ALGORITHM OF GLOBAL EXTREMUM SEARCH AREA DEFINITION FOR SEVERAL VARIABLES FUNCTION
DOI:
https://doi.org/10.32461/2226-3209.3.2018.171104Keywords:
multicriteria optimization, multiextremal function, global extremum, extremum drift, solution search area, decision support system.Abstract
Abstract: The article is devoted to the problem of global extremum search for several variables function. A
modified algorithm is developed for the search of global extremum function, based on evolutionary calculations and differing by the approach of an area development to create an initial population of agents. They developed the algorithm for the function extremum search area definition, which ultimately performs the decomposition of the research area into subsets. It is suggested to take into account the knowledge of an expert, an agent and the available group agents. Based on the available knowledge, the region is divided into three subsets with different priorities. At that, the possibility of the function extremum drift is taken into account and a separate procedure of a search area definition is implemented, taking into account the retrospective information on the drift of parameters.
Keywords: multicriteria optimization, multiextremal function, global extremum, extremum drift, solution
search area, decision support system.
References
Casado, L.G., I. Garcia and Ya. D. Sergeyev, 2002. Interval Algorithms for Finding the Minimal Root in a Set of Multiextremal One-Dimensional Nondifferentiable Functions. Journal on Scientific Computing, 2(24): 359-376.
Johannes, M.D. and B. Hartke, 2012. Empirical Review of Standard Benchmark Functions Using Evolutionary Global Optimization. Applied Mathematics, 10A(3). Date Views 6.02.2018 http://file.scirp.org/Html/39-7400992_24149.htm.
Evolutionary Algorithms, 2011. Croatia: InTech: 596.
Karpenko A.A., 2012. Population algorithms of global search engine optimization. The review of new and little-known algorithms. Information technologies (applications), 7: 2-32.
Frantsuzova G.A., Shilkova N.Yu., 2016. About the influence of initial conditions on the properties of a single-loop system of extreme regulation based on the localization method. Automation and software engineering, 4 (18): 10-18.
Montendruck, J.M., Durre, H.B., Ebenbauer, C. and Allgower, F., 2015. Extremum Seeking with Drift. IFAC-PapersOnLine. Date Views 6.02.2018 https://doi.org/10.1016/j.ifacol.2015.09.171.
Tang, K., Li, X., Suganthan, P.N., Yang, Z. and Weise, T., 2010. Benchmark Functions for the CEC'2010 Special Session and Competition on Large-Scale Global Optimization. Technical Report, Nature Inspired Computation and Applications Laboratory USTC, China. Date Views 6.02.2018 http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.308.7555&rep=rep1&type=pdf.
Chernorutsky I.G., 2011. Optimizartion methods. Computer technologies. The monograph, pp. 384.
Rouban, A.I., 2007. Method for Global Minimax Optimization in Continuous Space. Advances in Modelling and Analysis, 2(44): 46–65.
Blum, C., Andrea, R. and Michel, S. (eds.), 2008. Hybrid Metaheuristics. An Emerging Approach to Optimization. Springer-Verlag. Berlin, pp:290.
Kureichik V.V., Kureichik V.M., Rodzin S.I., 2012. The theory of evolutionary computations. Monograph, pp. 260.
Lebedev B.K., Lebedev O.B., Lebedev V.B., 2017. Hybridization of swarm intelligence and genetic evolution using the example of location. Software products, systems and algorithms, 4: 1-5.
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