Engineering Optimization: Theory and Practice, Fourth Edition

B Some Computational Aspects of Optimization

Several methods were presented for solving different types of optimization problems

in Chapters 3 to 14. This appendix is intended to give some guidance to the reader in

choosing a suitable method for solving a particular problem along with some computa-

tional details. Most of the discussion is aimed at the solution of nonlinear programming

problems.

B.1 Choice of Method

Several factors are to be considered in deciding a particular method to solve a given

optimization problem. Some of them are

1.The type of problem to be solved (general nonlinear programming problem,

geometric programming problem, etc.)

2.The availability of a ready-made computer program

3.The calender time required for the development of a program

4.The necessity of derivatives of the functionsfandgj, j= 1 , 2 ,... , m

5.The available knowledge about the efficiency of the method

6.The accuracy of the solution desired

7.The programming language and quality of coding desired

8.The robustness and dependability of the method in finding the true optimum

solution

9.The generality of the program for solving other problems

10.The ease with which the program can be used and its output interpreted

B.2 Comparison of Unconstrained Methods

A number of studies have been made to evaluate the various unconstrained minimization

methods. More, Garbow, and Hillstrom [B.1] provided a collection of 35 test functions ́

for testing the reliability and robustness of unconstrained minimization software. The

performance of eight unconstrained minimization methods was evaluated by Box [B.2]

using a set of test problems with up to 20 variables. Straeter and Hogge [B.3] compared

four gradient-based unconstrained optimization techniques using two test problems.

784 Engineering Optimization: Theory and Practice, Fourth Edition Singiresu S. Rao
Copyright © 2009 by John Wiley & Sons, Inc.