Abstract
In most real world optimization problems several optimization goals have to be considered in parallel. For this reason, there has been a growing interest in Multi-Objective Optimization (MOO) in the past years. Several alternative approaches have been proposed to cope with the occurring problems, e.g. how to compare and rank the different elements. The available techniques produce very good results, but they have mainly been studied for problems of “low dimension”, i.e. with less than 10 optimization objectives.
In this paper we study MOO for high dimensional spaces. We first review existing techniques and discuss them in our context. The pros and cons are pointed out. A new relation called ε-Preferred is presented that extends existing approaches and clearly outperforms these for high dimensions. Experimental results are presented for a very complex industrial scheduling problem, i.e. a utilization planning problem for a hospital. This problem is also well known as nurse rostering, and in our application has more than 20 optimization targets. It is solved using an evolutionary approach. The new algorithms based on relation ε-Preferred do not only yield better results regarding quality, but also enhances the robustness significantly.
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
Goldberg, D.E.: Genetic Algorithms in Search, Optimization & Machine Learning. Addison-Wesley, Reading (1989)
Zitzler, E., Thiele, L.: Multiobjective evolutionary algorithms: A comparative case study and the strength pareto approach. IEEE Trans. on Evolutionary Comp. 3(4), 257–271 (1999)
Deb, K.: Multi-objective Optimization using Evolutionary Algorithms. John Wiley and Sons, New York (2001)
Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable test problems for evolutionary multi-objective optimization. Technical Report 112, Computer Engineering and Networks Laboratory (TIK), Swiss Federal Institute of Technology (ETH), Zurich, Switzerland (2001)
Khare, V.R., Yao, X., Deb, K.: Performance scaling of multi-objective evolutionary algorithms. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Deb, K., Thiele, L. (eds.) EMO 2003. LNCS, vol. 2632, pp. 376–390. Springer, Heidelberg (2003)
Deb, K., Sundar, S.: Reference point based multi-objective optimization using evolutionary algorithms. In: GECCO ’06: Proceedings of the 8th Annual Conference on Genetic and Evolutionary Computation, pp. 635–642 (2006)
Deb, K., Chaudhuri, S., Miettinen, K.: Towards estimating nadir objective vector using evolutionary approaches. In: GECCO ’06: Proceedings of the 8th Annual Conference on Genetic and Evolutionary Computation, pp. 643–650 (2006)
Drechsler, N., Drechsler, R., Becker, B.: Multi-objective optimisation based on relation favour. In: Zitzler, E., Deb, K., Thiele, L., Coello Coello, C.A., Corne, D.W. (eds.) EMO 2001. LNCS, vol. 1993, pp. 154–166. Springer, Heidelberg (2001)
Schmiedle, F., Drechsler, N., Große, D., Drechsler, R.: Priorities in multi-objective optimization for genetic programming. In: GECCO ’01: Proceedings of the 6th Annual Conference on Genetic and Evolutionary Computation, pp. 129–136 (2001), http://ira.informatik.uni-freiburg.de/papers/Year_2001/SDGD_2001.ps.gz
Burke, E.K., De Causmaecker, P., Berghe, G.V., Landeghem, H.V.: The state of the art of nurse rostering. Journal of Scheduling 7, 441–499 (2004)
Keijzer, M., Merelo, J.J., Romero, G., Schoenhauer, M.: Evolving objects: a general purpose evolutionary computation library. In: Artificial Evolution, pp. 321–244 (2001)
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. on Evolutionary Comp. 6, 182–197 (2000)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Sülflow, A., Drechsler, N., Drechsler, R. (2007). Robust Multi-Objective Optimization in High Dimensional Spaces. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds) Evolutionary Multi-Criterion Optimization. EMO 2007. Lecture Notes in Computer Science, vol 4403. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70928-2_54
Download citation
DOI: https://doi.org/10.1007/978-3-540-70928-2_54
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-70927-5
Online ISBN: 978-3-540-70928-2
eBook Packages: Computer ScienceComputer Science (R0)