Introduction to Evolutionary Algorithmson Numerical Calculations

Fatiha, GHEDJEMIS (2025) Introduction to Evolutionary Algorithmson Numerical Calculations. Doctoral thesis, Université Mohamed Khider (Biskra - Algérie).

Text finalThesis.pdf Download (1MB)

Abstract

This thesis proposes a new hybrid computational method that combines the accuracy of spectral methods with the optimization abilities of the Flower Pollination Algorithm to find solutions of differential equations, particularly boundary value problems. The approach uses Chebyshev polynomials for spectral approximation and combines FPA to minimize residual errors and optimize the coefficients, leading to accurate numerical solutions. The study begins by exploring the structures of spectral methods and metaheuristic algorithms, concentrating on their mathematical properties and practical roles in optimization. It then introduces a new three-step hybrid methodology: extracting an initial approximation, calculating the residual error, and optimizing undetermined coefficients via FPA. The efficiency of this method is confirmed through several case studies, involving linear and nonlinear boundary value problems. Experimental results validate that the proposed hybrid approach improves solution accuracy and computational efficiency contrast classical methods. The findings highlight the method’s adaptability and potential in broader applications such as fluid dynamics, structural analysis, and data-driven modelling. This work contributes a robust and flexible approach for solving complex differential problems, paving the way for future research in advanced numerical and optimization strategies.

Actions (login required)

View Item