| Titre : | Improvement of Performance of Certain Numerical Computational Methods using Swarm Intelligence Algorithms Improvement of Gregory’s Formula using Artificial Bee Colony Algorithm. |
| Auteurs : | Samiha Aichouche, Auteur ; Naceur Khelil, Directeur de thèse |
| Type de document : | Monographie imprimée |
| Editeur : | Biskra [Algérie] : Faculté des Sciences Exactes et des Sciences de la Nature et de la Vie, Université Mohamed Khider, 2016 |
| Format : | 1 vol. (78 p.) / couv. ill. / 30 cm |
| Langues: | Anglais |
| Mots-clés: | Gregory Formula, Artificial Bee Colony (ABC) Algorithm, Numerical Integration. |
| Résumé : |
In this work, we prove that the Gregory Formula (G) can be optimized by minimizing some of their coefficients in the remainder term by using Artificial Bee Colony (ABC) Algorithm. Experimental tests prove that obtained Formula can be rendered a powerful formula for library use. |
| Sommaire : |
Abstract i Acknowledgements iii Contents iv List of Figures v List of Tables vi Abbreviations vii Introduction 1 1 Preliminary 3 1.1 The Algebra of Formal Power Series . . . . . . . . . . . . . . . . . . 3 1.1.1 The Ordrer of Power Series . . . . . . . . . . . . . . . . . . 7 1.1.2 Polynomial Algebra . . . . . . . . . . . . . . . . . . . . . . . 9 1.1.3 Generating Functions, Conjugate Sequences . . . . . . . . . 9 1.1.4 Compositional Umbral . . . . . . . . . . . . . . . . . . . . . 10 1.2 Linear Functionals . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 1.3 Expansion of Formal Series by Series Delta . . . . . . . . . . . . . . 16 1.4 Illustration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 2 Artificial Bee Colony (ABC) 24 2.1 Artificial Intelligence . . . . . . . . . . . . . . . . . . . . . . . . . . 24 2.2 What is Swarm Intelligence? . . . . . . . . . . . . . . . . . . . . . . 26 2.2.1 Main Idea . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 2.2.2 Fundamentals of SI in Social Insects . . . . . . . . . . . . . 28 2.2.3 Swarm Intelligence Models . . . . . . . . . . . . . . . . . . . 29 2.3 Artificial Bee Colony (ABC) . . . . . . . . . . . . . . . . . . . . . . 30 2.3.1 Description of The Foraging Behavior of Reel Honey Bees . 30 2.3.2 Studies on ABC Optimizations . . . . . . . . . . . . . . . . 33 2.3.3 Artificial Bee Colony (ABC) Algorithm Optimization . . . . 34 2.3.4 Simulation Studies . . . . . . . . . . . . . . . . . . . . . . . 38 3 Improvement of Gregory’s Formula using Artificial Bee Colony Algorithm 47 3.1 Gregory’s Formula for Solving Numerical Integration . . . . . . . . 47 3.2 Improvement of Gregory’s Formula using Artificial Bee Colony Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3.3 Simulation Results . . . . . . . . . . . . . . . . . . . . . . . . . . . 53 Conclusion and Future Work 55 A MATLAB Code 56 A.1 ABC Algorithm Coded using MATLAB Language . . . . . . . . . . 56 A.2 The Fitness Function Coded using MATLAB Language . . . . . . . 62 A.3 The Complete MATLAB Code for Figure 2.7 . . . . . . . . . . . . . 63 A.4 The Objective Function Coded using MATLAB Language . . . . . 64 Bibliography 65 |
| En ligne : | http://thesis.univ-biskra.dz/2802/1/Th%C3%A8se_73_2016.pdf |
Disponibilité (1)
| Cote | Support | Localisation | Statut |
|---|---|---|---|
| TM/65 | Théses de doctorat | bibliothèque sciences exactes | Consultable |
