16 Application of Multi-agent Optimization Methods …
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Fig. 16.4 Four point of the
Catmull–Rom curve
Fig. 16.5 Four point of the
Bezier curve
x
Bezier4
= arg max
t∈[0,1]
f
(1 − t)
3 P 1 + 3(1 − t)
2 t P 2 + 3(1 − t)t
2 P 3 + t
3 P 4
.
(16.16)
Step 6.4 Select P 1 = x
(1)
, P 4 = x
(2)
, P 2 = x
(3)
, P 3 = x
(4) the current
population I 0 (Fig. 16.6) and solve the problem
x B = arg max
t∈[0,1]
f
1
2
−t(1 − t) 2 P 1 +
2 − 5t 2 + 3t 3
P 2 + t
1 + 4t − 3t 2
P 3
−t 2 (1 − t)P 4
.
(16.17)
Step 6.5 Reduce the population. Place individuals of the current population,
replenished with x
Bezier3 , x
C R , x
Bezier4 , x
B members increasing the value
of the fitness function. Leave only N P best.
Step 7
Reduce the population.
Fig. 16.6 Three point of B-spline