Abstract
Real-world optimization problems often require the consideration of multiple contradicting objectives. These multiobjective problems are even more challenging when facing a limited budget of evaluations due to expensive experiments or simulations. In these cases, a specific class of multiobjective optimization algorithms (MOOA) has to be applied. This paper provides a review of contemporary multiobjective approaches based on the singleobjective meta-model-assisted ’Efficient Global Optimization’ (EGO) procedure and describes their main concepts. Additionally, a new EGO-based MOOA is introduced, which utilizes the \(\mathcal{S}\)-metric or hypervolume contribution to decide which solution is evaluated next. A benchmark on recently proposed test functions is performed allowing a budget of 130 evaluations. The results point out that the maximization of the hypervolume contribution within a real multiobjective optimization is superior to straightforward adaptations of EGO making our new approach capable of approximating the Pareto front of common problems within the allowed budget of evaluations.
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.
References
Zitzler, E.: Evolutionary Algorithms for Multiobjective Optimization: Methods and Applications. Dissertation, Swiss Federal Institute of Technology (ETH), Zürich (1999)
Knowles, J.: ParEGO: A hybrid algorithm with on-line landscape approximation for expensive multiobjective optimization problems. IEEE Trans. Evolutionary Computation 10(1), 50–66 (2006)
Biermann, D., Weinert, K., Wagner, T.: Model-based optimization revisited: Towards real-world processes. In: [29], pp. 2980–2987
Jeong, S., Obayashi, S.: Efficient global optimization (EGO) for multi-objective problem and data mining. In: [30], pp. 2138–22145
Jones, D.R., Schonlau, M., Welch, W.J.: Efficient global optimization of expensive black-box functions. Global Optimization 13(4), 455–492 (1998)
Wang, G.G., Shan, S.: Review of metamodeling techniques in support of engineering design optimization. Journal of Mechanical Design 129(4), 370–380 (2007)
Sacks, J., Welch, W.J., Mitchell, T.J., Wynn, H.P.: Design and analysis of computer experiments. Statistical Science 4(4), 409–423 (1989)
Gonzalez, L.F., Walker, R., Periaux, K.S.,, J.: Multidisciplinary design optimisation of unmanned aerial systems (UAS) using meta model assisted evolutionary algorithms. In: 16th Australasian Fluid Mechanics Conf., pp. 471–474 (2007)
D’Angelo, S., Minisci, E.: Multi-objective evolutionary optimization of subsonic airfoils by kriging approximation and evolution control. In: [30], pp. 1262–1267
Emmerich, M., Naujoks, B.: Metamodel-assisted multiobjective optimisation strategies and their application in airfoil design. In: Parmee, I.C. (ed.) Adaptive Computing in Design and Manufacture VI, pp. 249–260. Springer, Heidelberg (2004)
Naujoks, B., Beume, N., Emmerich, M.: Metamodel-assisted SMS-EMOA applied to airfoil optimisation tasks. In: Schilling, R., et al. (eds.) Evolutionary and Deterministic Methods for Design, Optimization and Control with Applications to Industrial and Societal Problems (EUROGEN 2005) (CD-ROM). FLM (2005)
Emmerich, M., Giannakoglou, K., Naujoks, B.: Single- and multi-objective evolutionary optimization assisted by gaussian random field metamodels. IEEE Trans. Evolutionary Computation 10(4), 421–439 (2006)
Keane, A.J.: Statistical improvement criteria for use in multiobjective design optimization. AIAA 44, 879–891 (2006)
Sasena, M., Papalambros, P., Goovaerts, P.: Exploration of metamodeling sampling criteria for constrained global optimization. Engineering Optimization 34, 263–278 (2002)
Ponweiser, W., Wagner, T.: Clustered multiple generalized expected improvement: A novel infill sampling criterion for surrogate models. In: [29], pp. 3514–3521
Knowles, J.D., Hughes, E.J.: Multiobjective optimization on a budget of 250 evaluations. In: [31], pp. 176–190
Deb, K., Agrawal, S., Pratab, A., Meyarivan, T.: A Fast Elitist Non-Dominated Sorting Genetic Algorithm for Multi-Objective Optimization: NSGA-II. In: Schoenauer, M., et al. (eds.) Proc. 6th Int’l Conf. Parallel Problem Solving from Nature, pp. 849–858. Springer, Heidelberg (2000)
Zitzler, E., Thiele, L.: Multiobjective optimization using evolutionary algorithms – A comparative case study. In: Eiben, A.E., et al. (eds.) PPSN 1998. LNCS, vol. 1498, pp. 292–301. Springer, Heidelberg (1998)
Knowles, J.: Local-Search and Hybrid Evolutionary Algorithms for Pareto Optimization. PhD thesis, Department of Computer Science, University of Reading (2002)
Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C., Fonseca, V.: Performance assessment of multiobjective optimizers: An analysis and review. Trans. Evolutionary Computation 8(2), 117–132 (2003)
Wagner, T., Beume, N., Naujoks, B.: Pareto-, aggregation-, and indicator-based methods in many-objective optimization. In: Obayashi, S., et al. (eds.) Proc. 4th Int’l Conf. Evolutionary Multi-Criterion Optimization, pp. 742–756. Springer, Heidelberg (2007)
Emmerich, M., Beume, N., Naujoks, B.: An emo algorithm using the hypervolume measure as selection criterion. In: [31], pp. 62–76 (2005)
Huang, V.L., Qin, A.K., Deb, K., Zitzler, E., Suganthan, P.N., Liang, J.J., Preuss, M., Huband, S.: Problem definitions for performance assessment of multi-objective optimization algorithms. Technical report, Nanyang Technological University, Singapore (2007)
Zitzler, E., Deb, K., Thiele, L.: Comparison of multiobjective evolutionary algorithms: Empirical results. MIT Evolutionary Computation 8(2), 173–195 (2000)
Okabe, T., Jin, Y., Olhofer, M., Sendhoff, B.: On test functions for evolutionary multi-objective optimization. In: Yao, X., et al. (eds.) PPSN 2004. LNCS, vol. 3242, pp. 792–802. Springer, Heidelberg (2004)
Hansen, N., Ostermeier, A.: Completely derandomized self-adaptation in evolution strategies. Evolutionary Computation 9(2), 159–195 (2001)
Fonseca, C., Paquete, L., Lopez-Ibanez, M.: An improved dimension-sweep algorithm for the hypervolume indicator. In: Congr. Evolutionary Computation, pp. 1157–1163. IEEE, Los Alamitos (2006)
Hansen, M.P., Jaszkiewicz, A.: Evaluating the quality of approximations to the non-dominated set. Technical Report IMM1998-7, Technical University of Denmark (1998)
Michalewicz, Z., et al. (eds.): Proc. Congr. Evolutionary Computation. IEEE, Los Alamitos (2008)
Corne, D., et al. (eds.): Proc. Congr. Evolutionary Computation. IEEE, Los Alamitos (2005)
Coello, C.A.C., et al. (eds.): Proc. 3rd Int’l Conf. Evolutionary Multi-Criterion Optimization. Springer, Heidelberg (2005)
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
Ponweiser, W., Wagner, T., Biermann, D., Vincze, M. (2008). Multiobjective Optimization on a Limited Budget of Evaluations Using Model-Assisted \(\mathcal{S}\)-Metric Selection. 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_78
Download citation
DOI: https://doi.org/10.1007/978-3-540-87700-4_78
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)