A new approach for online multiobjective optimization of mechatronic systems

  • Katrin WittingEmail author
  • Bernd Schulz
  • Michael Dellnitz
  • Joachim Böcker
  • Norbert Fröhleke
Special Section SFB 614


We present a new concept for online multiobjective optimization and its application to the optimization of the operating point assignment for a doubly-fed linear motor. This problem leads to a time-dependent multiobjective optimization problem. In contrast to classical optimization where the aim is to find the (global) minimum of a single function, we want to simultaneously minimize k objective functions. The solution to this problem is given by the set of optimal compromises, the so-called Pareto set. In the case of the linear motor, there are two conflicting aims which both have to be maximized: the degree of efficiency and the inverter utilization factor. The objective functions depend on velocity, force and power, which can be modeled as time-dependent parameters. For a fixed point of time, the entire corresponding Pareto set can be computed by means of a recently developed set-oriented numerical method. An online computation of the time-dependent Pareto sets is not possible, because the computation itself is too complex. Therefore, we combine the computation of the Pareto set with numerical path following techniques. Under certain smoothness assumptions the set of Pareto points can be characterized as the set of zeros of a certain function. Here, path following allows to track the evolution of a given solution point through time.


Multiobjective online optimization Time-dependent Pareto sets Decision making Numerical path following methods Linear motor Operating point assignment Self-optimization 


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  1. 1.
    Allgower, E.L., Georg, K.: Numerical Continuation Methods. Springer, Heidelberg (1990)zbMATHGoogle Scholar
  2. 2.
    Dellnitz, M., Schütze, O., Hestermeyer, T.: Covering Pareto sets by multilevel subdivision techniques. J. Optim. Theory Appl. 124, 113–155 (2005)CrossRefMathSciNetzbMATHGoogle Scholar
  3. 3.
    Deuflhard, P., Hohmann, A.: Numerical Analysis in Modern Scientific Computing. Springer, Heidelberg (2003)zbMATHGoogle Scholar
  4. 4.
    Ettingshausen, C., Hestermeyer, T., Otto S.: Aktive Spurführung und Lenkung von Schienenfahrzeugen. 6. Magdeburger Maschinenbautage; Magdeburg (2003)Google Scholar
  5. 5.
    Frank, U., Giese, H., Klein, F., Oberschelp, O., Schmidt, A., Schulz, B., Vöcking, H., Witting, K.: Selbstoptimierende Systeme des Maschinenbaus—Definitionen und Konzepte. Number Band 155 in HNI-Verlagsschriftenreihe 1st edn. Bonifatius GmbH, Paderborn, Germany, (2004)Google Scholar
  6. 6.
    Hestermeyer, T., Schlautmann, P., Ettingshausen, C.: Active suspension system for railway vehicles—system design and kinematics. In: 2nd IFAC Conference on Mechatronic Systems, Berkely (2002)Google Scholar
  7. 7.
    Hillermeier, C.: Nonlinear Multiobjective Optimization—A Generalized Homotopy Approach. Birkhäuser (2001)Google Scholar
  8. 8.
    Ortega, J.M., Rheinboldt, W.C.: Iterative Solution of Nonlinear Equations in several variables. Academic Press, Inc., New York (1970)zbMATHGoogle Scholar
  9. 9.
    Kuhn, H., Tucker, A.: Nonlinear programming. In: Neumann, J. (ed.) Proc. Berkeley Symp. Math. Statist. Probability, pp. 481–492 (1951)Google Scholar
  10. 10.
    Miettinen, K.: Nonlinear Multiobjective Optimization. Kluwer, Dordrecht (1999)zbMATHGoogle Scholar
  11. 11.
    Web-Page of the “Collaborative Research Center 614”.
  12. 12.
    Web-Page of the “Neue Bahntechnik Paderborn”-Project.
  13. 13.
    Pottharst, A.: Energieversorgung und Leittechnik einer Anlage mit Linearmotor getriebenen Bahnfahrzeugen. Dissertation, University of Paderborn, Powerelectronic and Electrical Drives, (2005)Google Scholar
  14. 14.
    Pottharst, A., Baptist, K., Schütze, O., Böcker, J., Fröhlecke, N., Dellnitz, M.: Operating point assignment of a linear motor driven vehicle using multiobjective optimization methods. In: Proceedings of the 11th International Conference EPE-PEMC 2004, Riga, Latvia, 09/2004Google Scholar
  15. 15.
    Schäffler, S., Schultz, R., Weinzierl, K.: A stochastic method for the solution of unconstrained vector optimization problems. J. Opt. Th. Appl. 114(1), 209–222 (2002)CrossRefzbMATHGoogle Scholar
  16. 16.
    Schütze, O.: A new data structure for the nondominance problem in multi-objective optimization. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Deb, K., Thiele, L. (eds.) Evolutionary Multi-Criterion Optimization (EMO 03), vol. 2. Springer, Heidelberg (2003)Google Scholar
  17. 17.
    Schütze, O.: Set Oriented Methods for Global Optimization. PhD Thesis, University of Paderborn (2004)Google Scholar
  18. 18.
    Schütze, O., Dell’Aere, A., Dellnitz, M.: On continuation methods for the numerical treatment of multi-objective optimization problems. In: Branke, J., Deb, K., Miettinen, K., Steuer, R.E. (eds.) Practical Approaches to Multi-Objective Optimization, number 04461 in Dagstuhl Seminar Proceedings. Internationales Begegnungs- und Forschungszentrum (IBFI), Schloss Dagstuhl, Germany, 2005. <>
  19. 19.
    Schütze, O., Dell’Aere, A., Dellnitz, M.: A new method for the computation of implicitly defined manifolds with special attention to multi-objective optimization (in progress, 2006)Google Scholar
  20. 20.
    Schütze, O., Mostaghim, S., Dellnitz, M., Teich, J.: Covering Pareto sets by multilevel evolutionary subdivision techniques. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Deb, K., Thiele, L. (eds.) Evolutionary Multi-Criterion Optimization, Lecture Notes in Computer Science (2003)Google Scholar
  21. 21.
    Yang, B., Henke, M., Grotstollen, H.: Pitch analysis and control design for the linear motor of a railway carriage. In: IEEE Industrial Applications Society Annual Meeting (IAS), Chicago, USA, pp. 2360–2365, (2001)Google Scholar

Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Katrin Witting
    • 1
    Email author
  • Bernd Schulz
    • 1
  • Michael Dellnitz
    • 1
  • Joachim Böcker
    • 1
  • Norbert Fröhleke
    • 1
  1. 1.Faculty of Computer Science, Electrical Engineering and MathematicsUniversity of PaderbornPaderbornGermany

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