Engineering optimization [[electronic resource] ] : an introduction with metaheuristic applications / / Xin-She Yang

• Record Nr.: UNINA9910140843303321
• Autore: Yang Xin-She
• Pubbl/distr/stampa: Hoboken, NJ, : Wiley, c2010
• ISBN: 1-282-70777-9; 9786612707773; 0-470-64042-1; 0-470-64041-3
• Descrizione fisica: 1 online resource (377 p.)
• Disciplina: 620.001/5196
• Soggetti: Heuristic programming; Mathematical optimization; Engineering mathematics
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references and index.
• Nota di contenuto: Engineering Optimization: An Introduction with Metaheuristic Applications; CONTENTS; List of Figures; Preface; Acknowledgments; Introduction; PART I FOUNDATIONS OF OPTIMIZATION AND ALGORITHMS; 1 A Brief History of Optimization; 1.1 Before 1900; 1.2 Twentieth Century; 1.3 Heuristics and Metaheuristics; Exercises; 2 Engineering Optimization; 2.1 Optimization; 2.2 Type of Optimization; 2.3 Optimization Algorithms; 2.4 Metaheuristics; 2.5 Order Notation; 2.6 Algorithm Complexity; 2.7 No Free Lunch Theorems; Exercises; 3 Mathematical Foundations; 3.1 Upper and Lower Bounds; 3.2 Basic Calculus; 3.3 Optimality3.3.1 Continuity and Smoothness; 3.3.2 Stationary Points; 3.3.3 Optimality Criteria; 3.4 Vector and Matrix Norms; 3.5 Eigenvalues and Definiteness; 3.5.1 Eigenvalues; 3.5.2 Definiteness; 3.6 Linear and Affine Functions; 3.6.1 Linear Functions; 3.6.2 Affine Functions; 3.6.3 Quadratic Form; 3.7 Gradient and Hessian Matrices; 3.7.1 Gradient; 3.7.2 Hessian; 3.7.3 Function approximations; 3.7.4 Optimality of multivariate functions; 3.8 Convexity; 3.8.1 Convex Set; 3.8.2 Convex Functions; Exercises; 4 Classic Optimization Methods I; ; 4.1 Unconstrained Optimization; 4.2 Gradient-Based Methods4.2.1 Newton's Method; 4.2.2 Steepest Descent Method; 4.2.3 Line Search; 4.2.4 Conjugate Gradient Method; 4.3 Constrained Optimization; 4.4 Linear Programming; 4.5 Simplex Method; 4.5.1 Basic Procedure; 4.5.2 Augmented Form; 4.6 Nonlinear Optimization; 4.7 Penalty Method; 4.8 Lagrange Multipliers; 4.9 Karush-Kuhn-Tucker Conditions; Exercises; 5 Classic Optimization Methods II; 5.1 BFGS Method; 5.2 Nelder-Mead Method; 5.2.1 A Simplex; 5.2.2 Nelder-Mead Downhill Simplex; 5.3 Trust-Region Method; 5.4 Sequential Quadratic Programming; 5.4.1 Quadratic Programming; 5.4.2 Sequential Quadratic ProgrammingExercises; 6 Convex Optimization; 6.1 KKT Conditions; 6.2 Convex Optimization Examples; 6.3 Equality Constrained Optimization; 6.4 Barrier Functions; 6.5 Interior-Point Methods; 6.6 Stochastic and Robust Optimization; Exercises; 7 Calculus of Variations; 7.1 Euler-Lagrange Equation; 7.1.1 Curvature; 7.1.2 Euler-Lagrange Equation; 7.2 Variations with Constraints; 7.3 Variations for Multiple Variables; 7.4 Optimal Control; 7.4.1 Control Problem; 7.4.2 Pontryagin's Principle; 7.4.3 Multiple Controls; 7.4.4 Stochastic Optimal Control; Exercises; 8 Random Number Generators8.1 Linear Congruential Algorithms; 8.2 Uniform Distribution; 8.3 Other Distributions; 8.4 Metropolis Algorithms; Exercises; 9 Monte Carlo Methods; 9.1 Estimating π; 9.2 Monte Carlo Integration; 9.3 Importance of Sampling; Exercises; 10 Random Walk and Markov Chain; 10.1 Random Process; 10.2 Random Walk; 10.2.1 ID Random Walk; 10.2.2 Random Walk in Higher Dimensions; 10.3 Lévy Flights; 10.4 Markov Chain; 10.5 Markov Chain Monte Carlo; 10.5.1 Metropolis-Hastings Algorithms; 10.5.2 Random Walk; 10.6 Markov Chain and Optimisation; Exercises; PART II METAHEURISTIC ALGORITHMS
• Sommario/riassunto: An accessible introduction to metaheuristics and optimization, featuring powerful and modern algorithms for application across engineering and the sciences From engineering and computer science to economics and management science, optimization is a core component for problem solving. Highlighting the latest developments that have evolved in recent years, Engineering Optimization: An Introduction with Metaheuristic Applications outlines popular metaheuristic algorithms and equips readers with the skills needed to apply these techniques to their own optimization problems. With insigh