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Engineering Optimization.pdf
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The book consists of fourteen chapters and three appendixes. Chapter 1 provides an
introduction to engineering optimization and optimum design and an overview of optimization
methods. The concepts of design space, constraint surfaces, and contours of
objective function are introduced here. In addition, the formulation of various types of
optimization problems is illustrated through a variety of examples taken from various
fields of engineering. Chapter 2 reviews the essentials of differential calculus useful
in finding the maxima and minima of functions of several variables. The methods of
constrained variation and Lagrange multipliers are presented for solving problems with
equality constraints. The Kuhn–Tucker conditions for inequality-constrained problems
are given along with a discussion of convex programming problems.
Chapters 3 and 4 deal with the solution of linear programming problems. The
characteristics of a general linear programming problem and the development of the
simplex method of solution are given in Chapter 3. Some advanced topics in linear
programming, such as the revised simplex method, duality theory, the decomposition
principle, and post-optimality analysis, are discussed in Chapter 4. The extension of
linear programming to solve quadratic programming problems is also considered in
Chapter 4.
Chapters 5–7 deal with the solution of nonlinear programming problems. In
Chapter 5, numerical methods of finding the optimum solution of a function of a single
variable are given. Chapter 6 deals with the methods of unconstrained optimization.
The algorithms for various zeroth-, first-, and second-order techniques are discussed
along with their computational aspects. Chapter 7 is concerned with the solution of
nonlinear optimization problems in the presence of inequality and equality constraints.
Both the direct and indirect methods of optimization are discussed. The methods
presented in this chapter can be treated as the most general techniques for the solution
of any optimization problem.
Chapter 8 presents the techniques of geometric programming. The solution techniques
for problems of mixed inequality constraints and complementary geometric
programming are also considered. In Chapter 9, computational procedures for solving
discrete and continuous dynamic programming problems are presented. The problem
of dimensionality is also discussed. Chapter 10 introduces integer programming and
gives several algorithms for solving integer and discrete linear and nonlinear optimization
problems. Chapter 11 reviews the basic probability theory and presents techniques
of stochastic linear, nonlinear, and geometric programming. The theory and applications
of calculus of variations, optimal control theory, and optimality criteria methods
are discussed briefly in Chapter 12. Chapter 13 presents several modern methods of
optimization including genetic algorithms, simulated annealing, particle swarm optimization,
ant colony optimization, neural-network-based methods, and fuzzy system
optimization. Several of the approximation techniques used to speed up the convergence
of practical mechanical and structural optimization problems, as well as parallel
computation and multiobjective optimization techniques are outlined in Chapter 14.
Appendix A presents the definitions and properties of convex and concave functions.
A brief discussion of the computational aspects and some of the commercial optimization
programs is given in Appendix B. Finally, Appendix C presents a brief introduction
to Matlab, optimization toolbox, and use of Matlab programs for the solution of optimization
problems.
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