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**A new improved teaching-learning-based optimization (ITLBO) algorithm for solving nonlinear inverse partial differential equation problems.**
*(English)*
Zbl 1509.65088

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.

### 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
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\textit{A. A. Boroujeni} et al., Comput. Appl. Math. 42, No. 2, Paper No. 99, 45 p. (2023; Zbl 1509.65088)

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