A modified teaching–learning-based optimization for optimal control of Volterra integral systems
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This study aimed to utilize a novel modified approach based on teaching–learning-based optimization (MTLBO), to achieve an approximate solution of optimal control problem governed by nonlinear Volterra integro-differential systems. The scheme was based upon Chebyshev wavelet and its derivative operational matrix, which eventually led to a nonlinear programming problem (NLP). The resulted NLP was solved by the MTLBO. The novel algorithm used a heuristic mechanism to intensify learning on the best students in learner phase. The new strategy was applied to improve learners’ knowledge and to structure the MTLBO. The applicability and efficiency of the MTLBO were shown for three numerical examples. The proposed algorithm was compared with the traditional TLBO algorithm and the Legendre wavelets and collocation method in the literature. The experimental results showed that the proposed MTLBO not only obtained the high-quality solutions with respect to the absolute errors but also provided results with the high speed of convergence.
KeywordsTeaching–learning-based optimization Modified learner phase Optimal control Nonlinear Volterra integro-differential equation Collocation method Chebyshev wavelet
The first author acknowledges Gonbad Kavous University, the second author appreciates the Young Researchers and Elite Club, Najafabad Branch, Islamic Azad University, Najafabad, and the third author thanks K.N. Toosi University of Technology for supporting this research work.
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Conflict of interest
The authors declare that there is no conflict of interests regarding the publication of this paper.
- Adibi H, Assari P (2010) Chebyshev wavelet method for numerical solution of Fredholm integral equations of the first kind. Math Probl Eng 2010, Article ID 138408Google Scholar
- Maleknejad K, Ebrahimzadeh A (2014) Optimal control of Volterra integro-differential systems based on Legendre wavelets and collocation method. Int J Math Comput Sci 1(7):50–54Google Scholar
- Maleknejad, K., Nosrati Sahlan, M., Ebrahimizadeh, A.: Wavelet Galerkin method for the solution of nonlinear Klein-Gordon equations by using B-spline wavelets. In: The international conference on scientific computing, Las Vegas, Nevada (2012)Google Scholar
- Rao RV, Patel V (2012) An elitist teaching learning-based optimization algorithm for solving complex constrained optimization problems. Int J Ind Eng Comput 3(4):535–560Google Scholar
- Rao RV, Patel V (2013) Comparative performance of an elitist teaching learning based optimization algorithm for solving unconstrained optimization problems. Int J Ind Eng Comput 4(1):29–50Google Scholar