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dc.contributor.authorYang, Shengxiangen
dc.contributor.authorGong, Wenyinen
dc.contributor.authorWang, Yongen
dc.contributor.authorCai, Z.en
dc.date.accessioned2017-03-15T13:16:24Z
dc.date.available2017-03-15T13:16:24Z
dc.date.issued2017
dc.identifier.citationGong,W., Wang, Y., Cai, Z. and Yang, S. (2017) A weighted biobjective transformation technique for locating multiple optimal solutions of nonlinear equation systems. IEEE Transactions on Evolutionary Computation, 21 (5), pp. 697-713en
dc.identifier.urihttp://hdl.handle.net/2086/13608
dc.descriptionThe file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.en
dc.description.abstractDue to the fact that a nonlinear equation system may contain multiple optimal solutions, solving nonlinear equation systems is one of the most important challenges in numerical computation. When applying evolutionary algorithms to solve nonlinear equation systems, two issues should be considered: i) how to transform a nonlinear equation system into a kind of optimization problem, and ii) how to develop an optimization algorithm to solve the transformed optimization problem. In this paper, we tackle the first issue by transforming a nonlinear equation system into a weighted biobjective optimization problem. By the above transformation, not only do all the optimal solutions of an original nonlinear equation system become the Pareto optimal solutions of the transformed biobjective optimization problem, but also their images are different points on a linear Pareto front in the objective space. In addition, we suggest an adaptive multiobjective differential evolution, the goal of which is to effectively locate the Pareto optimal solutions of the transformed biobjective optimization problem. Once these solutions are found, the optimal solutions of the original nonlinear equation system can also be obtained correspondingly. By combining the weighted biobjective transformation technique with the adaptive multiobjective differential evolution, we propose a generic framework for the simultaneous locating of multiple optimal solutions of nonlinear equation systems. Comprehensive experiments on 38 nonlinear equation systems with various features have demonstrated that our framework provides very competitive overall performance compared with several state-of-the-art methods.en
dc.language.isoen_USen
dc.publisherIEEE Pressen
dc.subjectNonlinear equation systemsen
dc.subjecttransformation techniqueen
dc.subjectevolutionary multiobjective optimizationen
dc.subjectdifferential evolutionen
dc.titleA weighted biobjective transformation technique for locating multiple optimal solutions of nonlinear equation systemsen
dc.typeArticleen
dc.identifier.doihttps://dx.doi.org/10.1109/TEVC.2017.2670779
dc.researchgroupCentre for Computational Intelligenceen
dc.peerreviewedYesen
dc.funderEPSRC (Engineering and Physical Sciences Research Council)en
dc.funderEU Horizon 2020 Marie Sklodowska-Curie Individual Fellowshipen
dc.funderNational Natural Science Foundation of Chinaen
dc.funderNational Natural Science Foundation of Chinaen
dc.funderNational Natural Science Foundation of Chinaen
dc.projectidEP/K001310/1en
dc.projectid661327en
dc.projectid61673397,en
dc.projectid61573324,en
dc.projectid61375066en
dc.cclicenceCC-BY-NCen
dc.date.acceptance2017-02-15en
dc.exception.reasonopen access articleen
dc.researchinstituteInstitute of Artificial Intelligence (IAI)en


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