Aircraft design optimization and airline allocation problems are two separate and wellresearched disciplines, but very little literature exists that solved the design and allocation problems simultaneously. Among the limited number of related efforts that combine them, most follow a sequential decomposition strategy. This sequential strategy has been successful in addressing the combined large-scale problem but the approach does not capture the coupling that exists between the aircraft design and airline allocation disciplines. Solving the aircraft design and airline allocation as a monolithic problem makes it a Mixed Integer Non-Linear Programming problem which is very difficult to solve for large numbers of integer variables. Because no existing generalized MINLP solver can address this problem, this work proposes a new algorithm combining branch and bound, Efficient Global Optimization, Kriging Partial Least Squares, and gradient-based optimization to solve MINLP problems with 100's of integer design variables, 1000's of continuous design variables. The algorithm was applied to an 8 route coupled aircraft design and allocation problem with the 19 allocation variables and solving a 6000 variable aircraft design optimization problem using an Euler CFD simulation. This test problem provides several key challenges for a MINLP problem: a moderate integer design space, a large continuous design space, and expensive analysis models.

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The aircraft design optimization problem is typically formulated to maximize performance at a small number of representative operating conditions. This approach makes simplifying assumptions such as ignoring the climb and descent phases, but they can be avoided by performing simultaneous designmission-allocation optimization with surrogate models for the aircraft design disciplines. As a first step towards this goal, this paper presents a method for simultaneous allocation-mission optimization. We integrate aerodynamic and propulsion surrogates, a mission analysis tool, and allocation models within a computational framework that automates solving the coupled simulation and computing derivatives using the adjoint method for gradient-based optimization. We solve the mixed-integer allocation-mission optimization problem by using the linear allocation-only optimization to generate a good starting point and applying the branch-and-bound method to find an optimum for the mixedinteger nonlinear allocation-mission problem. The results show that this approach efficiently finds good local optima with, on average, roughly 10 node evaluations in the branch-and-bound method and most of the continuous optimizations converging almost immediately. The results show that adding next-generation aircraft to a fleet yields a 200-400 % profit increase for a 3-route test problem.

Traditional approaches to design and optimization of a new system often use a systemcentric objective and do not take into consideration how the operator will use this new system alongside other existing systems. When the new system design is incorporated into the broader group of systems, the performance of the operator-level objective can be sub-optimal due to the unmodeled interaction between the new system and the other systems. Among the few available references that describe attempts to address this disconnect, most follow an MDO-motivated sequential decomposition approach of first designing a very good system and then providing this system to the operator who, decides the best way to use this new system along with the existing systems. This paper addresses this issue by including aircraft design, airline operations, and revenue management "subspaces"; and presents an approach that could simultaneously solve these subspaces posed as a monolithic optimization problem rather than the traditional approach described above. The monolithic approach makes the problem an expensive Mixed Integer Non-Linear Programming problem, which are extremely difficult to solve. To address the problem, we use a recently developed optimization framework that simultaneously solves the subspaces to capture the "synergy" in the problem that the previous decomposition approaches did not exploit, addresses mixed-integer/discrete type design variables in an efficient manner, and accounts for computationally expensive analysis tools. This approach solves an 11-route airline network problem consisting of 94 decision variables including 33 integer and 61 continuous type variables. Simultaneously solving the subspaces leads to significant improvement in the fleet-level objective of the airline when compared to the previously developed sequential subspace decomposition approach. NomenclatureBH a, j = Block hours of aircraft type a on route j dem j = Daily passenger demand on route j E I = Expected Improvement f leet a = Number of aircraft type a k I = Number of integer type design variables of the problem M H a, j = Maintenance hour per block hour of aircraft type a on route j pax a, j = Number of passengers per flight on aircraft type a on route j