Abstract
The hypervolume measure is one of the most frequently applied measures for comparing the results of evolutionary multiobjective optimization algorithms (EMOA). The idea to use this measure for selection is self-evident. A steady-state EMOA will be devised, that combines concepts of non-dominated sorting with a selection operator based on the hypervolume measure. The algorithm computes a well distributed set of solutions with bounded size thereby focussing on interesting regions of the Pareto front(s). By means of standard benchmark problems the algorithm will be compared to other well established EMOA. The results show that our new algorithm achieves good convergence to the Pareto front and outperforms standard methods in the hypervolume covered. We also studied the applicability of the new approach in the important field of design optimization. In order to reduce the number of time consuming precise function evaluations, the algorithm will be supported by approximate function evaluations based on Kriging metamodels. First results on an airfoil redesign problem indicate a good performance of this approach, especially if the computation of a small, bounded number of well-distributed solutions is desired.
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
Deb, K.: Multi-Objective Optimization using Evolutionary Algorithms. John Wiley & Sons, Chichester (2001)
Coello Coello, C.A., Van Veldhuizen, D.A., Lamont, G.B.: Evolutionary Algorithms for Solving Multi-Objective Problems. Kluwer Academic Publishers, New York (2002)
Zitzler, E., Thiele, L.: Multiobjective Optimization Using Evolutionary Algorithms—A Comparative Study. In: Eiben, A.E. (ed.) Parallel Problem Solving from Nature V, Amsterdam, pp. 292–301. Springer, Heidelberg (1998)
Fleischer, M.: The Measure of Pareto Optima. Applications to Multi-objective Metaheuristics. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Deb, K., Thiele, L. (eds.) EMO 2003. LNCS, vol. 2632, pp. 519–533. Springer, Heidelberg (2003)
Knowles, J., Corne, D.: Properties of an Adaptive Archiving Algorithm for Storing Nondominated Vectors. IEEE Transactions on Evolutionary Computation 7, 100–116 (2003)
Knowles, J.D., Corne, D.W., Fleischer, M.: Bounded Archiving using the Lebesgue Measure. In: Proceedings of the, Congress on Evolutionary Computation (CEC’2003), vol. 4, pp. 2490–2497. IEEE Press, Canberra (2003)
Knowles, J., Corne, D.: On Metrics for Comparing Nondominated Sets. In: Congress on Evolutionary Computation (CEC 2002), Piscataway, New Jersey, vol. 1, pp. 711–716. IEEE Service Center (2002)
Zitzler, E.: Evolutionary Algorithms for Multiobjective Optimization: Methods and Applications. PhD thesis, Swiss Federal Institute of Technology (ETH), Zurich, Switzerland (1999)
Deb, K., Mohan, M., Mishra, S.: Towards a Quick Computation of Well-Spread Pareto-Optimal Solutions. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Deb, K., Thiele, L. (eds.) EMO 2003. LNCS, vol. 2632, pp. 222–236. Springer, Heidelberg (2003)
Deb, K., Mohan, M., Mishra, S.: A Fast Multi-objective Evolutionary Algorithm for Finding Well-Spread Pareto-Optimal Solutions. KanGAL report 2003002, Indian Institute of Technology, Kanpur, India (2003)
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A Fast and Elitist Multiobjective Genetic Algorithm: NSGA–II. IEEE Transactions on Evolutionary Computation 6, 182–197 (2002)
Zitzler, E., Deb, K., Thiele, L.: Comparison of Multiobjective Evolutionary Algorithms: Empirical Results. Evolutionary Computation 8(2), 173–195 (2000)
Naujoks, B., Willmes, L., Bäck, T., Haase, W.: Evaluating multi-criteria evolutionary algorithms for airfoil optimisation. In: Guervós, J.J.M., Adamidis, P., Beyer, H.G., Fernández-Villacañas, J.L., Schwefel, H.P. (eds.) Parallel Problem Solving from Nature – PPSN VII, Proc. Seventh Int’l Conf., Granada, Berlin, pp. 841–850. Springer, Heidelberg (2002)
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, London (2004)
Sacks, J., Welch, W.J., Mitchell, W.J., Wynn, H.P.: Design and analysis of computer experiments. Statistical Science 4, 409–435 (1989)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Emmerich, M., Beume, N., Naujoks, B. (2005). An EMO Algorithm Using the Hypervolume Measure as Selection Criterion. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds) Evolutionary Multi-Criterion Optimization. EMO 2005. Lecture Notes in Computer Science, vol 3410. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31880-4_5
Download citation
DOI: https://doi.org/10.1007/978-3-540-31880-4_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24983-2
Online ISBN: 978-3-540-31880-4
eBook Packages: Computer ScienceComputer Science (R0)