Evolutionary multimodal optimization: Difference between revisions

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== Background ==
 
Classical techniques of optimization would need multiple restart points and multiple runs in the hope that a different solution may be discovered every run, with no guarantee however. [[Evolutionary algorithm]]s (EAs) due to their population based approach, provide a natural advantage over classical optimization techniques. They maintain a population of possible solutions, which are processed every generation, and if the multiple solutions can be preserved over all these generations, then at termination of the algorithm we will have multiple good solutions, rather than only the best solution. Note that this is against the natural tendency of classical optimization techniques, which will always converge to the best solution, or a sub-optimal solution (in a rugged, “badly behaving” function).''' Finding''' and '''maintenance''' of multiple solutions is wherein lies the challenge of using EAs for multi-modal optimization. '''Niching'''<ref>Mahfoud, S. W. (1995), "[http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.30.8270&rep=rep1&type=pdf Niching methods for genetic algorithms]"</ref> is a generic term referred to as the technique of finding and preserving multiple stable ''niches'', or favorable parts of the solution space possibly around multiple solutions, so as to prevent convergence to a single solution.
 
The field of [[Evolutionary algorithm]]s encompasses [[genetic algorithm]]s (GAs), [[evolution strategy]] (ES), [[differential evolution]] (DE), [[particle swarm optimization]] (PSO), and other methods. Attempts have been made to solve multi-modal optimization in all these realms and most, if not all the various methods implement niching in some form or the other.
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* D. Goldberg and J. Richardson. (1987) "[https://books.google.com/books?hl=en&lr=&id=MYJ_AAAAQBAJ&oi=fnd&pg=PA41&dq=%22Genetic+algorithms+with+sharing+for+multimodal+function+optimization%22&ots=XwsKxp3zHA&sig=5xS0qPl-83-h3FlY2vGoPN0kmK8#v=onepage&q=%22Genetic%20algorithms%20with%20sharing%20for%20multimodal%20function%20optimization%22&f=false Genetic algorithms with sharing for multimodal function optimization]". In Proceedings of the Second International Conference on Genetic Algorithms on Genetic algorithms and their application table of contents, pages 41–49. L. Erlbaum Associates Inc. Hillsdale, NJ, USA, 1987.
* A. Petrowski. (1996) "A clearing procedure as a niching method for genetic algorithms". In Proceedings of the 1996 IEEE International Conference on Evolutionary Computation, pages 798–803. Citeseer, 1996.
* Deb, K., (2001) "Multi-objective Optimization using Evolutionary Algorithms", Wiley ([https://books.google.com/books?id=OSTn4GSy2uQC&printsec=frontcover&dq=multi+objective+optimization&source=bl&ots=tCmpqyNlj0&sig=r00IYlDnjaRVU94DvotX-I5mVCI&hl=en&ei=fHnNS4K5IMuLkAWJ8OgS&sa=X&oi=book_result&ct=result&resnum=8&ved=0CD0Q6AEwBw#v=onepage&q&f=false Google Books)]
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* Ronkkonen, J., (2009). [https://web.archive.org/web/20141225150016/https://oa.doria.fi/bitstream/handle/10024/50498/isbn%209789522148520.pdf Continuous Multimodal Global Optimization with Differential Evolution Based Methods]
* Wong, K. C., (2009). [http://portal.acm.org/citation.cfm?id=1570027 An evolutionary algorithm with species-specific explosion for multimodal optimization. GECCO 2009: 923–930]
* J. Barrera and C. A. C. Coello. "[http://delta.cs.cinvestav.mx/~ccoello/EMOO/barrera09a.pdf.gz A Review of Particle Swarm Optimization Methods used for Multimodal Optimization]", pages 9–37. Springer, Berlin, November 2009.
* Wong, K. C., (2010). [http://www.springerlink.com/content/jn23t10366778017/ Effect of Spatial Locality on an Evolutionary Algorithm for Multimodal Optimization. EvoApplications (1) 2010: 481–490]
* Deb, K., Saha, A. (2010) [http://portal.acm.org/citation.cfm?id=1830483.1830568 Finding Multiple Solutions for Multimodal Optimization Problems Using a Multi-Objective Evolutionary Approach. GECCO 2010: 447–454]