Boroujeni, Ahmad Aliyari; Pourgholi, Reza; Tabasi, Seyed Hashem A new improved teaching-learning-based optimization (ITLBO) algorithm for solving nonlinear inverse partial differential equation problems. (English) Zbl 1509.65088 Comput. Appl. Math. 42, No. 2, Paper No. 99, 45 p. (2023). Summary: Teaching-learning-based optimization (TLBO) algorithm is a novel population-oriented meta-heuristic algorithm. In this paper, we introduce an improved teaching-learning-based algorithm (ITLBO) and combine it with numerical methods to solve some problems of nonlinear inverse partial differential equations. The basic TLBO algorithm has been enhance to increase its exploration and optimization capacities as well as diversity, increase the number of solutions and further converge to the appropriate solution by introducing the concept of grouping, elitism, elite group, elitism rate and the number of teachers. The most important advantage in implementing this scheme is that in addition to the fact that we have improved the TLBO algorithm with a new method, without guessing the type of answer function or the type of unknown function of the nonlinear inverse problems, we can determine the unknown and the answer of the inverse problems with great accuracy by optimizing the initial numerical values in a given interval. Furthermore, the experimental results on CEC benchmark function verify the feasibility and optimization performance of ITLBO. Accurate results were obtained by implementation proposed algorithms on 3.70 GHz clock speed CPU. Cited in 2 Documents MSC: 65M32 Numerical methods for inverse problems for initial value and initial-boundary value problems involving PDEs 65M30 Numerical methods for ill-posed problems for initial value and initial-boundary value problems involving PDEs 90C59 Approximation methods and heuristics in mathematical programming 35R30 Inverse problems for PDEs 35R25 Ill-posed problems for PDEs 35Q53 KdV equations (Korteweg-de Vries equations) 35Q92 PDEs in connection with biology, chemistry and other natural sciences Keywords:improved TLBO algorithm; evolutionary algorithms; nonlinear inverse partial differential equations problems; optimization; numerical methods Software:MTHSA-DHEI; CEC 05 × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Ahrari, A.; Atai, AA, Grenade explosion method—a novel tool for optimization of multimodal functions, Appl Soft Comput, 10, 4, 1132-40 (2010) · doi:10.1016/j.asoc.2009.11.032 [2] Alifanov, OM, Inverse heat transfer problems (1994), New York: Springer, New York · Zbl 0979.80003 · doi:10.1007/978-3-642-76436-3 [3] Amiri, B., Application of teaching-learning-based optimization algorithm on cluster analysis, J Basic Appl Sci Res, 2, 11, 11795-11802 (2012) [4] Anderssen, RS, Inverse problems: a pragmatist’s approach to the recovery of information from indirect measurements, Aust NZ Ind Appl Math J, 46, C588-C622 (2005) · Zbl 1078.65572 [5] Azizi, N.; Pourgholi, R., Applications of Sine-Cosine wavelets method for solving Drinfel’d-Sokolov-Wilson system, Adv Syst Sci Appl, 21, 3, 75-90 (2021) [6] Azizi, N.; Pourgholi, R., Applications of Sine-Cosine wavelets method for solving the generalized Hirota-Satsuma coupled KdV equation, Math Sci, 26, 1-4 (2022) [7] Baykasoglu, A.; Hamzadayi, A.; Köse, SY, Testing the performance of teaching-learning based optimization (TLBO) algorithm on combinatorial problems: flow shop and job shop scheduling cases, Inf Sci, 276, 204-218 (2014) · doi:10.1016/j.ins.2014.02.056 [8] Beck, JV; Murio, DC, Combined function specification-regularization procedure for solution of inverse heat condition problem, AIAA J, 24, 180-185 (1986) · Zbl 0587.76155 · doi:10.2514/3.9240 [9] Blum, C., Ant colony optimization: introduction and recent trends, Phys Life Rev, 2, 353-73 (2005) · doi:10.1016/j.plrev.2005.10.001 [10] Cabeza, JMG; Garcia, JAM; Rodriguez, AC, A sequential algorithm of inverse heat conduction problems using singular value decomposition, Int J Therm Sci, 44, 235-244 (2005) · doi:10.1016/j.ijthermalsci.2004.06.009 [11] Cannon, JR; Duchateau, P., An inverse problem for a nonlinear diffusion equation, SIAM J Appl Math, 39, 2, 272-289 (1980) · Zbl 0452.35112 · doi:10.1137/0139024 [12] Dong, H.; Xu, Y.; Cao, D.; Zhang, W.; Yang, Z.; Li, X., An improved teaching-learning-based optimization algorithm with a modified learner phase and a new mutation-restarting phase, Knowl-Based Syst, 258 (2022) · doi:10.1016/j.knosys.2022.109989 [13] Foadian, S.; Pourgholi, R.; Hashem, TS, Cubic B-spline method for the solution of an inverse parabolic system, Appl Anal, 97, 3, 438-65 (2018) · Zbl 1466.65103 · doi:10.1080/00036811.2016.1272102 [14] Foadian, S.; Pourgholi, R.; Tabasi, SH; Damirchi, J., The inverse solution of the coupled nonlinear reaction-diffusion equations by the Haar wavelets, Int J Comput Math, 96, 1, 105-25 (2019) · Zbl 1499.65469 · doi:10.1080/00207160.2017.1417593 [15] Foadian, S.; Pourgholi, R.; Tabasi, SH; Zeidabadi, H., Solving an inverse problem for a generalized time-delayed Burgers-Fisher equation by Haar wavelet method, J Appl Anal Comput, 10, 2, 391-410 (2020) · Zbl 1459.65218 [16] Foadian S, Pourgholi R, Esfahani A (2022) Numerical solution of the linear inverse wave equation. 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