Engineering Optimization: Theory and Practice, Fourth Edition

786 Some Computational Aspects of Optimization

formulated test problems that are not related to real-life problems. Thus each new prac-

tical problem has to be tackled almost independently based on past experience. The

following guidelines are applicable for a general problem.

The sequential quadratic programming approach can be used for solving a variety of

problems efficiently. The GRG method and Zoutendijk’s method of feasible directions,

although slightly less efficient, can also be used for the efficient solution of constrained

problems. The ALM and penalty function methods are less efficient but are robust and

reliable in finding the solution of constrained problems.

B.4 Availability of Computer Programs

Many computer programs are available to solve nonlinear programming problems.

Notable among these is the book by Kuester and Mize [B.13], which gives Fortran

programs for solving linear, quadratic, geometric, dynamic, and nonlinear programming

problems. During practical computations, it is important to note that a method that

works well for a given class of problems may work poorly for others. Hence it is

usually necessary to try more than one method to solve a particular problem efficiently.

Further, the efficiency of any nonlinear programming method depends largely on the

values of adjustable parameters such as starting point, step length, and convergence

requirements. Hence a proper set of values to these adjustable parameters can be given

only by using a trial-and-error procedure or through experience gained in working with

the method for similar problems. It is also desirable to run the program with different

starting points to avoid local and false optima. It is advisable to test the two convergence

criteria stated in Section 7.21 before accepting a point as a local minimum.

More and Wright present information on the current state of numerical optimization ́

software in [B.16]. Several software systems such as IMSL, MATLAB, and ACM

contain programs to solve optimization problems. The relevant addresses are

IMSL

7500 Bellaire Boulevard

Houston, TX 77036

MATLAB

The MathWorks, Inc.

24 Prime Park Way

Natick, MA 01760

ACM Distribution Service

c/o International Mathematics and Statistics Service

7500 Bellaire Boulevard

Houston, TX 77036

In addition, the commercial structural optimization packages listed in Table B.1

are available in the market [B.14, B.15]. Most of these softwares are based on a

finite-element-based analysis for objective and constraint function evaluations and use

several types of approximation strategies.