CHAPTER
1
Introduction
This manual contains solutions for most of the exercises in the textbook,
Introduction to Optimum Design, Fourth Edition. It also contains suggestions
for organization of undergraduate and graduate level courses on the subject
of optimization. A few copies of exams and projects for an undergraduate
course that can be common to most branches of engineering are also
included.
The philosophy of the fourth edition of the book is to explain an organized
Three main objectives were set for the fourth edition: (1) to enhance
presentation of the basic material, (2) to illustrate the numerical process of
refinement of an initial formulation of a design optimization problem, and
(3) to reorganize the advanced material.
The first objective is achieved by making the material more concise,
organizing the material with more second, third and fourth level headings,
and illustrating the example problems with more details.
The second objective is achieved by describing and illustrating the
Chapter 1 Introduction
Arora, Introduction to Optimum Design, 4e 1-2
obtain the final formulation for a design optimization problem. Other
aspects of the numerical solution process are also discussed in this chapter.
The third objective is achieved by consolidating all the nature–inspired
methods in Chapter 17: Nature–inspired Search Methods. Also all the direct
search methods are now consolidated in Chapter 11: More on Numerical
Methods for Unconstrained Optimum Design. In addition most of the
different types of courses depending on instructor’s preference and the
learning objectives for the course. Three types of courses are suggested;
however, several variations of them are possible:
Undergraduate/First Year Graduate Level Course
• Formulation of optimization problem (Chapters 1 and 2)
challenging project–type problems by the end of the semester. Note:
advanced project type exercises and sections with advanced material
are marked with an “*” in the text which may be omitted for this
course.
Chapter 1 Introduction
First Graduate Level Course
• Theory and numerical methods for unconstrained optimization
(Chapters 1-4, 10, 11)
• Theory and numerical methods for constrained optimization
Second Graduate Level Course
• Advanced topics on optimum design: duality theory in nonlinear
programming, rate of convergence of iterative algorithms,
derivation of numerical methods, direct search methods
(Chapters 1 to 14)
• Methods for discrete variable problems (Chapter 15)
• Nature–inspired search methods (Chapter 17)