Unit Commitment Optimization Using Gradient-Genetic Algorithm and Fuzzy Logic Approaches - Complex System Modelling and Control Through Intelligent Soft Computations - page 685

With:
F max Maximum of the function F r ,
L

Penalty coef cient,

K Scaling coef cient,

(

b h ¼ ð Þ 6 ¼

1 if C P ih ; U 0

b h Constant de ned as follows:

b h ¼ 0 if C ð P ih ; U Þ ¼ 0

In a second step, we have adopted the biased roulette wheel method in order to
select the best chromosomes according to their performances according to the
following equation:

c i Þ
P i¼1 f ð c i Þ

f ð

perf ð c i Þ ¼ ð 15 Þ

where, l is the length of a binary string.
Subsequently, we cross these chromosomes in order to obtain a population of
children. Hence, we can randomly mutate the genes according to (Zhao et al. 2006 )
(Fig. 3 ).
In passing from one generation to another, the old population should be replaced
by the descendant ' s population newly created to maintain the search for better

Fig. 3 Operations of the genetic algorithm