Fundamentals of optimization techniques with algorithms
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| Main Author: | |
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| Format: | eBook Book |
| Language: | English |
| Published: |
London
Academic Press
2020
Elsevier Science & Technology |
| Edition: | 1 |
| Subjects: | |
| ISBN: | 0128211261, 9780128211267 |
| Online Access: | Get full text |
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Table of Contents:
- 9.5 Lexicographic model -- 9.6 Goal programming method -- 9.6.1 Practice set -- Further reading -- 10. Nature-inspired optimization -- 10.1 Genetic algorithm -- 10.1.1 Genetic operations on binary strings -- 10.1.1.1 Selection -- 10.1.1.2 Crossover -- 10.1.1.3 Mutation -- 10.1.2 Analysis of GA -- 10.2 Neural network-based optimization -- 10.2.1 Architecture of ANN -- 10.2.2 Paradigms of learning -- 10.2.3 Learning processes -- 10.2.4 Activation functions -- 10.2.5 Applications of ANN in optimization -- 10.3 Ant colony optimization -- 10.4 Particle swarm optimization -- Further reading -- Index -- Back Cover
- 4.2 Unidirectional search method -- 4.3 Evolutionary search method -- 4.3.1 Box's evolutionary optimization method -- 4.4 Simplex search method -- 4.5 Hooke-Jeeves pattern search method -- 4.5.1 Exploratory move -- 4.5.2 Pattern move -- 4.6 Conjugate direction method -- 4.6.1 Parallel subspace property -- 4.6.2 Extended parallel subspace property -- 4.7 Steepest descent method -- 4.7.1 Cauchy's (steepest descent) method -- 4.8 Newton's method -- 4.9 Marquardt's method -- Practice set -- Further reading -- 5. Multivariable constrained nonlinear optimization -- 5.1 Classical methods for equality constrained optimization -- 5.1.1 Solution by direct substitution -- 5.1.2 Solution by the method of constrained variation -- 5.1.3 Solution by the method of Lagrange multipliers -- 5.1.3.1 Necessary conditions -- 5.1.3.2 Sufficient condition -- 5.2 Classical methods for inequality constrained optimization -- 5.3 Random search method -- 5.4 Complex method -- 5.4.1 Iterative procedure -- 5.5 Sequential linear programming -- 5.6 Zoutendijk's method of feasible directions -- 5.7 Sequential quadratic programming -- 5.7.1 Derivation -- 5.7.2 Solution procedure -- 5.8 Penalty function method -- 5.9 Interior penalty function method -- 5.10 Convex programming problem -- 5.11 Exterior penalty function method -- Practice set -- Further reading -- 6. Geometric programming -- 6.1 Posynomial -- 6.2 Unconstrained geometric programming program -- 6.2.1 Arithmetic-geometric inequality -- 6.2.2 Primal-dual relationship and sufficiency conditions in the unconstrained case -- 6.2.3 Primal and dual problems -- 6.2.4 Computational procedure -- 6.3 Constrained optimization -- 6.3.1 Solution of a constrained geometric programming problem -- 6.3.2 Optimum design variables -- 6.3.3 Primal and dual programs in the case of less-than inequalities
- Front Cover -- Fundamentals of Optimization Techniques With Algorithms -- Copyright Page -- Dedication -- Contents -- Preface -- Acknowledgments -- 1. Introduction to optimization -- 1.1 Optimal problem formulation -- 1.1.1 Design variables -- 1.1.2 Constraints -- 1.1.3 Objective function -- 1.1.4 Variable bounds -- 1.2 Engineering applications of optimization -- 1.3 Optimization techniques -- Further reading -- 2. Linear programming -- 2.1 Formulation of the problem -- Practice set 2.1 -- 2.2 Graphical method -- 2.2.1 Working procedure -- Practice set 2.2 -- 2.3 General LPP -- 2.3.1 Canonical and standard forms of LPP -- Practice set 2.3 -- 2.4 Simplex method -- 2.4.1 Reduction of feasible solution to a basic feasible solution -- 2.4.2 Working procedure of the simplex method -- Practice set 2.4 -- 2.5 Artificial variable techniques -- 2.5.1 Big M method -- 2.5.2 Two-phase method -- Practice set 2.5 -- 2.6 Duality Principle -- 2.6.1 Formulation of a dual problem -- 2.6.1.1 Formulation of a dual problem when the primal has equality constraints -- 2.6.1.2 Duality principle -- Practice set 2.6 -- 2.7 Dual simplex method -- 2.7.1 Working procedure for a dual simplex method -- Practice set 2.7 -- Further reading -- 3. Single-variable nonlinear optimization -- 3.1 Classical method for single-variable optimization -- 3.2 Exhaustive search method -- 3.3 Bounding phase method -- 3.4 Interval halving method -- 3.5 Fibonacci search method -- 3.6 Golden section search method -- 3.7 Bisection method -- 3.8 Newton-Raphson method -- 3.9 Secant method -- 3.10 Successive quadratic point estimation method -- Further reading -- 4. Multivariable unconstrained nonlinear optimization -- 4.1 Classical method for multivariable optimization -- 4.1.1 Definition: rth differential of a function f(X) -- 4.1.2 Necessary condition -- 4.1.3 Sufficient condition
- 6.4 Geometric programming with mixed inequality constraints -- Practice set -- Further reading -- 7. Dynamic programming -- 7.1 Characteristics of dynamic programming -- 7.2 Terminologies -- 7.3 Developing optimal decision policy -- 7.4 Multiplicative separable return function and single additive constraint -- 7.5 Additive separable return function and single additive constraint -- 7.6 Additively separable return function and single multiplicative constraint -- 7.7 Dynamic programming approach for solving a linear programming problem -- 7.8 Types of multilevel decision problem -- 7.8.1 Concept of suboptimization and the principle of optimality -- 7.8.2 Formulation of water tank optimization problem into a dynamic programming problem and the solution procedure -- 7.8.3 Procedure -- Practice set -- Further reading -- 8. Integer programming -- 8.1 Integer linear programming -- 8.1.1 Types of integer programming problems -- 8.1.2 Enumeration and concept of cutting plane solution -- 8.1.3 Gomory's all integer cutting plane method -- 8.1.3.1 Method for constructing additional constraint (cut) -- 8.1.3.2 Procedure -- 8.1.3.3 Steps of Gomory's all integer programming algorithm -- 8.1.4 Gomory's mixed-integer cutting plane method -- 8.1.4.1 Method for constructing additional constraint (cut) -- 8.1.5 Branch and bound method -- 8.1.5.1 Procedure -- 8.1.6 Applications of zero-one integer programming -- 8.2 Integer nonlinear programming -- 8.2.1 Representation of an integer variable by an equivalent system of binary variables -- Practice set -- Further reading -- 9. Multiobjective optimization -- 9.1 Global criterion method -- 9.1.1 Methods for a priori articulation information given -- 9.2 Utility function method -- 9.3 Inverted utility method -- 9.4 Bounded objective function method -- 9.4.1 Methods for mixed ordinal and cardinal information given