Abstract
We propose a multi-objective generalisation for the well known Counting Ones problem, called the Multi-objective Counting Ones (MOCO) function. It is shown that the problem has four qualitative different regions. We have constructed a convergence time model for the Simple Evolutionary Multi-objective Optimiser (SEMO) algorithm. The analysis gives insight in the convergence behaviour in each region of the MOCO problem. The model predicts a ℓ2 ln ℓ running time, which is confirmed by the experimental runs.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
P.A.N Bosman and D. Thierens. The balance between proximity and diversity in multi-objective evolutionary algorithms. IEEE Transactions on Evolutionary Computation, 2003. Accepted for publication.
K. Deb. Multi-objective optimization using evolutionary algorithms. Wiley, Chichester, UK, 2001.
S. Droste, T. Jansen, and I. Wegener. On the analysis of the (1+1) evolutionary algorithm for separable functions with Boolean inputs. Evolutionary Computation, 6(2):185–196, 1998.
S. Droste, T. Jansen, and I. Wegener. On the analysis of the (1+1) evolutionary algorithm. Theoretical Computer Science, 276(1–2):51–81, 2002.
T. Hanne. On the convergence of multiobjective evolutioanry algorithms. European Journal of Operations Research, 117(3):553–564, 1999.
T. Hanne. Global multiobjective optimization with evolutionary algorithms: selection mechanisms and mutation control. In Proceedings of the International Conference on Multi-Criterion Optimization, pages 197–212. Springer, 2001.
M. Laumanns, L. Thiele, K. Deb, and E. Zitzler. Combining convergence and diversity in evolutionary computation. Evolutionary Computation, 10(3):263–282, 2002.
M. Laumanns, L. Thiele, E. Zitzler, E. Welzl, and K. Deb. Running time analysis of mulit-objective evolutionary algorithms on a simple discrete optimization problem. In J.J. Merelo Guervós et al., editor, Proceedings of the 7th International Conference on Parallel Problem Solving from Nature, pages 44–53. Springer, 2002.
H. Muehlenbein. How genetic algorithms really work: Mutation and hill-climbing. In R. Manner et B. Manderick, editor, Proceedings of the International Conference on Parallel Problem Solving from Nature, pages 15–26. North-Holland, 1992.
H. Muhlenbein and D. Schlierkamp-Voosen. Predictive models for the breeder genetic algorithm: I. continuous parameter optimization. Evolutionary Computation, 1(1):25–49, 1993.
G. Rudolph. On a multi-objective evolutionary algorithm and its convergence to the Pareto set. In Proceedings of the International Conference on Evolutionary Computation, pages 511–516. IEEE Press, 1998.
G. Rudolph and A. Agapie. Convergence properties of some multi-objective evolutionary algorithms. In Proceedings of the International Congress on Evolutionary Computation, pages 1010–1016. IEEE Press, 2000.
D. Thierens and D.E. Goldberg. Convergence models of genetic algorithm selection schemes. In International Conference on Evolutionary Computation: The Third Conference on Parallel Problem Solving from Nature, pages 119–129. Springer-Verlag, 1994.
D. Thierens, D.E. Goldberg, and A.G. Pereira. Domino convergence, drift, and the temporal-salience structure of problems. In Proceedings of the 1998 IEEE World Congress on Computational Intelligence, pages 535–540. IEEE Press, 1998.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Thierens, D. (2003). Convergence Time Analysis for the Multi-objective Counting Ones Problem. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Thiele, L., Deb, K. (eds) Evolutionary Multi-Criterion Optimization. EMO 2003. Lecture Notes in Computer Science, vol 2632. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36970-8_25
Download citation
DOI: https://doi.org/10.1007/3-540-36970-8_25
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-01869-8
Online ISBN: 978-3-540-36970-7
eBook Packages: Springer Book Archive