Abstract
The Quasi-Random Weighted Criteria method is proposed for multicriteria design optimization. This quasi-Monte Carlo method features increased computational efficiency and is particularly suitable for exploring alternative design configurations. A quasi-random sequence generates a set of candidate solutions representative of the range of available solutions for each design alternative. The method can be used recursively to produce more detailed Pareto surface descriptions near selected points.
In this paper the method is used to select between vehicle anti-lock brake system (ABS) control algorithm approaches and to optimize the parameters within each. An ABS system is highly nonlinear and therefore the control algorithms draw upon the methods of nonlinear control theory. Stochastic optimization was incorporated to ensure that the ABS system will perform well despite the uncertainties in the vehicle and in the environment. A variety of ABS design studies are presented.
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.
Similar content being viewed by others
References
Albin, S. L.: The Lognormal Distribution for Modeling Quality Data when the Mean is Near Zero, Journal of Quality Technology, Volume 22, No 2, (1990) pp. 105–110.
Athan, T.W: A Quasi-Random Method for Multicriteria Optimization, Doctoral Dissertation, Department of Mechanical Engineering and Applied Mechanics, The University of Michigan, Ann Arbor, 1994.
Birge, J. R., and L. Qi: Subdifferential Convergence in Stochastic Programs,” SIAM J. Optimization, to appear.
Bosch GmbH: Bosch Technische Berichte, Technical and Scientific Report 1, English Edition, Stuttgart 1982.
Dubov, Yu. A., S.I. Travker and V. N. Yakinets: Multicriteria Models of Alternative Generation and Selection, Nauka, Moscow 1986.
Gibson, J. E.: Nonlinear Automatic Control, McGraw-Hill, New York 1963.
Halton, J. H.: On the Efficiency of Certain Quasi-random Sequences of Points in Evaluating Multidimensional Integrals, Numerische Mathematik 2 (1960), pp. 84–90 and corrigenda p. 196.
Hammersley, J. M. and D.C. Handscomb: Monte Carlo Methods, Methuen, London 1964.
Kaplan, W.: Advanced Mathematics for Engineers, p. 785, Addison-Wesley, Reading, Massachusetts 1981.
Lieberman, Elliot R.: Soviet Multi-Objective Mathematical Programming Methods: An Overview, Management Science, Vol. 37, No. 9, September, 1991, pp. 1147–1165.
Meisel, W. S.: “Tradeoff Decisions in Multiple Criteria Decision Making,” In: James L. Cochrane and Milan Zeleny (eds): Multiple Criteria Decision Making, University of South Carolina Press, Columbia, South Carolina 1973, pp. 461–476.
Niederreiter, H.: Random Number Generation and Quasi-Monte Carlo Methods, The Society for Industrial and Applied Mathematics, Philadelphia 1992.
Osyczka, A.: Multicriteria Optimization in Engineering, John Wiley, New York 1984.
Romeijn, H. E., and R. L. Smith: Simulated Annealing for Constrained Global Optimization, Technical Report 9242/A, Econometric Institute, Erasmus University, Rotterdam 1992.
Sazykin, B. V.: “Sequential Decision Making in Multicriteria Optimization of Nonlinear Systems,” In: B. Naumov (ed.) Nonlinear Control Systems, MIR Publishers, Moscow, and CRC Press, Boca Raton, Florida 1990. Original source: [5].
Schittkowski, K.:Design, Implementation, and Test of a Nonlinea Programming Algorithm, 1984 Report, Institut Fuer Informatik, Universitaet Stuttgart 1984. Version 2.3 (April 1987) was the version of the program used.
Schittkowski, K.: NLPQL: A Fortran Subroutine Solving Constrained Nonlinear Programming Problems, Annals of Operations Research, Vol. 5, (1986), pp. 485–500.
Sobol’, I.M. and R. B. Statnikov: Nailuchshie resheniyla — gde ikh iskat’, Seriya matematika, kibernetika, 1, Znanie, Moscow 1982. English translation in Lieberman, E. R.:Soviet Multi-Objective Mathematical Programming Methods: An Overview, Management Science, Vol. 37, No. 9, September, 1991, pp. 1147-1165.
Sobol’, I.M. and R. B. Statnikov: Vybor Optimal’nykh parametrov v zadachakh so mnogimi kriteriyami, Nauka, Moscow 1981. English translation in Lieberman, E. R., 1991: Soviet Multi-Objective Mathematical Programming Methods: An Overview, Management Science, Vol. 37, No. 9, September, 1991, pp. 1147-1165.
Stadler, W., and J. Dauer: “Multicriteria Optimization in Engineering, in: M.P. Kamat (ed.) Structural Optimization: Status and Promise, Progress in Astronautics and Aeronautics, AIAA, Washington, DC, 1993 Chapter 10.
Statnikov, R.B. and I.B. Matusov: Mnogokriterial’noe proektirovanie mashin, Novoe v zhizni nauke, teknike.Ser., Matematika kibernetika, 5 1989. English translation in Lieberman, E. R.:Soviet Multi-Objective Mathematical Programming Methods: An Overview, Management Science, Vol. 37, No. 9, September, 1991, pp. 1147-1165.
Statnikov, Roma B.: Multicriteria Design of Machines, presented at the IXth International Conference on Multiple Criteria Decision Making, Fairfax, VA, August 1990.
Tan, Han-Schue: Adaptive and Robust Controls with Application to Vehicle Traction Control, Ph.D Thesis, University of California, Berkeley 1988.
Tan, H-S, and M. Tomizuka: Discrete-time Controller Design for Robust Vehicle Traction, IEEE Control Systems Magazine, v. 10 n. 3, 1990, pp. 107–113.
UMTRI (University of Michigan Transportation Research Institute): Transportation Data Center Data Set Codebook, NASS GES 1989, Version Dec0390, Number 91-92, Ann Arbor, Michigan 1991.
UMTRI (University of Michigan Transportation Research Institute) .Transportation Data Center Data Set Codebook, NASS GES 1990, Version Aug0891, Number 92-5, Ann Arbor, Michigan 1992.
van der Corput, J. C.: Verteilungsfunktioner, Proc. Kon. Akad. Wet. Amsterdam, 38, (1935) pp. 813–821, 1058-1066.
Wozniakowski, H. Average-case Complexity of Multivariate Integration, Bull. Amer. Math. Soc. (New Series) 24, (1991) pp. 185–194.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Athan, T.W., Papalambros, P.Y. (1997). Multicriteria Optimization of ABS Control Algorithms Using a Quasi-Monte Carlo Method. In: Fandel, G., Gal, T. (eds) Multiple Criteria Decision Making. Lecture Notes in Economics and Mathematical Systems, vol 448. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59132-7_49
Download citation
DOI: https://doi.org/10.1007/978-3-642-59132-7_49
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-62097-6
Online ISBN: 978-3-642-59132-7
eBook Packages: Springer Book Archive