Page 344 - Decision Making Applications in Modern Power Systems

306 Decision Making Applications in Modern Power Systems

The selection returns to winning solution i based on two fundamental
criteria:

If j has better hierarchy, r i , r j .
If j has the same hierarchy, but i has a better stacking distance, d i . d j .

12.2.3.4 Determination of final set descending
Before finalizing a generation of algorithm, a process of preselection and
preservation of elite solutions is performed, which involves getting the set of
solution parents and offspring obtained through the selection of operators,
crossover, and mutation.
Thus the present population increases to double the initial population of
individuals. It is necessary to classify the full set of fronts in their respective
dominance and preserve individuals who belong to the best quality fronts, as
is shown in Fig. 12.2.
If it is not possible to enter all the alternatives of a particular forward,
then those individuals are disposed with a smaller distance to the crowd.

12.2.3.5 Pseudocode for the nondominated sorting genetic
algorithm II
The steps used in NSGA-II are as follows:
1. Generate a population of size N.
2. Identify the dominance of fronts and evaluate stacking distances on every
front.
3. Using selection, crossover, and mutation generates a downward popula-
tion, the same size as P.
4. Parents and children together in a set of 2N rank the dominance fronts.
5. Determine the final set down by selecting the fronts of the best features
or hierarchy. If exceeded the threshold population of N, eliminate solu-
tions with the shortest distance across stacking the last selected.
6. With the fulfillment of convergence criterion, the process ends, if not,
return to step 3.

FIGURE 12.2 Determination of new population. In the figure, P t is the current population, Q t
is the offspring population, and R t is the population after recombination.