Engineering Optimization – An Introduction with Metaheuristic Applications

Modern optimization techniques are widely applicable to many applications, and metaheuristics form a class of emerging powerful algorithms for optimization. This book introduces state-of-the-art metaheuristic algorithms and their applications in optimization, using both MATLAB(r) and Octave allowing readers to visualize, learn, and solve optimization problems. It provides step-by-step explanations of all algorithms, case studies, real-world applications, and detailed references to the latest literature. It is ideal for researchers and professionals in mathematics, industrial engineering, and computer science, as well as students in computer science, engineering optimization, and computer simulation.

Table of Contents:
List of Figures. Preface. Acknowledgments. Introduction. PART I Foundations of Optimization and Algorithms. 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. 3.4 Vector and Matrix Norms. 3.5 Eigenvalues and Definiteness. 3.6 Linear and Affine Functions. 3.7 Gradient and Hessian Matrices. 3.8 Convexity. Exercises. 4 Classic Optimization Methods I. 4.1 Unconstrained Optimization. 4.2 Gradient-Based Methods. 4.3 Constrained Optimization. 4.4 Linear Programming. 4.5 Simplex Method. 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. 5.3 Trust-Region Method. 5.4 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. 7.2 Variations with Constraints. 7.3 Variations for Multiple Variables. 7.4 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 p. 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. 10.3 Levy Flights. 10.4 Markov Chain. 10.5 Markov Chain Monte Carlo. 10.6 Markov Chain and Optimisation. Exercises. PART II Metaheuristic Algorithms. 11 Genetic Algorithms. 11.1 Introduction. 11.2 Genetic Algorithms. 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. 14.3 Applications. Exercises. 15 Particle Swarm Optimization. 15.1 Swarm Intelligence. 15.2 PSO algorithms. 15.3 Accelerated PSO. 15.4 Implementation. 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. 17.3 Implementation. 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(r) Programs. B.1 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.