Abstract
We present upper bounds on the time and space complexity of finding the global optimum of additively separable functions, a class of functions that has been studied extensively in the evolutionary computation literature. The algorithm presented uses efficient linkage discovery in conjunction with local search. Using our algorithm, the global optimum of an order-k additively separable function defined on strings of length ℓ can be found using O(ℓ ln(ℓ)2k) function evaluations, a bound which is lower than all those that have previously been reported.
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.: The Design of Innovation: Lessons from and for competent genetic algorithms. Kluwer Academic Publishers, Boston (2002)
Goldberg, D.E., Deb, K., Kargupta, H., Harik, G.: Rapid, accurate optimization of difficult problems using fast messy genetic algorithms. In: Proc. Fifth Int’l. Conf. on Genetic Algorithms, pp. 56–64 (1993)
Harik, G.R., Goldberg, D.E.: Learning linkage through probabilistic expression. Computer Methods in Applied Mechanics and Engineering 186(2-4), 295–310 (2000)
Heckendorn, R.B., Wright, A.H.: Efficient linkage discovery by limited probing. In: Proc. 2003 Genetic and Evolutionary Computation Conf., pp. 1003–1014 (2003)
Kauffman, S.A.: The Origins of Order. Oxford University Press, New York (1993)
Larrañaga, P., Lozano, J.A.: Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation. Kluwer Academic Publishers, Boston (2001)
Munemoto, M., Goldberg, D.E.: Linkage identification by non-monotonicity detection for overlapping functions. Evolutionary Computation 7(4), 377–398 (1999)
Pelikan, M.: Bayesian Optimization Algorithm: From Single Level to Hierarchy. Ph.D thesis, University of Illinois Urbana-Champaign (2002)
Pelikan, M., Goldberg, D.E., Cantú-Paz, E.: Linkage problem, distribution estimation, and Bayesian networks. Evolutionary Computation 8(3), 311–340 (2000)
Weinberger, E.D.: NP completeness of Kauffman’s NK model, a tunable rugged fitness landscape. Santa Fe Institute T.R. 96-02-003 (1996)
Streeter, M.J.: http://www.cs.cmu.edu/~matts/gecco_2004/index.html
Wright, H., Heckendorn, R.B.: Personal communication (January 2004)
Wright, H., Thompson, R.K., Zhang, J.: The computational complexity of N-K fitness functions. IEEE Transactions on Evolutionary Computation 4(4), 373–379 (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Streeter, M.J. (2004). Upper Bounds on the Time and Space Complexity of Optimizing Additively Separable Functions. In: Deb, K. (eds) Genetic and Evolutionary Computation – GECCO 2004. GECCO 2004. Lecture Notes in Computer Science, vol 3103. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24855-2_17
Download citation
DOI: https://doi.org/10.1007/978-3-540-24855-2_17
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22343-6
Online ISBN: 978-3-540-24855-2
eBook Packages: Springer Book Archive