Abstract
In this paper we address the problem of approximating the ’knee’ of a bi-objective optimization problem with stochastic search algorithms. Knees or entire knee-regions are of particular interest since such solutions are often preferred by the decision makers in many applications. Here we propose and investigate two update strategies which can be used in combination with stochastic multi-objective search algorithms (e.g., evolutionary algorithms) and aim for the computation of the knee and the knee-region, respectively. Finally, we demonstrate the applicability of the approach on two examples.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Branke, J., Deb, K., Dierolf, H., Osswald, M.: Finding knees in multi-objective optimization. In: Yao, X., Burke, E.K., Lozano, J.A., Smith, J., Merelo-Guervós, J.J., Bullinaria, J.A., Rowe, J.E., Tiňo, P., Kabán, A., Schwefel, H.-P. (eds.) PPSN VIII 2004. LNCS, vol. 3242, pp. 722–731. Springer, Heidelberg (2004)
Branke, J., Kaussler, T., Schmeck, H.: Guidance in evolutionary multi-objective optimization. Advances in Engineering Software 32, 499–507 (2001)
Das, I.: On characterizing the ”knee” of the Pareto curve based on Normal Boundary Intersection. Structural Optimization 18, 107–115 (1999)
Deb, K.: Multi-objective evolutionary algorithms: introducing bias among pareto-optimal solutions, pp. 263–292 (2003)
di Pierro, F., Khu, S.F., Savic, D.A.: An investigation on preference order ranking scheme for multiobjective evolutionary optimization. IEEE Transactions on Evolutionary Computation 11(1), 17–45 (2007)
Handl, J., Knowles, J.: Exploiting the trade-off: the benefits of multiple objectives in data clustering. In: Proceedings of the Third International Conference on Evolutionary Multicriterion Optimization, pp. 547–560
Ishibuchi, H., Nojima, Y., Narukawa, K., Doi, T.: Incorporation of decision maker’s preference into evolutionary multiobjective optimization algorithms. In: GECCO, pp. 741–742 (2006)
Kukkonen, S., Deb, K.: A fast and effective method for pruning of non-dominated solutions in many-objective problems. In: PPSN, pp. 553–562 (2006)
Mattson, C.A., Mullur, A.A., Messac, A.: Smart Pareto filter: Obtaining a minimal representation of multiobjective design space. Engineering Optimization 36, 721–740 (2004)
Mehnen, J., Trautmann, H.: Integration of expert’s preferences in pareto optimization by desirability function techniques. In: Proceedings of the 5th CIRP International Seminar on Intelligent Computation in Manufacturing Engineering (CIRP ICME 2006) (2006)
Miettinen, K.: Nonlinear Multiobjective Optimization. Kluwer Academic Publishers, Dordrecht (1999)
Rachmawati, L., Srinivasan, D.: A multi-objective evolutionary algorithm with weighted-sum niching for convergence on knee regions. In: Proceedings of the 8th annual conference on Genetic and evolutionary computation, pp. 749–750 (2006)
Rachmawati, L., Srinivasan, D.: A Multi-Objective Genetic Algorithm with Controllable Convergence on Knee Regions. In: IEEE Congress on Evolutionary Computation, CEC 2006, pp. 1916–1923 (2006)
Witting, K., Hessel-von Molo, M.: Private communication (2006)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Schütze, O., Laumanns, M., Coello, C.A.C. (2008). Approximating the Knee of an MOP with Stochastic Search Algorithms. In: Rudolph, G., Jansen, T., Beume, N., Lucas, S., Poloni, C. (eds) Parallel Problem Solving from Nature – PPSN X. PPSN 2008. Lecture Notes in Computer Science, vol 5199. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-87700-4_79
Download citation
DOI: https://doi.org/10.1007/978-3-540-87700-4_79
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-87699-1
Online ISBN: 978-3-540-87700-4
eBook Packages: Computer ScienceComputer Science (R0)