{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T18:02:30Z","timestamp":1775066550695,"version":"3.50.1"},"reference-count":20,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2017,12,4]],"date-time":"2017-12-04T00:00:00Z","timestamp":1512345600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>The chaos-based optimization algorithm (COA) is a method to optimize possibly nonlinear complex functions of several variables by chaos search. The main innovation behind the chaos-based optimization algorithm is to generate chaotic trajectories by means of nonlinear, discrete-time dynamical systems to explore the search space while looking for the global minimum of a complex criterion function. The aim of the present research is to investigate the numerical properties of the COA, both on complex optimization test-functions from the literature and on a real-world problem, to contribute to the understanding of its global-search features. In addition, the present research suggests a refinement of the original COA algorithm to improve its optimization performances. In particular, the real-world optimization problem tackled within the paper is the estimation of six electro-mechanical parameters of a model of a direct-current (DC) electrical motor. A large number of test results prove that the algorithm achieves an excellent numerical precision at a little expense in the computational complexity, which appears as extremely limited, compared to the complexity of other benchmark optimization algorithms, namely, the genetic algorithm and the simulated annealing algorithm.<\/jats:p>","DOI":"10.3390\/e19120665","type":"journal-article","created":{"date-parts":[[2017,12,4]],"date-time":"2017-12-04T11:16:38Z","timestamp":1512386198000},"page":"665","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["An Improved Chaotic Optimization Algorithm Applied to a DC Electrical Motor Modeling"],"prefix":"10.3390","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5964-7464","authenticated-orcid":false,"given":"Simone","family":"Fiori","sequence":"first","affiliation":[{"name":"Dipartimento di Ingegneria dell\u2019Informazione, Universit\u00e0 Politecnica delle Marche, 60131 Ancona, Italy"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Ruben","family":"Di Filippo","sequence":"additional","affiliation":[{"name":"Master\u2019s Program Systems and Control, Technische Universiteit Eindhoven, 5612 Eindhoven, The Netherlands"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2017,12,4]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"96","DOI":"10.1145\/219717.219797","article-title":"Principles and applications of chaotic systems","volume":"38","author":"Ditto","year":"1995","journal-title":"Commun. ACM"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Hagmair, S., Bachler, M., Braunisch, M.C., Lorenz, G., Schmaderer, C., Hasenau, A.-L., von St\u00fclpnagel, L., Bauer, A., Rizas, K.D., and Wassertheurer, S. (2017). Challenging recently published parameter sets for entropy measures in risk prediction for end-stage renal disease patients. Entropy, 19.","DOI":"10.3390\/e19110582"},{"key":"ref_3","unstructured":"Ott, E., Sauer, T., and Yorke, J.A. (1994). Coping with Chaos\u2014Analysis of Chaotic Data and Exploitation of Chaotic Systems. Wiley Series in Nonlinear Science, John Wiley. [1st ed.]."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"821","DOI":"10.1103\/PhysRevLett.64.821","article-title":"Synchronization in chaotic systems","volume":"64","author":"Pecora","year":"1990","journal-title":"Phys. Rev. Lett."},{"key":"ref_5","unstructured":"Rubinstein, R.Y., and Kroese, D.P. (2004). The Cross-Entropy Method\u2014A Unified Approach to Combinatorial Optimization, Monte-Carlo Simulation and Machine Learning, Springer."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"409","DOI":"10.1080\/019697298125678","article-title":"Optimizing complex functions by chaos search","volume":"29","author":"Li","year":"1998","journal-title":"Cybern. Syst. Int. J."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"1366","DOI":"10.1016\/j.chaos.2006.04.057","article-title":"On the efficiency of chaos optimization algorithms for global optimization","volume":"34","author":"Yang","year":"2007","journal-title":"Chaos Solitons Fractals"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1229","DOI":"10.1016\/j.cnsns.2013.08.017","article-title":"Chaos optimization algorithms based on chaotic maps with different probability distribution and search speed for global optimization","volume":"19","author":"Yang","year":"2014","journal-title":"Commun. Nonlinear Sci. Numer. Simul."},{"key":"ref_9","unstructured":"Brachem, C. (2009). Implementation and Test of a Simulated Annealing Algorithm in the Bayesian Analysis Toolkit (BAT). [Bachelor\u2019s Thesis, Georg-August-Universit\u00e4t G\u00f6ttingen]."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"31","DOI":"10.1002\/cplx.6130010108","article-title":"Genetic algorithms: An overview","volume":"1","author":"Mitchell","year":"1995","journal-title":"Complexity"},{"key":"ref_11","unstructured":"Goldberg, D.E. (1989). Genetic Algorithms in Search, Optimization & Machine Learning, Addison-Wesley."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"1624","DOI":"10.3390\/e15051624","article-title":"Genetic algorithm-based identification of fractional-order systems","volume":"15","author":"Zhou","year":"2013","journal-title":"Entropy"},{"key":"ref_13","doi-asserted-by":"crossref","unstructured":"Zang, W., Zhang, W., Zhang, W., and Liu, X. (2017). A kernel-based intuitionistic fuzzy C-means clustering using a DNA genetic algorithm for magnetic resonance image segmentation. Entropy, 19.","DOI":"10.3390\/e19110578"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"671","DOI":"10.1126\/science.220.4598.671","article-title":"Optimization by simulated annealing","volume":"220","author":"Kirkpatrick","year":"1983","journal-title":"Science"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"8031","DOI":"10.3390\/e17127859","article-title":"An information-based approach to precision analysis of indoor WLAN localization using location fingerprint","volume":"17","author":"Zhou","year":"2015","journal-title":"Entropy"},{"key":"ref_16","first-page":"30","article-title":"DC motor parameter identification using speed step responses","volume":"2012","author":"Wu","year":"2012","journal-title":"Model. Simul. Eng."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"647","DOI":"10.1016\/S0967-0661(01)00024-7","article-title":"Least squares and genetic algorithms for parameter identification of induction motors","volume":"9","author":"Alonge","year":"2001","journal-title":"Control Eng. Pract."},{"key":"ref_18","unstructured":"Razik, H., and Rezzoug, A. (2000, January 28\u201330). Identification of electrical parameters of an induction motor, a comparison between R.L.S. and genetic algorithm. Proceedings of the International Conference on Electrical Machines (ICEM 2000), Espoo, Finland."},{"key":"ref_19","first-page":"69","article-title":"Softcomputing identification techniques of asynchronous machine parameters: Evolutionary strategy and chemotaxis algorithm","volume":"17","year":"2009","journal-title":"Turk. J. Electr. Eng. Comput. Sci."},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"5711","DOI":"10.3390\/e17085711","article-title":"Fruit classification by wavelet-entropy and feedforward neural network trained by fitness-scaled chaotic ABC and biogeography-based optimization","volume":"17","author":"Wang","year":"2015","journal-title":"Entropy"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/19\/12\/665\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T18:52:32Z","timestamp":1760208752000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/19\/12\/665"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2017,12,4]]},"references-count":20,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2017,12]]}},"alternative-id":["e19120665"],"URL":"https:\/\/doi.org\/10.3390\/e19120665","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2017,12,4]]}}}