13.7 Neural-Network-Based Optimization 727
subject to
λ≤μf(X)
λ≤μg(l)
j(X)
, j= 1 , 2 ,... , m
λ≤μg(u)
j (X)
, j= 1 , 2 ,... , m (13.59)
13.6.4 Numerical Results
The minimization of the error between the generated and specified outputs of the
four-bar mechanism shown in Fig. 13.9 is considered. The design vector is taken as
X= {a b c β}T. The mechanism is constrained to be a crank-rocker mecha-
nism so that
a−b≤ 0 , a−c≤ 0 , a≤ 1
d=[(a+c)−(b+ 1 )][(c−a)^2 − (b− 1 )^2 ]≤ 0
The maximum deviation of the transmission angle(μ)from 90◦is restricted to be less
than a specified value,tmax= 53 ◦. The specified output angle is
θs(φ)=
{
20 ◦+φ 3 , 0 ◦≤ φ≤ 240 ◦
unspecified, 240 ◦≤ φ< 360 ◦
Linear membership functions are assumed for the response characteristics [13.22]. The
optimum solution is found to beX= { 0 .2537 0.8901 0. 8865 − 0. 7858 − 1. 0 }T
withf∗= 1. 6 562 andλ∗= 0 .4681.This indicates that the maximum level of satisfac-
tion that can be achieved in the presence of fuzziness in the problem is 0.4681. The
transmission angle constraint is found to be active at the optimum solution [13.22].
13.7 Neural-Network-Based Optimization
The immense computational power of nervous system to solve perceptional problems
in the presence of massive amount of sensory data has been associated with its parallel
q 2 = f
q 3
b
w 2 q^4
r 2 = a
1
r 3 = b
r 4 = c
Ω
Figure 13.9 Four-bar function generating mechanism.
