Engineering Optimization: Theory and Practice, Fourth Edition

768 Practical Aspects of Optimization

• 4- x(2); ...
  x(2)- 4; ...
  x(2)+4*x(1)- 4; ...


• 1- x(1); ...
  x(1)- 2- x(2)]

ceq = [];

Step 3: Ctreate an m-file for the main program and save it as fgoalat-

tain_main.m

clc; clear all;

x0 = [0.1 0.1]

weight = [0.20.50.3]

goal = [5 -8 20]

x,fval,attainfactor,exitflag] = fgoalattain (@fgoalattainobj,

x0,goal,weight,[],[],[],[],[],[],@fgoalattaincon)

Step 4:Run the programfgoalattain_main.mto obtain the following result:

Initial design vector: 0.1,0.1

Initial objective values: 4.8981 -12.9546 17.1383

Constraints at initial design: -4.1000

-3.9000

-4.1000

-3.9000

-3.5000

-1.1000

-2.0000

Optimum design vector: 0.8308 0.6769

Optimum objective values: 3.8999 -12.9712 18.3498

Constraints at optimum design: -4.8308

-3.1692

-4.6769

-3.3231

-0.0000

-1.8308

-1.8462

References and Bibliography

14.1 L. A. Schmidt, Jr., and B. Farshi, Some approximation concepts for structural synthesis,

AIAA Journal, Vol. 12, No. 5, pp. 692–699, 1974.

14.2 E. J. Haug, K. K. Choi, and V. Komkov,Design Sensitivity Analysis of Structural Sys-

tems, Academic Press, New York, 1986.