How Design Quality Improves with Increasing Computational Abilities: General Formulas and Case Study of Aircraft Fuel Efficiency
Joe Lorkowski*, Olga Kosheleva*, Vladik Kreinovich*, and Sergei Soloviev**,***
*University of Texas at El Paso
500 W. University, El Paso, TX 79968, USA
**Institut de Recherche en Informatique de Toulouse (IRIT)
Porte 421, 118 route de Narbonne, 31062 Toulouse cedex 4, France
***St. Petersburg State University of Information Technologies, Mechanics, and Optics (ITMO)
St. Petersburg, 197101, Russia
It is known that the problems of optimal design are NP-hard – meaning that, in general, a feasible algorithm can only produce close-to-optimal designs. The more computations we perform, the better design we can produce. In this paper, we theoretically derive quantitative formulas describing how the design qualities improves with the increasing computational abilities. We then empirically confirm the resulting theoretical formula by applying it to the problem of aircraft fuel efficiency.
-  C. Babers, “Architecture Development Made Simple,” Lulu.com, 2006.
-  International Council on Systems Engineering (INCOSE), “Systems Engineering Handbook,” Wiley, Hoboken, New Jersey, 2015.
-  P. A. Laplante, “Requirements Engineering for Software and Systems,” CRC Press, Boca Raton, 2014.
-  D. A. Madsen and D. P. Madsen, “Engineering Drawing and Design,” Delmar, Cengage Learning, Clifton Park, New York, 2012.
-  K. Sabbagh, “Twenty-First-Century Jet: The Making and Marketing of the Boeing 777,” Scribner, New York, 1996.
-  V. Kreinovich, A. Lakeyev, J. Rohn, and P. Kahl, “Computational Complexity and Feasibility of Data Processing and Interval Computations,” Kluwer, Dordrecht, 1998. [Pardalos 1993] P. M. Pardalos, “Complexity in Numerical Optimization,” World Scientific, Singapore, 1993.
-  M. E. Garey and D. S. Johnson, “Computers and Intractability: A Guide to the Theory of NP-Completeness,” Freeman, San Francisco, 1979.
-  C. H. Papadimitriou, “Computational Complexity,” Addison Wesley, San Diego, 1994.
-  D. J. Sheskin, “Handbook of Parametric and Nonparametric Statistical Procedures,” Chapman & Hall/CRC, Boca Raton, Florida, 2011.
-  J. Beirlant, Y. Goegevuer, J. Teugels, and J. Segers, “Statistics of Extremes: Theory and Applications,” Wiley, Chichester, 2004.
-  L. de Haan and A. Ferreira, “Extreme Value Theory: An Introduction,” Springer Verlag, Berlin, Hiedelberg, New York, 2006.
-  P. Embrechts, C. Klüuppelberg, and T. Mikosch, “Modelling Extremal Events for Insurance and Finance,” Springer Verlag, Berlin, Heidelberg, New York, 2012.
-  E. J. Gumbel, “Statistics of Extremes,” Dover Publ., New York, 2004.
-  J. J. Lee, S. P. Lukachko, I. A. Waitz, and A. Schafer, “Historical and future trends in aircraft performance, cost and emissions,” Annual Review of Energy Environment, Vol.26. pp. 167-200, 2001.
-  P. M. Peeters, J. Middel, and A. Hoolhorst, “Fuel Efficiency of Commercuial Aircraft: An Overview of Historical and Future Trends,” Netherlands National Aerospace Laboratory NLR, Technical Report NLR-CR-2005-669, 2005.
-  J. E. Penner, D. H. Lister, D. J. Griggs, D. J. Dokken, and M. McFarland, “Aviation and the Global Atmosphere: A Special Report of Intergovernmental Panel on Climate Change (IPCC) Working Groups I and III,” Cambridge University Press, Cambridge, UK, 1999.
-  J. L. Hennessy and D. A. Patterson, “Computer Architecture: A Quantitative Approach,” Morgan Kaufmann, Waltham, Massachusetts, 2012.
-  G. E. Moore, “Cramming More Components onto Integrated Circuits,” Electronics, pp. 114-117, April 19, 1965.