Abstract
Nash equilibrium and evolutionary algorithm are used to optimize a wing of a regional turboprop aircraft, with the aim to compare different optimization strategies in the aircraft design field. Since the aircraft design field is very complex in terms of number of involved variables and space of analysis, it is not possible to perform an optimization process accounting for all possible parameters. This leads to the need to reduce the number of the variables to the most significant ones. A multi-objective optimization approach is here performed, paying attention to the variables which mainly influence the objective functions. Results of Nash-Genetic algorithm are compared against those of both a typical Pareto front and a scalarization, showing that the proposed approach locates almost all solutions on the Pareto front, while the scalarization results are confined only in a zone of this front. The optimization elapsed time for a single optimization point is less than 32% of an entire Pareto front, but the designer must initially choose the players’ cards assignment.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Basar T, Olsder GJ (1995) Dynamic non cooperative game theory. In: Classics in Applied Mathematics, 23. Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA
Blackwell Jr JA (1969) A finite-step method for calculation of theoretical load distributions for arbitrary lifting-surface arrangements at subsonic speeds. Washington, D.C., Document ID: 19690021959
D’Amato E, Daniele E, Mallozzi, L., Petrone, G. (2012b) Equilibrium strategies via GA to Stackelberg games under multiple follower’s best reply. Int J Intell Syst 27, Wiley Subscription Services, Inc., A Wiley Company
D’Amato E, Daniele E, Mallozzi L, Petrone G, Tancredi S (2012a) A hierarchical multi-modal hybrid Stackelberg-Nash GA for a leader with multiple followers game. In: Sorokin A, Murphey R, Thai MT, Pardalos PM (eds) Dynamics of information systems: mathematical foundations. Springer Proceedings in Mathematics & Statistics, vol. 20, pp 267–280, Springer, New York
Deb K, Agrawal S, Pratap A, Meyarivan T (2000) A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. In: Schoenauer M, Deb K, Rudolph G, Yao X, Lutton E, Merelo JJ, Schwefel H-P (eds) Parallel problem solving from nature–PPSN VI. Springer, Berlin, pp 849–858
Della Vecchia P, Daniele E, D’Amato E (2014) An airfoil shape optimization technique coupling parsec parametrization and evolutionary algorithm. Aerosp Sci Technol 32(1):103–110
Della Vecchia P, Stingo L, Corcione S, Ciliberti D, Nicolosi F, De Marco A, Nardone G (2017) Game theory and evolutionary algorithms applied to MDO in the AGILE European project, In: 18th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference. Denver, Colorado
Fonseca CM, Fleming PJ (1995) An overview of evolutionary algorithms in multiobjective optimisation. Evol Comput 3:1–16
Fudenberg D, Tirole J (1991) Game theory. The MIT Press, Boston
Greiner D, Periaux J, Emperador JM, Galvan B, Winter G (2016) Nash evolutionary algorithms: testing problem size in reconstruction problems in frame structures. ECCOMAS Congress
Haupt RL, Haupt SE (2004) Practical genetic algorithms. Wiley-Interscience, Hoboken
Lefebvre T, Bartoli N, Dubreuil S, Panzeri M, Lombardi R, D’Ippolito R, Della Vecchia P, Nicolosi F, Ciampa PD (2017) Methodological enhancements in MDO process investigated in the AGILE European project. In: 18th AIAA/ISSMO Multidisciplinary Analysis and Optimization Conference, Denver, Colorado
Mallozzi L, Reina GP, Russo S, de Nicola C (2016) Game theoretical tools for wing design. In: Pardalos PM, Conca P, Giuffrida G, Nicosia G (eds) Machine learning, optimization, and big data, LNCS lecture notes in computer science, vol. 10122, pp 419–426, Springer, Berlin (ISBN 978-3-319-51468-0)
Nash JF (1950) Equilibrium points in n-person games. Proc Natl Acad Sci USA 36:46–49
Nash JF (1951) Non-cooperative games. Ann Math Second Ser Princeton University, NJ, USA 54:286–295
Periaux J, Gonzalez F, Lee DSC (2015) Evolutionary optimization and game strategies for advanced multi-disciplinary design. In: Intelligent systems, control and automation: science and engineering. Software Pioneers. Springer, New York
Raymer D (2002) Aircraft design: a conceptual approach. American Institute of Aeronautics and Astronautics Inc., Washington, D.C
Sefrioui M, Periaux J (2000) Nash genetic algorithms: examples and applications. In: Proceedings of the IEEE Congress on Evolutionary Computation. pp 509–516
Wang JF, Periaux J, Sefrioui M (2002) Parallel evolutionary algorithms for optimization problems in aerospace engineering. J Comput Appl Math 149:155–169
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer International Publishing AG, part of Springer Nature
About this chapter
Cite this chapter
Della Vecchia, P., Stingo, L., Nicolosi, F., De Marco, A., Daniele, E., D’Amato, E. (2019). Application of Game Theory and Evolutionary Algorithm to the Regional Turboprop Aircraft Wing Optimization. In: Andrés-Pérez, E., González, L., Periaux, J., Gauger, N., Quagliarella, D., Giannakoglou, K. (eds) Evolutionary and Deterministic Methods for Design Optimization and Control With Applications to Industrial and Societal Problems. Computational Methods in Applied Sciences, vol 49. Springer, Cham. https://doi.org/10.1007/978-3-319-89890-2_26
Download citation
DOI: https://doi.org/10.1007/978-3-319-89890-2_26
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-89889-6
Online ISBN: 978-3-319-89890-2
eBook Packages: EngineeringEngineering (R0)