In the subproject A1, the mathematical basics for self-optimization are developed. Based on models from engineering sciences the research focuses on optimization, optimal control, multiobjective optimization, decision making, and hierarchical optimization. In the third funding period, besides the advancement of algorithms for multiobjective optimization and optimal control, also multiparametric multiobjective optimization problems and dynamical properties of hybrid systems will be investigated.

In the subproject A1 the mathematical basics for realizing the principles of self-optimization for mechatronic systems are developed. Here, the existence of mathematical models is required which are provided from engineering sciences or created in cooperation, and which allow the optimization of the system behavior, its structure and the system parameters.

During the last two funding phases novel numerical, set-oriented methods for multiobjective and hierarchical optimization have been developed, implemented, and tested in real applications that are considered in the subprojects D1, D2 and C3.  For example, the new algorithms were applied to the optimization of a linear drive (time-dependent), a hybrid energy storage system, and an active suspension of a quarter-vehicle. Moreover, optimal control problems, amongst others with multiple objectives, have been considered and the developed algorithms have been used for the optimization of an active guidance module of the RailCab in cooperation with the subproject D1.  In the field of robust planning, methods of intelligent lookahead have been successfully applied to aircraft planning (flight scheduling under disturbances), the energy management of a hybrid energy storage system (subproject D1) and to the resource management of self-optimizing real time operating systems (subproject C2). For distributed systems with selfish agents fast algorithms for the computation of equilibria have been developed which are based on best response dynamics. These algorithms were tested, for example, on the motorway network of North Rhine-Westphalia. They also work in systems with monotonely decreasing latency functions as they would typically occur for RailCabs.

One main research aspect in the third funding phase is the advancement of algorithms for multiobjective optimization and decision making. Here, especially the study of multiparametric multiobjective optimization problems plays an important role. The algorithms for the computation of robust Pareto points are to be extended with respect to robustness against multiple parameters. Possible applications are given by the topics “parameter uncertainties” and “actor failures” in mechatronic systems. Furthermore, the numerical path following techniques will be adapted for a behavior-based detection of incorrect model parameters, which itself will be developed in the subproject A2.

The research in the field of hierarchical optimization will not be continued within the subproject A1, but in C3. Especially, it will be studied in close combination with the hierarchical modeling which is also considered in C3.

Based on results for optimal control with multiple objectives obtained in the second funding phase, in the third funding phase not only problems with multiple objectives that have to be optimized simultaneously are considered, but also problems involving objectives varying over different time periods. We expect that this idea will be better applicable to practical applications because the computational time will be reduced significantly.

A new aspect for the actual funding phase is given by the analysis and optimization of hybrid systems. This is motivated by the fact that self-optimizing systems can often be modeled in a hybrid way. For the analysis of these systems including both continuous and discrete dynamics a set-oriented method will be extended which is already implemented for systems with continuous state space within the software package GAIO. In particular, we consider hybrid systems with complicated, i. e. in general nonlinear, continuous dynamics, and a simple discrete logic. In cooperation with the subproject C2, information about the hybrid system will be made useable for online verification. Applications are in the field of controller switching of self-optimizing systems. Information on the points in time and the duration of switching processes which will be computed by our methods can then be integrated into the hybrid statecharts developed in the subproject B1.

Directors of the Subproject:

 Prof. Dr. rer. nat. Michael Dellnitz

 Jun. Prof. Dr. rer. nat. Sina Ober-Blöbaum

Coordinator of the Subproject:

 Katrin Witting

Publications (since 6/2005)

Begutachtete Veröffentlichungen

Blesken, M.; Rückert, U.; Steenken, D.; Witting, K.; Dellnitz, M.: Multiobjective Optimization for Transistor Sizing of CMOS Logic Standard Cells Using Set-Oriented Numerical Techniques. In: 27th Norchip Conference, Trondheim, Norway, November, 2009

Dellnitz, M.; Witting, K.: Computation of robust Pareto points. In: International Journal of Computing Science and Mathematics (IJCSM) Vol. 2, No. 3, 2009, pp. 243-266

Dell'Aere, A.: Multi-Objective Optimization in Self-Optimizing Systems. In: Proceedings of the IEEE 32nd Annual Conference on Industrial Electronics (IECON), Paris, 2006, pp. 4755-4760

Dumrauf, D.; Gairing, M.: Price of Anarchy for Polynomial Wardrop Games. In: Proceedings of the WINE 2006, 2nd Workshop on Internet and Network Economics. Patra, Greece, 2006

Ehrhoff, J.; Grothklags, S.; Lorenz, U.: Parallelism for Perturbation Management and Robust Plans. In: Cunha, J. C., Medeiros, P. D. (Eds.): Euro-Par 2005 Parallel Processing: 11th International Euro-Par Conference, Lisbon, Portugal, August 30 - September 2, 2005, Proceedings (Lecture Notes in Computer Science), Springer, Volume 3648/2005, Berlin, 2005, pp. 1265-1274

Feldmann, R.; Mavronicolas, M.; Pieris, A.: Facets of the Fully Mixed Nash Equilibrium Conjecture. In: Monien, B., Schroeder, U. (Eds.): Algorithmic Game Theory, First International Symposium, Proceedings of SAGT 2008, April 30-May 2, 2008, Paderborn, Germany (Lecture Notes in Computer Science), Springer, Volume 4997, 2008, pp. 145-157

Flaßkamp, K.; Ober-Blöbaum, S.; Kobilarov, M.: Solving optimal control problems by using inherent dynamical properties. In: PAMM, 2010

Grüne, L.; Junge, O.: Constructing robust feedback laws by set oriented numerical methods. In: Proceedings in Applied Mathematics and Mechanics, Special Issue: GAMM Annual Meeting 2005 - Luxembourg, WILEY-VCH Verlag, Volume 5 (1), Weinheim, 2005, pp. 157-160

Grüne, L.; Junge, O.: Optimal stabilization of hybrid systems using a set oriented approach. In: Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems, Japan, 2006, 2006, pp. 2089-2093

Grüne, L.; Junge, O.: Approximately optimal nonlinear stabilization with preservation of the Lyapunov function property. In: Proceedings of the 46th IEEE Conference on Decision and Control, New Orleans, Louisiana, 2007, 2007, pp. 702-707

Grüne, L.; Junge, O.: Global optimal control of perturbed systems. Journal of Optimization Theory and Applications, Volume 136 (3), Springer Netherlands, 2008

Gairing, M.; Lücking, T.; Mavronicolas, M.; Monien, B.: The Price of Anarchy for Restricted Parallel Links. Parallel Processing Letters (PPL), Volume 16(1), World Scientific Publishing, Singapore, 2006, pp. 117-131

Gairing, M.; Lücking, T.; Mavronicolas, M.; Monien, B.; Rode, M.: Nash Equilibria in Discrete Routing Games with Convex Latency Functions. Journal of Computer and System Sciences, Volume 74, Springer, Berlin, 2008, pp. 1199-1225

Gairing, M.; Monien, B.; Tiemann, K.: Routing (Un-) Splittable Flow in Games with Player-Specific Linear Latency Functions. In: Proceedings of the ICALP 2006, 33rd International Colloquium on Automata, Languages and Programming, July 9 - 16, 2006, Venice, Italy, Springer-Verlag, Venice, Volume 4051, 2006, pp. 501-512

Gairing, M.; Monien, B.; Tiemann, K.: Selfish Routing with Incomplete Information. Theory of Computing Systems, Volume 42 (1), ACM, New York, 2007, pp. 91-130

Gairing, M.; Schoppmann, F.: Total Latency in Singleton Congestion Games. In: Deng, X., Graham, F. C. (Eds.): Internet and Network Economics, Proceedings of the Third International Workshop, WINE 2007, December 12-14, 2007, San Diego, CA, USA (Lecture Notes in Computer Science), Springer, Volume 4858, Berlin, 2007, pp. 381-387

Geisler, J.; Witting, K.; Trächtler, A.; Dellnitz, M.: Multiobjective Optimization of Control Trajectories for the Guidance of a Rail-bound Vehicle. In: 17th IFAC World Congress, July 6-11, 2008, Seoul, Korea, 2008

Geisler, J.; Witting, K.; Trächtler, A.; Dellnitz, M.: Self-Optimization of the Guidance Module of a Rail-bound Vehicle. 7th International Heinz Nixdorf Symposium "Selfoptimizing Mechatronic Systems: Design the Future", February 20-21, 2008, Paderborn, HNI-Verlagsschriftenreihe, 2008, pp. 85-100

Gausemeier, J.; Znamenshchykov, O.; Oberthür, S.; Podlogar, H.: An Approach for Achieving Self-Optimization in Mechatronic Systems supported by Active Patterns. In: Proceedings of the 8th International Conference on Intelligent Systems Design and Applications, 2008

Junge, O.; Marsden, J. E.; Ober-Blöbaum, S.: Discrete Mechanics and Optimal Control. In: Proceedings of the 16th IFAC World Congress, July 3-8, 2005, Praha, Czech Republic, Elsevier Science Ltd, 2005

Klöpper, B.; Podlogar, H.; Gausemeier, J.; Witting, K.: Domain Spanning Search for Solution Patterns for the Conceptual Design of Self-Optimizing Systems. In: Bhowmick, S. S., Küng, J., (Eds.), R. W.: 19th International Conference on Database and Expert Systems Applications (DEXA 2008), September 1-5, 2008, Turin, Springer Verlag, Volume 5181, Berlin, 2008

Knoke, T.; Romaus, C.; Böcker, J.; Dell'Aere, A.; Witting, K.: Energy Management for an Onboard Storage System Based on Multi-Objective Optimization. In: Proceedings of the IEEE 32nd Annual Conference on Industrial Electronics (IECON), Paris, 2006, pp. 4677-4682

Mavronicolas, M.; Milchtaich, I.; Monien, B.; Tiemann, K.: Congestion Games with Player-Specific Constants. In: Proceedings of the MFCS 2007, 32nd International Symposium on Mathematical Foundations of Computer Science. Cesky Krumlov, Czech Republic, 2007, pp. 633-644

Monien, B.; Tiemann, K.: Routing and Scheduling with Incomplete Information. In: Proceedings of the DISC 2007, 21st International Symposium on Distributed Computing, September 24-26, 2007, Lemesos, Cyprus (Lecture Notes in Computer Science), Springer-Verlag, Berlin, 2007, pp. 1-2

Oberthür, S.; Znamenshchykov, A.; Klöpper, B.; Vöcking, H.: Improved Flexible Resource Management by Means of Look-Ahead Scheduling and Bayesian Forecasting. 7th International Heinz Nixdorf Symposium "Self-optimizing Mechatronic Systems: Design the Future", February 20-21, 2008, Paderborn, HNI-Verlagsschriftenreihe, Paderborn, 2008, pp. 361-376

Ober-Blöbaum, S.; Junge, O.; Marsden, J. E.: Discrete mechanics and optimal control: an analysis. In: ESAIM: Control, Optimisation and Calculus of Variations, 2010

Ober-Blöbaum, S.; Leyendecker, S.: A variational approach to multirate integration. In: Proceedings of the 4th European Conference on Computational Mechanics, Paris, Frankreich, 16.-21. Mai, 2010

Ober-Blöbaum, S.; Walther, A.: Computation of derivatives for structure preserving optimal control using automatic differentiation. In: PAMM, 2010

Romaus, C.; Böcker, J.; Witting, K.; Seifried, A., Znamenshchykov, O.: Optimal Energy Management for a Hybrid Energy Storage System Combining Batteries and Double Layer Capacitors. In: Accepted for the 1st IEEE Energy Conversion Congress and Exposition (ECCE2009), San Jose, USA, 2009

Schneider, T.; Schulz, B.; Henke, C.; Witting, K.; Steenken, D.; Böcker, J.: Energy Transfer via Linear Doubly-Fed Motor in Different Operating Modes. In: International Electric Machines and Drives Conference, May 3-6, Miami, Florida, USA, 2009

Schütze, O.; Coello Coello, C. A.; Mostaghim, S.; Talbi, E.-g.; Dellnitz, M.: Hybridizing Evolutionary Strategies with Continuation Methods for Solving Multi-Objective Problems. Engineering Optimization, Volume 40(5), 2008, pp. 383-402

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.: Practical Approaches to Multi-Objective Optimization, Internationales Begegnungs- und Forschungszentrum (IBFI), Schloss Dagstuhl, Germany, Dagstuhl, Germany, 2005

Schütze, O.; Laumanns, M.; Coello Coello, C. A.; Dellnitz, M.; Talbi, E.-g.: Convergence of Stochastic Search Algorithms to Finite Size Pareto Set Approximations. Journal of Global Optimization, Volume 41, Kluwer Academic Publishers, 2007, pp. 559-577

Schütze, O.; Vasile, M.; Junge, O.; Dellnitz, M.; Izzo, D.: Designing Optimal Low Thrust Gravity Assist Trajectories Using Space Pruning and a Multi-Objective Approach. Engineering Optimization 41:2, 2009, pp. 155-181

Witting, K.; Schulz, B.; Dellnitz, M.; Böcker, J.; Fröhleke, N.: A new approach for online multiobjective optimization of mechatronic systems. International Journal on Software Tools for Technology Transfer STTT, Volume 10(3), 2008, pp. 223-231

Dissertationen

Dell'Aere, A.: Numerical Methods for the Solution of Bi-Level Multi-Objective Optimization Problems. Dissertation, Fakultät für Elektrotechnik, Informatik und Mathematik, Universität Paderborn, 2008

Gairing, M.: Selfish routing in networks. Dissertation, Fakultät für Elektrotechnik, Informatik und Mathematik, Universität Paderborn, 2006

Meyerhenke, H.: Disturbed Diffusive Schemes for Solving Partitioning Problems on Graphs. Dissertation, Fakultät für Elektrotechnik, Informatik und Mathematik, Universität Paderborn, 2008

Ober-Blöbaum, Sina: Discrete mechanics and optimal control. Dissertation, Fakultät für Elektrotechnik, Informatik und Mathematik, Universität Paderborn, 2008