Document Type : Original Article
Author
Assistant Professor, Department of Computer Sciences, Golestan University, Gorgan, Iran
Abstract
Inverse Partial Differential Equations (IPDEs) represent a class of ill-posed problems that frequently arise in engineering and applied sciences, such as heat conduction, diffusion, and imaging. Conventional approaches for solving IPDEs often rely on iterative or regularization techniques, which may suffer from instability and sensitivity to measurement errors. Recently, metaheuristic algorithms have emerged as powerful alternatives due to their global search ability and robustness. However, most of the existing studies, including those employing Teaching-Learning Based Optimization (TLBO), still face challenges in balancing accuracy, convergence speed, and computational cost. In this paper, we propose a novel hybrid metaheuristic algorithm combining Grey Wolf Optimizer (GWO) and Cuckoo Search (CS), referred to as HGWO-CS, for solving IPDEs. The hybrid strategy leverages the leadership hierarchy and hunting mechanism of GWO with the Lévy flight-based exploration of CS to achieve both efficient exploitation and diverse exploration. The method is applied to several benchmark IPDE problems, including inverse heat conduction problems, without requiring any prior assumption about the form of the unknown function. Numerical experiments demonstrate that the HGWO-CS approach achieves higher accuracy, faster convergence, and improved stability compared to existing algorithms such as TLBO, GA, and PSO. The main novelties of this work summarized as follows: the proposed method does not assume any predefined functional form for the unknown boundary conditions; the hybridization strategy effectively balances exploration and exploitation, resulting in improved accuracy, convergence speed, and robustness against noisy measurements. The proposed algorithm thus provides a promising tool for tackling complex IPDEs in engineering applications.
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