778 Practical Aspects of Optimization
f 1 (X)= − 25 (x 1 − 2 )^2 −(x 2 − 2 )^2 −(x 3 − 1 )^2 −(x 4 − 4 )^2 −(x 5 − 1 )^2
f 2 (X)=x 12 +x 22 +x^23 +x^24 +x 52 +x^26
subject to
−x 1 −x 2 + 2 ≤ 0 ;x 1 +x 2 − 6 ≤ 0 ; −x 1 +x 2 − 2 ≤ 0 ;x 1 − 3 x 2 − 2 ≤ 0 ;
(x 3 − 3 )^2 +x^24 − 4 ≤ 0 ; −(x 5 − 3 )^2 −x 6 + 4 ≤ 0 ; 0 ≤xi≤ 10 , i= 1 , 2 , 6
1 ≤xi≤ 5 , i= 3 , 5 ; 0 ≤x 4 ≤ 6
Find the minima of the individual objective functions under the stated constraints using
the MATLAB functionfmincon.
14.24 Find the solution of the two-objective optimization problem stated in Problem 14.23
using the weighting function method with the weightsw 1 =w 2 =1. Use the MATLAB
functionfminconfor the solution.
14.25 Find the solution of the two-objective optimization problem stated in Problem 14.23
using the global criterion method withp=2. Use the MATLAB functionfminconfor
the solution.
14.26 Find the solution of the two-objective optimization problem stated in Problem 14.23
using the bounded objective function method. Take the lower and upper bounds onf 2
as 80 and 120% of the optimum valuef 2 ∗found in Problem 13.23. Use the MATLAB
functionfminconfor the solution.
14.27 Find the solution of the two-objective optimization problem stated in Problem 14.23
using the goal attainment method. Use the MATLAB functionfgoalattainfor the
solution. Use suitable goals for the objectives.
14.28 Consider the following three-objective optimization problem:
FindX= {x 1 x 2 }Tto minimize
f 1 (X)= 1. 5 −x 1 ( 1 −x 2 )
f 2 (X)= 2. 25 −x 1 ( 1 −x^22 )
f 3 (X)= 2. 625 −x 1 ( 1 −x 23 )
subject to
−x 12 −(x 2 − 0. 5 )^2 + 9 ≤ 0
(x 1 − 1 )^2 +(x 2 − 0. 5 )^2 − 6. 25 ≤ 0
− 10 ≤xi≤ 10 ;i= 1 , 2
Find the minima of the individual objectives under the stated constraints using the
MATLAB functionfmincon.
14.29 Find the solution of the 3-objective problem stated in Problem 14.28 using the weight-
ing function method with the weightsw 1 =w 2 =w 3 =1. Use the MATLAB function
fminconfor the solution.
14.30 Find the solution of the multiobjective problem stated in Problem 14.28 using the goal
attainment method. Use the MATLAB functionfgoalattainfor the solution. Use
suitable goals for the objectives.