Abstract
In this paper, the landscape framework is used to analysis the tracking performance of univariate marginal distribution algorithm (UMDA) in dynamic environment. A set of stochastic differential equations (SDEs) is used to describe the evolutionary dynamics of the algorithm. The corresponding potential function is constructed from these SDEs. Dynamic mean first passage time, which is a new concept, is defined as the time it takes from an optimum to another in a dynamic environment. This concept can be used to measure the tracking property of the algorithm.
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
Jin, Y., Branke, J.: Evolutionary Optimization in Uncertain Environments: A Survey. IEEE Transaction on Evolutionary Computation 9(3), 303–317 (2005)
Cartwright, H., Tuson, A.: Genetic Algorithms and Flowshop Scheduling: Towards the Development of A Real-time Process Control System. Evolutionary Computing, 277–290 (1994)
Grefenstette, J.J.: Genetic Algorithms for Changing Environments. In: Manner, R., Manderick, B. (eds.) Parallel Problem Solving from Nature, pp. 137–144. Elsevier (1992)
Goldberg, D.E., Smith, R.E.: Nonstationary Function Optimization Using Genetic Algorithm with Dominance and Diploidy. In: Proc. of the 2nd Int. Conf. on Genetic Algorithms, pp. 59–68 (1987)
Branke, J., Kaußler, T., Thomas, K., Christian, S., Hartmut, S.: A Multi-population Approach to Dynamic Optimization Problems. In: Adaptive Computing in Design and Manufacturing, pp. 299–308. Springer (2000)
Oppacher, F., Wineberg, M.: The Shifting Balance Genetic Algorithm: Improving the GA in a Dynamic Environment. In: Proceedings of the Genetic and Evolutionary Computation Conference, pp. 504–510 (1999)
Stanhope, S.A., Daida, J.M.: (1+ 1) Genetic Algorithm Fitness Dynamics in a Changing Environment. In: Proceedings of the 1999 Congress on Evolutionary Computation, pp. 1851–1858. IEEE (1999)
Droste, S.: Analysis of the (1+ 1) EA for a Dynamically Changing Objective Function. HT014601767. University Dortmund (2001)
Droste, S.: Analysis of the (1+ 1) EA for a Dynamically Changing Onemax-variant. In: Proceedings of the 2002 Congress on Evolutionary Computation, pp. 55–60. IEEE (2002)
Droste, S.: Analysis of the (1+ 1) EA for a Dynamically Bitwise Changing OneMax. In: Cantú-Paz, E., Foster, J.A., Deb, K., Davis, L., Roy, R., O’Reilly, U.-M., Beyer, H.-G., Kendall, G., Wilson, S.W., Harman, M., Wegener, J., Dasgupta, D., Potter, M.A., Schultz, A., Dowsland, K.A., Jonoska, N., Miller, J., Standish, R.K. (eds.) GECCO 2003. LNCS, vol. 2724, p. 202. Springer, Heidelberg (2003)
Wright, S.: The Roles of Mutation, Inbreeding, Crossbreeding and Selection in Evolution. In: Proc. of the 6th Inter. Congress of Genetics, pp. 356–366 (1932)
Muhlenbein, H., Mahnig, T.: Evolutionary Computation and Wright’s Equation. Theoretical Computer Science 287(1), 145–165 (2002)
Gonzalez, G., Lozano, J.A., Larranaga, P.: Mathematical Modeling of Discrete Estimation of Distribution Algorithms. In: Estimation of Distribution Algorithms: A New Tool for Evolutionary Computation, pp. 147–163. Kluwer Academic (2002)
Yin, L., Ao, P.: Existence and Construction of Dynamical Potential in Nonequilibrium Processes without Detailed Balance. Journal of Physics A: Mathematical and General 39, 8593–8601 (2006)
Ao, P.: Potential in Stochastic Differential Equations: Novel Construction. Journal of Physics A: Mathematical and General 30, L25–L30 (2004)
van Kampen, N.G.: Stochastic Processes in Physics and Chemistry. North-Holland (2007)
Mahnig, T., Mulenbein, H.: Optimal Mutation Rate Using Bayesian Priors for Estimation of Distribution Algorithms. In: Steinhöfel, K. (ed.) SAGA 2001. LNCS, vol. 2264, pp. 460–463. Springer, Heidelberg (2001)
Hisashi, H.: The Effectiveness of Mutation Operation in the Case of Estimation of Distribution Algorithms. Biosystems 87, 243–251 (2007)
Gardiner, C.W.: Handbook of Stochastic Processes. Springer (1991)
Mahnig, T., Muhlenbein, H.: Mathematical Analysis of Optimization Methods Using Search Distributions. In: Proceedings of the 2000 Genetic and Evolutionary Computation Conference, pp. 205–208 (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Long, R., Gong, L., Yuan, B., Ao, P., Ren, Q. (2012). Tracking Property of UMDA in Dynamic Environment by Landscape Framework. In: Huang, T., Zeng, Z., Li, C., Leung, C.S. (eds) Neural Information Processing. ICONIP 2012. Lecture Notes in Computer Science, vol 7665. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-34487-9_43
Download citation
DOI: https://doi.org/10.1007/978-3-642-34487-9_43
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-34486-2
Online ISBN: 978-3-642-34487-9
eBook Packages: Computer ScienceComputer Science (R0)