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 Optimality -- 3.3.1 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 Methods -- 4.2.1 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 Programming -- Exercises -- 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 Generators -- 8.1 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 -- 11 Genetic Algorithms -- 11.1 Introduction -- 11.2 Genetic Algorithms -- 11.2.1 Basic Procedure -- 11.2.2 Choice of Parameters -- 11.3 Implementation -- Exercises -- 12 Simulated Annealing -- 12.1 Annealing and Probability -- 12.2 Choice of Parameters -- 12.3 SA Algorithm -- 12.4 Implementation -- Exercises -- 13 Ant Algorithms -- 13.1 Behaviour of Ants -- 13.2 Ant Colony Optimization -- 13.3 Double Bridge Problem -- 13.4 Virtual Ant Algorithm -- Exercises -- 14 Bee Algorithms -- 14.1 Behavior of Honey Bees -- 14.2 Bee Algorithms.

14.2.1 Honey Bee Algorithm -- 14.2.2 Virtual Bee Algorithm -- 14.2.3 Artificial Bee Colony Optimization -- 14.3 Applications -- Exercises -- 15 Particle Swarm Optimization -- 15.1 Swarm Intelligence -- 15.2 PSO algorithms -- 15.3 Accelerated PSO -- 15.4 Implementation -- 15.4.1 Multimodal Functions -- 15.4.2 Validation -- 15.5 Constraints -- Exercises -- 16 Harmony Search -- 16.1 Music-Based Algorithms -- 16.2 Harmony Search -- 16.3 Implementation -- Exercises -- 17 Firefly Algorithm -- 17.1 Behaviour of Fireflies -- 17.2 Firefly-Inspired Algorithm -- 17.2.1 Firefly Algorithm -- 17.2.2 Light Intensity and Attractiveness -- 17.2.3 Scaling and Global Optima -- 17.2.4 Two Special Cases -- 17.3 Implementation -- 17.3.1 Multiple Global Optima -- 17.3.2 Multimodal Functions -- 17.3.3 FA Variants -- Exercises -- PART III APPLICATIONS -- 18 Multiobjective Optimization -- 18.1 Pareto Optimality -- 18.2 Weighted Sum Method -- 18.3 Utility Method -- 18.4 Metaheuristic Search -- 18.5 Other Algorithms -- Exercises -- 19 Engineering Applications -- 19.1 Spring Design -- 19.2 Pressure Vessel -- 19.3 Shape Optimization -- 19.4 Optimization of Eigenvalues and Frequencies -- 19.5 Inverse Finite Element Analysis -- Exercises -- Appendices -- Appendix A: Test Problems in Optimization -- Appendix B: Matlab® Programs -- B.l Genetic Algorithms -- B.2 Simulated Annealing -- B.3 Particle Swarm Optimization -- B.4 Harmony Search -- B.5 Firefly Algorithm -- B.6 Large Sparse Linear Systems -- B.7 Nonlinear Optimization -- B.7.1 Spring Design -- B.7.2 Pressure Vessel -- Appendix C: Glossary -- Appendix D: Problem Solutions -- References -- Index.