Unit Commitment Optimization Using Gradient-Genetic Algorithm and Fuzzy Logic Approaches - Complex System Modelling and Control Through Intelligent Soft Computations - page 684

Fig. 2 Configuration of the fuzzy logic system

The solution in the unit commitment problem is represented by a binary matrix
U of dimension (l N g ). The proposed method for coding is a mix of binary and

decimal numbers. Each column vector in the solution matrix (which is the operation
schedule of one unit) of length l is converted to its equivalent decimal number. The
solution matrix is then converted into one row vector (chromosome) of N g decimal
numbers (U l , U 2 …

×

U n ); each variable represents the schedule of one unit. The
numbers U l , U 2 … U n are integers ranging from 0 to (2 N g 1). Accordingly, a

population of size (POP) is randomly generated in a matrix N POP N g

.

s population, only the strongest, or in other words the best
suited to the natural environment, survive and can give offspring. In each evolution
stage, the genetic operators (selection, crossover and mutation) operate basing on
the data structures in order to allow each individual to sweep the solutions horizon
and to distinguish the global optimum among the local optimum (Damousis et al.
2004 ; Sudhakaran et al. 2010 ; Marrouchi and Chebbi 2013 ). At

In one individual '

first, from an initial

population of individuals, the evaluation function satis es the following relation:

<
:

1

F ð U P Þ ¼

;

F max
Fr

1 þ K ð 1 Þ

1

with F r ¼

P

N g

P

P d P

N g

P i U ih Þþ P

H H

1 ½ / i ð

P ih Þþ ST i ð 1 U i ð h 1 Þ Þ U ih þ k i ð

1 b h

L

i ¼ 1 h ¼ i ¼ 1 h ¼

ð 14 Þ