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In [[applied mathematics]], '''multimodal optimization''' deals with [[Mathematical optimization|optimization]] tasks that involve finding all or most of the multiple (at least locally optimal) solutions of a problem, as opposed to a single best solution.
Evolutionary multimodal optimization is a branch of [[Evolutionary computation]], which is closely related to [[Machine learning]]. Wong provides a short survey,<ref>Wong, K. C. (2015), [http://arxiv.org/abs/1508.00457 Evolutionary Multimodal Optimization: A Short Survey] arXiv preprint arXiv:1508.00457</ref> wherein the chapter of Shir<ref>Shir, O.M.: [http://link.springer.com/book/10.1007/978-3-540-92910-9 Niching in Evolutionary Algorithms]</ref> and the book of Preuss<ref>Preuss, Mike (2015), [http://www.springer.com/de/book/9783319074061 Multimodal Optimization by Means of Evolutionary Algorithms]</ref>
== Motivation ==
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De Jong's crowding method, Goldberg’s sharing function approach, Petrowski’s clearing method, restricted mating, maintaining multiple subpopulations are some of the popular approaches that have been proposed by the community. The first two methods are especially well studied, however, they do not perform explicit separation into solutions belonging to different basins of attraction.
The application of multimodal optimization within ES was not explicit for many years, and has been explored only recently.
A niching framework utilizing derandomized ES was introduced by Shir <ref>Shir, O.M. (2008), "Niching in Derandomized Evolution Strategies and its Applications in Quantum Control"</ref>, '''proposing the [[CMA-ES]] as a niching optimizer for the first time'''. The underpinning of that framework was the selection of a peak individual per subpopulation in each generation, followed by its sampling to produce the consecutive dispersion of search-points. The ''biological analogy'' of this machinery is an ''alpha-male'' winning all the imposed competitions and dominating thereafter its ''ecological niche'', which then obtains all the sexual resources therein to generate its offspring.
Recently, an evolutionary [[multiobjective optimization]] (EMO) approach was proposed,<ref>Deb, K., Saha, A. (2010) "Finding Multiple Solutions for Multimodal Optimization Problems Using a Multi-Objective Evolutionary Approach" (GECCO 2010, In press)</ref> in which a suitable second objective is added to the originally single objective multimodal optimization problem, so that the multiple solutions form a '' weak pareto-optimal'' front. Hence, the multimodal optimization problem can be solved for its multiple solutions using an EMO algorithm. Improving upon their work,<ref>Saha, A., Deb, K. (2010) "A Bi-criterion Approach to Multimodal Optimization: Self-adaptive Approach " (Lecture Notes in Computer Science, 2010, Volume 6457/2010, 95–104)</ref> the same authors have made their algorithm self-adaptive, thus eliminating the need for pre-specifying the parameters.
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* S. Das, S. Maity, B-Y Qu, P. N. Suganthan, "Real-parameter evolutionary multimodal optimization — A survey of the state-of-the-art", Vol. 1, No. 2, pp. 71–88, Swarm and Evolutionary Computation, June 2011.
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== External links ==
* [http://tracer.uc3m.es/tws/pso/multimodal.html Multi-modal optimization using Particle Swarm Optimization (PSO)]
* [http://
* [http://ls11-www.cs.uni-dortmund.de/rudolph/multimodal/start Multimodal optimization page at Chair 11, Computer Science, TU Dortmund University]
* [http://www.epitropakis.co.uk/ieee-mmo/ IEEE CIS Task Force on Multi-modal Optimization]
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