Optimization Algorithms and Applications

Choose the Correct Solution Method for Your Optimization Problem Optimization: Algorithms and Applications presents a variety of solution techniques for optimization problems, emphasizing concepts rather than rigorous mathematical details and proofs. The book covers both gradient and stochastic methods as solution techniques for unconstrained and constrained optimization problems. It discusses the conjugate gradient method, Broyden–Fletcher–Goldfarb–Shanno algorithm, Powell method, penalty function, augmented Lagrange multiplier method, sequential quadratic programming, method of feasible directions, genetic algorithms, particle swarm optimization (PSO), simulated annealing, ant colony optimization, and tabu search methods. The author shows how to solve non-convex multi-objective optimization problems using simple modifications of the basic PSO code. The book also introduces multidisciplinary design optimization (MDO) architectures—one of the first optimization books to do so—and develops software codes for the simplex method and affine-scaling interior point method for solving linear programming problems. In addition, it examines Gomory’s cutting plane method, the branch-and-bound method, and Balas’ algorithm for integer programming problems. The author follows a step-by-step approach to developing the MATLAB® codes from the algorithms. He then applies the codes to solve both standard functions taken from the literature and real-world applications, including a complex trajectory design problem of a robot, a portfolio optimization problem, and a multi-objective shape optimization problem of a reentry body. This hands-on approach improves your understanding and confidence in handling different solution methods. The MATLAB codes are available on the book’s CRC Press web page.

IntroductionHistorical ReviewOptimization ProblemModeling of the Optimization ProblemSolution with the Graphical MethodConvexityGradient Vector, Directional Derivative, and Hessian MatrixLinear and Quadratic ApproximationsOrganization of the Book 1-D Optimization AlgorithmsIntroductionTest ProblemSolution TechniquesComparison of Solution Methods Unconstrained OptimizationIntroductionUnidirectional SearchTest ProblemSolution TechniquesAdditional Test FunctionsApplication to Robotics Linear ProgrammingIntroductionSolution with the Graphical MethodStandard Form of an LPPBasic SolutionSimplex MethodInterior-Point MethodPortfolio Optimization Guided Random Search MethodsIntroductionGenetic AlgorithmsSimulated AnnealingParticle Swarm OptimizationOther Methods Constrained OptimizationIntroductionOptimality ConditionsSolution TechniquesAugmented Lagrange Multiplier MethodSequential Quadratic ProgrammingMethod of Feasible DirectionsApplication to Structural Design Multiobjective OptimizationIntroductionWeighted Sum Approache-Constraints MethodGoal ProgrammingUtility Function MethodApplication Geometric ProgrammingIntroductionUnconstrained ProblemDual ProblemConstrained OptimizationApplication Multidisciplinary Design OptimizationIntroductionMDO ArchitectureMDO FrameworkResponse Surface Methodology Integer ProgrammingIntroductionInteger Linear ProgrammingInteger Nonlinear Programming Dynamic ProgrammingIntroductionDeterministic Dynamic ProgrammingProbabilistic Dynamic Programming Bibliography Appendix A: Introduction to MATLABAppendix B: MATLAB CodeAppendix C: Solutions to Chapter Problems Index Chapter Highlights, Formula Charts, and Problems appear at the end of each chapter.

Rajesh Kumar Arora is a senior engineer at the Indian Space Research Organization, where he has been working for more than two decades. He obtained his PhD in aerospace engineering from the Indian Institute of Science, Bangalore. His research interests include mission design, simulation of launch vehicle systems, and trajectory optimization.