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Licensed Unlicensed Requires Authentication Published by De Gruyter September 4, 2020

Differential evolution algorithm of solving an inverse problem for the spatial Solow mathematical model

  • Sergey Kabanikhin , Olga Krivorotko , Zholaman Bektemessov EMAIL logo , Maktagali Bektemessov and Shuhua Zhang


The differential evolution algorithm is applied to solve the optimization problem to reconstruct the production function (inverse problem) for the spatial Solow mathematical model using additional measurements of the gross domestic product for the fixed points. Since the inverse problem is ill-posed the regularized differential evolution is applied. For getting the optimized solution of the inverse problem the differential evolution algorithm is paralleled to 32 kernels. Numerical results for different technological levels and errors in measured data are presented and discussed.

MSC 2010: 65M32

Award Identifier / Grant number: 18-71-10044

Award Identifier / Grant number: AP05134121

Funding statement: This work is supported by the Russian Science Foundation (grant No. 18-71-10044), i.e. numerical investigation of spatial Solow mathematical model, and by the Ministry of Education and Science of the Republic of Kazakhstan (grant No. AP05134121), i.e. inverse problem statement (Section 2).


The authors thank to Professor Daniyar Nurseitov for problem statement and fruitfull discussions for concerning Solow mathematical model and thank to Dr. Igor Chernykh for help in parallel realization of DE algorithm.


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Received: 2020-08-18
Accepted: 2020-08-20
Published Online: 2020-09-04
Published in Print: 2020-11-01

© 2020 Walter de Gruyter GmbH, Berlin/Boston

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