Satadru Roy

Simultaneous aircraft allocation and mission optimization using a modular adjoint approach

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.

A mixed integer efficient global optimization algorithm for the simultaneous aircraft allocation-mission-design problem

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.

Hybrid Approach for Multi-Objective Combinatorial Optimization in Search of Greener Aircraft

Pursuing “greener aircraft” with lower emissions and noise than today’s commercial transport aircraft has become an important effort across government, industry and academia. A commonly held perspective of pursuing greener aircraft is that a broad suite of new technologies and, potentially, new aircraft configurations provide the means to attaining a greener aircraft rather than incremental improvements to existing designs. Determining the appropriate combination, or portfolio, of technologies requires a method that can both sort through the myriad possible combinations of available technologies and aircraft configurations along with determining the size and dimensions of the best aircraft for a given selection of technologies. Characterizing an aircraft as “greener” requires consideration of several different metrics (e.g. carbon emissions – as measured by fuel burn, NOx emissions) along with basic economic considerations (e.g. required yield or ticket price). This combination of features makes this a multi-objective aircraft design optimization problem with both discrete and continuous design variables. This paper presents a hybrid multi-objective algorithm and demonstrates its ability to find solutions for a constrained multi-objective mixed discrete nonlinear programming problem. The algorithm hybridizes Genetic Algorithm with a gradient-based sequential quadratic programming algorithm in a manner that seems to overcome the demerits of these two algorithms when used independently. Applied to the greener aircraft problem, the algorithm seeks to arrive at the best trade-offs between representative environmental and economic metrics. The paper also describes the aircraft sizing tool used to evaluate the objective function values. While the detail and fidelity of the aircraft sizing model limits the quality of the results, the application suggests that the hybrid algorithm does have promise to assist decision-makers in choosing the appropriate technology portfolio.

Next generation aircraft design considering airline operations and economics

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.

Assessing Effects of Aircraft and Fuel Technology Advancement on Select Aviation Environmental Impacts

The ability to simultaneously assess airline operations, economics, and emissions would help evaluate the progress toward reduction of aviation’s environmental impact as outlined in the NASA Environmentally Responsible Aviation program. Furthermore, assessment of aircraft utilization by airlines would guide future policies and investment decisions on technologies most urgently required. This paper describes the development of the Fleet-Level Environmental Evaluation Tool, which is a computational simulation tool developed to assess the impact of new aircraft concepts and technologies on aviation’s impact on environmental emissions and noise. This tool uses an aircraft allocation model that represents the airlines’ profit-seeking operational decisions as a mixed-integer programming problem. The allocation model is embedded in a system-dynamics framework that mimics the economics of airline operations, models their decisions regarding retirement and acquisition of aircraft, and estimates market demand growt...

Environmental and Economic Impacts of Advanced Aircraft Operations Technologies on a Duopolistic Airline Model

ion Simplification Rationale Effect on Analysis  Passenger air travel on WWLMINET 257 subset  US airport as at least origin or destination between set of 257 airports  Route/city reduction: 190 airports  Contains 80% of passenger traffic (65% of operations) based on BTS data  Aircraft fleet represented by 18 aircraft  One aircraft represents all aircraft in a class  Represent technology “age”  Reduction from 100+ different aircraft types  Resolution in fleet reduced  Single airline (monopoly) or lowcost and legacy airlines (duopoly)  One or two airlines serve nearly 80% of passenger traffic; reflects much of the US air travel  Allows large numbers of routes in allocation problem by representing one airline  Does not exploit scarcity  Omits some competitive behaviors  Simplifies revenue/profit modeling  Aircraft allocation using roundtrip assumption  Avoid time of day scheduling  Assume symmetric demand between cities  Significant reduction in the number of decision variables  Removes “balance constraint”  Omits some time of day issues C. Aircraft Types The airline represented in FLEET uses 18 different aircraft types to serve passenger demand. These 18 aircraft types represent the most widely-used aircraft today, as well as new aircraft that will be available in the future. Table 1 describes these aircraft in terms of size and technology level. The 18 types fall into six classes based on passenger capacity, and into three technology levels based on entry in service and equipage. For aircraft size, class 1 encompasses small regional jets, while class 6 includes large twin-aisle aircraft. FLEET assumes that the chosen aircraft in a given class represents all aircraft of similar capacity, and only purchases and deploys these 18 aircraft models. Table 2. Aircraft classes and technology levels in FLEET Class Seats Representative-in-Class Best-in-Class Equipped Aircraft (EIS 2015) Class 1 20-50 Canadair RJ200/RJ440 Embraer ERJ145 Embraer ERJ145 Class 2 51-99 Canadair RJ700 Embraer 170 Embraer 170 Class 3 100-149 Boeing 737-300 Boeing 737-700 Boeing 737-700 Class 4 150-199 Boeing 757-200 Boeing 737-800 Boeing 737-800 Class 5 200-299 Boeing 767-300 Boeing 787 (2013) Boeing 787 Class 6 300+ Boeing 747-400 Boeing 777-200ER Boeing 777-200ER The technology levels assumed this study are Representative-in-Class, Best-in-Class, and Equipped. (This differs from the technology levels described in other FLEET studies.) Representative-in-Class aircraft are those with the most operations in their class in the year 2005 the baseline year used for most FLEET studies based on data from the Bureau of Transportation Statistics. Best-in-Class are those operating in 2005 with the most recent entry-inservice (EIS) date. The Boeing 787 also appears in this Best-in-Class category, given its introduction to revenue service by US carriers in 2013. The third technology level, Equipped Aircraft, assumes the same airframes and engines as the Best-in-Class, but these aircraft have advanced cockpit equipage to take full advantage of future ATM technology improvements. The study’s simulations assume that all Representativeand Best-in-Class aircraft are not equipped to gain benefit from future ATM improvements. However, these aircraft types already owned by the airline can be retrofitted with advanced avionics, at a cost, if desired. Using the same airframe and engine for Equipped Aircraft as the Best-in-Class Aircraft allows the study to focus on the near-term benefits of equipage improvements only, rather than combining those benefits with improvements from new aircraft models. These assumptions make the studies simpler to organize and execute.

Hybrid Multi-Objective Combinatorial Optimization Technique with Improved Compatibility between GA and Gradient-Based Local Search

*† This paper presents a hybrid multi-objective algorithm and demonstrates the algorithm’s ability to find solutions for a constrained multi-objective mixed discrete non-linear programming problem. The hybrid algorithm uses a Genetic Algorithm as a global search tool with a gradient based Sequential Quadratic Programming algorithm for local search in a way that seems to overcome the demerits of these two algorithms when used independently. The approach here addresses some of the issues that current state-ofthe-art optimization techniques face. Handling constraints is a primary concern for most of the global optimization algorithms that seek to address mixed discrete non-linear programming problem. In general, hybrid optimization algorithms tend to outperform their individual counterparts. Often, the enhanced performance of the hybrid approach leverages the computational efficiency of the gradient-based search and the design space exploration of the global search. The approach used here adds to the expected improvements along with a mechanism to address mixed discrete, nonlinear problems with the global search and to address strict constraint enforcement with the local search. Hybridizing two algorithms has proven to outperform their individual counterparts. However, not much is exploited from the process of hybridizing two algorithms other than the computational efficiency of the gradient-based algorithm and exploring capability of the global search algorithms. The work here presents a compatible hybridization between GA and SQP with improved information sharing between the two algorithms. The hybrid approach first solves a set of test problems to demonstrate its abilities and shortcomings; then the hybrid approach solves a greener aircraft design problem posed as a mixed discrete non-linear programming problem. The results of the greener aircraft design problem present the trade-offs that exist between the various environmental, economic and the performance metrics.