Abstract
A comparative study of the use of Gray coding in multicriteria evolutionary optimisation is performed using the SPEA2 and NSGAII algorithms and applied to a frame structural optimisation problem. A double minimization is handled: constrained mass and number of different cross-section types. Influence of various mutation rates is considered. The comparative statistical results of the test case cover a convergence study during evolution by means of certain metrics that measure front amplitude and distance to the optimal front. Results in a 55 bar-sized frame test case show that the use of the Standard Binary Reflected Gray code compared versus Binary code allows to obtain fast and more accurate solutions, more coverage of non-dominated fronts; both with improved robustness in frame structural multiobjective optimum design.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Burns, S.A. (ed.): Recent Advances in Optimal Structural Design. Institute of American Society of ASCE-SEI (2002)
Caruana, R., Schaffer, J.: Representation and Hidden Bias: Gray vs. Binary Coding for Genetic Algorithms. In: Proceedings of the Fifth International Conference on Machine Learning, pp. 153–161. Morgan Kaufmann, San Francisco (1988)
Chakraborty, U.K., Janikow, C.Z.: An analysis of Gray versus binary encoding in genetic search. Information Sciences: an International Journal; Special Issue: Evolutionary Computation 156, 253–269 (2003)
Coello Coello, C.A., Christiansen, A.D.: Multiobjective optimization of trusses using genetic algorithms. Computers & Structures 75, 647–660 (2000)
Coello Coello, C.A.: An Empirical Study of Evolutionary Techniques for Multiobjective Optimization in Engineering Design, PhD Thesis, Tulane University, LA, U.S.A. (1996)
Coello, C., Van Veldhuizen, D., Lamont, G.: Evolutionary Algorithms for solving multi-objective problems. GENA Series. Kluwer Academic Publishers, Dordrecht (2002)
Cuthill, M.: Reducing the bandwidth of sparse symmetric matrixe. In: Proceedings ACM National Conference, New York (1969)
Deb, K.: Multiobjective Optimization using Evolutionary Algorithms. Series in Systems and Optimization. John Wiley & Sons, Chichester (2001)
Deb, K., Pratap, A., Agrawal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm NSGAII. IEEE Transactions on Evolutionary Computation 6(2), 182–197 (2002)
French, S.: Sequencing and Scheduling: An Introduction to the Mathematics of the Job-Shop. Wiley, New York (1982)
Galante, M.: Genetic Algorithms as an approach to optimise real-world trusses. International Journal for Numerical Methods in Engineering 39, 361–382 (1996)
Goldberg, D.E.: Genetic algorithms for search, optimisation, and machine learning. Addison Wesley, Reading (1989)
Goldberg, D.E., Samtani, M.P.: Engineering Optimization via genetic algorithm. In: Proceedings Ninth Conference on Electronic Computation, pp. 471–482. ASCE, New York (1986)
Greiner, D., Emperador, J.M., Winter, G.: Single and Multiobjective Frame Optimization by Evolutionary Algorithms and the Auto-adaptive Rebirth Operator. Computer Methods in Applied Mechanics and Engineering 193, 3711–3743 (2004)
Greiner, D., Emperador, J.M., Winter, G.: Multiobjective Optimisation of Bar Structures by Pareto-GA. In: European Congress on Computational Methods in Applied Sciences and Engineering, CIMNE (2000)
Greiner, D., Winter, G., Emperador, J.M.: Optimising Frame Structures by different strategies of GA. Finite Elements in Analysis and Design 37(5), 381–402 (2001)
Greiner, D., Winter, G., Emperador, J.M., Galván, B.: An efficient adaptation of the truncation operator in SPEA2. In: Herrera, et al. (eds.) Proceedings of the First Spanish Congress on Evolutionary and Bioinspired Algorithms, Mérida, Spain (February 2002) (in Spanish)
Grierson, D.E., Pak, W.H.: Optimal sizing, geometrical and topological design using a genetic algorithm. Structural Optimization 6(3), 151–159 (1993)
Hajela, P., Lin, C.Y.: Genetic search strategies in multicriterion optimal design. Structural Optimization 4, 99–107 (1992)
Hernández Ibáñez, S.: Structural Optimum Design Methods. Colección Seinor. Colegio de Ingenieros de Caminos, Canales y Puertos, Madrid (1990)
Hernández Ibáñez, S.: From Conventional Design to Optimum Design. Posibilities and Variants. Part I. Sensibility Analysis and local and global Optimisation. International Journal of Numerical Methods for Calculus and Engineering Design CIMNE, 91–110 (1993) (in Spanish)
Hinterding, R., Gielewski, H., Peachey, T.C.: The nature of mutation in genetic algorithms. In: Proceedings of the Sixth International Conference on Genetic Algorithms 1989, pp. 70–79. Morgan Kaufmann, San Francisco (1989)
Koski, J.: Multicriteria optimization in structural design: state of the art. In: Proceedings of the 19th Design Automation Conferences ASME, pp. 621–629 (1993)
Liu, M., Burns, S.A., Wen, Y.K.: Optimal seismic design of steel frame buildings based on life cycle cost considerations. Earthquake Eng. Struc. 32(9), 1313–1332 (2003)
Mathias, K.E., Whitley, D.: Trasforming the Search Space with Gray Coding. In: IEEE Int. Conference on Evolutionary Computation, pp. 513–518. IEEE Service Center, Los Alamitos (1994)
Radcliffe, N.J., Surry, P.D.: Fundamental Limitations on Search Algorithms: Evolutionary Computing in Perspective. In: van Leeuwen, J. (ed.) Computer Science Today. LNCS, vol. 1000, pp. 275–291. Springer, Heidelberg (1995)
Rowe, J., Whitley, D., Barbulescu, L., Watson, P.: Properties of Gray and Binary Representations. Evolutionary Computation 12(1), 46–76 (2004)
Sarma, K., Adeli, H.: Life-cycle cost optimization of steel structures. International Journal for Numerical Methods in Engineering 55, 1451–1462 (2002)
Savage, C.: A Survey of Combinatorial Gray Codes. SIAM Review 39(4), 605–629 (1997)
Whitley, D.: A free lunch proof for Gray versus Binary Codings. In: Proceedings of the Genetic and Evolutionary Computation Conference, pp. 726–733. Morgan Kaufmann, San Francisco (1999)
Whitley, D., Rana, S., Heckendorn, R.: Representation Issues in Neighborhood Search and Evolutionary Algorithms. In: Quagliarella, D., Périaux, J., Poloni, C., Winter, G. (eds.) Genetic Algorithms and Evolution Strategies in Engineering and Computer Science, pp. 39–57. John Wiley & Sons, Chichester (1997)
Wolpert, D.H., MacReady, W.G.: No Free Lunch Theorems for Search, Technical Report SFI-TR-95-02-010, Santa Fe Institute (July 1995)
Zitzler, E.: Evolutionary Algorithms for Multiobjective Optimization : Methods and Applications. PhD Thesis. Swiss Federal Institute of Technology (ETH), Zurich (1999)
Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the Strength Pareto Evolutionary Algorithm for Multiobjective Optimization. In: Evolutionary Methods for Design, Optimization and Control with Applications to Industrial Problems, CIMNE, pp. 95–100 (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Greiner, D., Winter, G., Emperador, J.M., Galván, B. (2005). Gray Coding in Evolutionary Multicriteria Optimization: Application in Frame Structural Optimum Design. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds) Evolutionary Multi-Criterion Optimization. EMO 2005. Lecture Notes in Computer Science, vol 3410. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31880-4_40
Download citation
DOI: https://doi.org/10.1007/978-3-540-31880-4_40
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24983-2
Online ISBN: 978-3-540-31880-4
eBook Packages: Computer ScienceComputer Science (R0)