integer/discrete type design variables in an efficient manner, and accounts for computationally expensive analysis tools. The framework combines concepts from efficient global optimization, Kriging partial least squares, and gradient-based optimization. This approach then demonstrates its ability to solve an 11 route airline network problem consisting of 94 decision variables including 33 integer and 61 continuous type variables. This application problem is a representation of an interacting group of systems and provides key challenges to the optimization framework to solve the MINLP problem, as reflected by the presence of a moderate number of integer and continuous type design variables and expensive analysis tool. The result indicates simultaneously solving the subspaces could lead to significant improvement in the fleet-level objective of the airline when compared to the previously developed sequential subspace decomposition approach. In developing the approach to solve the MINLP/MDNLP challenge problem, several test problems provided the ability to explore performance of the framework. While solving these test problems, the framework showed that it could solve other MDNLP problems including categorically discrete variables, indicating that the framework could have broader application than the new aircraft design-fleet allocation-revenue management problem.

Degree

Ph.D.

Advisors

Crossley, Purdue University.

Subject Area

Aerospace engineering

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