{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T08:34:58Z","timestamp":1773390898110,"version":"3.50.1"},"reference-count":85,"publisher":"MDPI AG","issue":"10","license":[{"start":{"date-parts":[[2022,5,18]],"date-time":"2022-05-18T00:00:00Z","timestamp":1652832000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002301","name":"the Estonian Research Council","doi-asserted-by":"publisher","award":["PRG658"],"award-info":[{"award-number":["PRG658"]}],"id":[{"id":"10.13039\/501100002301","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Sensors"],"abstract":"<jats:p>Neuroevolutionary machine learning is an emerging topic in the evolutionary computation field and enables practical modeling solutions for data-driven engineering applications. Contributions of this study to the neuroevolutionary machine learning area are twofold: firstly, this study presents an evolutionary field theorem of search agents and suggests an algorithm for Evolutionary Field Optimization with Geometric Strategies (EFO-GS) on the basis of the evolutionary field theorem. The proposed EFO-GS algorithm benefits from a field-adapted differential crossover mechanism, a field-aware metamutation process to improve the evolutionary search quality. Secondly, the multiplicative neuron model is modified to develop Power-Weighted Multiplicative (PWM) neural models. The modified PWM neuron model involves the power-weighted multiplicative units similar to dendritic branches of biological neurons, and this neuron model can better represent polynomial nonlinearity and they can operate in the real-valued neuron mode, complex-valued neuron mode, and the mixed-mode. In this study, the EFO-GS algorithm is used for the training of the PWM neuron models to perform an efficient neuroevolutionary computation. Authors implement the proposed PWM neural processing with the EFO-GS in an electronic nose application to accurately estimate Nitrogen Oxides (NOx) pollutant concentrations from low-cost multi-sensor array measurements and demonstrate improvements in estimation performance.<\/jats:p>","DOI":"10.3390\/s22103836","type":"journal-article","created":{"date-parts":[[2022,5,18]],"date-time":"2022-05-18T23:14:26Z","timestamp":1652915666000},"page":"3836","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":14,"title":["An Evolutionary Field Theorem: Evolutionary Field Optimization in Training of Power-Weighted Multiplicative Neurons for Nitrogen Oxides-Sensitive Electronic Nose Applications"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5238-6433","authenticated-orcid":false,"given":"Baris Baykant","family":"Alagoz","sequence":"first","affiliation":[{"name":"Department of Computer Engineering, Inonu University, Malatya 44000, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4192-0255","authenticated-orcid":false,"given":"Ozlem Imik","family":"Simsek","sequence":"additional","affiliation":[{"name":"Department of Computer Engineering, Inonu University, Malatya 44000, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6439-7957","authenticated-orcid":false,"given":"Davut","family":"Ari","sequence":"additional","affiliation":[{"name":"Department of Computer Engineering, Bitlis Eren University, Bitlis 13000, Turkey"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aleksei","family":"Tepljakov","sequence":"additional","affiliation":[{"name":"Department of Computer Systems, Tallinn University of Technology, 12618 Tallinn, Estonia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2167-6280","authenticated-orcid":false,"given":"Eduard","family":"Petlenkov","sequence":"additional","affiliation":[{"name":"Department of Computer Systems, Tallinn University of Technology, 12618 Tallinn, Estonia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Hossein","family":"Alimohammadi","sequence":"additional","affiliation":[{"name":"Department of Computer Systems, Tallinn University of Technology, 12618 Tallinn, Estonia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,18]]},"reference":[{"key":"ref_1","unstructured":"Dasgupta, D., and McGregor, D.R. 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