N-Branch Tournament Selection for Multiobjective
Optimization
Eric T. Martin*, William A. Crossley* and Sharon L. Padula
Multidisciplinary Optimization Branch, NASA Langley Research Center
*Purdue University
September 2002
RTA 706-32-21-02
Research Objective. Systems analysts need optimization-based
tools for trading off one mission goal against another. This research creates multiobjective
optimization tools for conceptual design problems. These methods differ from traditional optimization methods
in that they generate large sets of comparable designs, and they work well even
for discontinuous design spaces and discrete-valued design variables (e.g.,
selection of tail configuration or the number of seats abreast for passenger
aircraft).
Approach. Compare new N-branch tournament selection genetic algorithm method with multiobjective genetic algorithm (MOGA) method and with traditional gradient-based optimization methods. Compare these methods for several test problems with known solutions to assess their strengths and weaknesses for conceptual design tasks. Illustrate findings by using an aircraft sizing code to design a 50-seat commuter aircraft for the competing objectives of low takeoff gross weight WTO and low total trip time Ttrip.
Accomplishment Description. The
50-seat commuter problem illustrates the power of these multiobjective design
methods. The Langley aircraft
sizing code FLOPS is used to analyze the 500-nmi range mission shown in the figure.
The N-branch approach found 39 turboprop designs and 51 turbofan designs
minimizing some combination of WTO and Ttrip. The difference between turboprop and
turbofan is even more pronounced for the1000-nmi range mission. Extensive testing of interesting
academic problems suggests that the new N-branch approach is ideal for highly
constrained problems where the good designs appear in clusters amid large
regions of unacceptable designs.
On the other hand, the more traditional MOGA approach is ideal when the
systems analyst wants to find solutions over a large Pareto frontier with
“adjacent” objectives (objectives with optima near each other in
the design variable space).
Significance. The two Pareto plots shown in the figure contain a wealth of information that is particularly valuable when designing unconventional morphing vehicles where the trade spaces are not well understood. The design variables that change in value along the Pareto front are likely good candidates for morphing, while variables that remain unchanged are probably not as important for morphing. Information about the tradeoffs available between competing objectives can also be used to select a few designs for more extensive analysis. Moreover, such information in the Pareto plots enhances the designer’s intuition about design tradeoffs and suggests new opportunities for revolutionary concepts.
Future Plans. Optimization-based tools for conceptual design of aerospace vehicles form a fruitful new area of research for NASA. To be practical for Morphing vehicles, these tools must accept probabilistic and expert opinion-based inputs and must contend with computationally expensive and multidisciplinary analysis codes.
Figure: N-Branch Tournament Selection for Multiobjective Optimization
NASA POC: Sharon L. Padula
Telephone: (757) 864-2807
E-Mail: s.l.padula@larc.nasa.gov
Eric T. Martin, Rania A. Hassan and William A. Crossley, “Generalization of the Two-Branch Tournament for N-Objective Optimization”, Presented at the 9th AIAA/ISSMO Symposium on Multidisciplinary Analysis and Optimization, Atlanta, GA, September 4-6, 2002, Also AIAA 2002-5430.
Eric T. Martin and William A. Crossley, “Empirical Study of Selection Method for Multiobjective Genetic Algorithm”, Presented at the 40th AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, January 14-17, 2002, Also AIAA 2002-0177.
William A. Crossley, Eric T. Martin, and David W. Fanjoy, “A Multiobjective Investigation of 50-seat Commuter Aircraft Using a Genetic Algorithm”, Presented at the 1st AIAA Aircraft Technology Integration and Operations Forum, Los Angeles, CA, October 16-18, 2001, Also AIAA 2001-5247.
Crossley, W. A.; Cook, A. M.; Fanjoy, D. W.; and Venkayya, V. B.: Using the Two-Branch Tournament Genetic Algorithm for Multiobjective Design. AIAA Journal, February 1999, pp. 261-275.
Page Curator: D. H. Rudy
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Date last updated: April 20, 2006
