Optimization methods
|
Date |
30/05/2007 |
|
Author |
F. Moussouni, T. V. Tran, S.
Brisset, P. Brochet |
|
Affiliation |
L2EP
– EC Lille – France |
|
Email |
fouzia.moussouni@ec-lille.fr, tran.tuan-vu@ec-lille.fr, stephane.brisset@ec-lille.fr |
|
Method |
Non-dominated
Sorting Genetic Algorithm |
|
References |
[1] K. Deb, [2] M. Mohan, K. Deb, and [3] H. G. Beyer, and K. Deb, "On
self-adaptive features in real-parameter evolutionary algorithm", IEEE
Trans. Evol. Comp., Vol. 5, No.
3, pp. 250-270, Jun. 2001. |
|
Description of the method |
NSGA-II
is one of the most efficient multi-objective evolutionary algorithms using
elitist approach [1], [2]. Its particular fitness assignment scheme consists
in sorting the population in different fronts using the non-domination order relation.
Then, to form the next generation, the algorithm combines the current
population and its offspring generated with the standard bimodal crossover
and polynomial operators. Finally, the best individuals in terms of
non-dominance and diversity are chosen. This new version of NSGA has a low
time complexity of O(N logN), where N is the population size. In
this study, standard bimodal crossover (SBX) [3] and
polynomial mutation operators are used. For the algorithm parameters, the
following values are used: population size N=100, maximum number of
generations T=100, mutation probability 0.1, crossover probability 0.9, and
the distribution indexes for crossover and mutation operators are As
optimization of the safety isolating transformer is a non-linear constrained
problem the external penalty approach is used. The objective function and
non-linear constraints are combined to formulate the following sub-problem:
Where f1(X) = Mtot
(X), f2(X) = 1-ren(X), are the both
original objective functions to be optimized, gi(X) are the
m=6 inequality constraints. The parameter µ is a penalty factor
updated at each generation k as follow:
a is a positive parameter set to 10. µ0 is the
upper limit of µ(k), given by the
users and must be positive and very large. |
|
Publication of the method |
|
