M individuals are used to explore the N-dimensional parameter space
X_{i}^k = (X_{i, 1}^k, X_{i, 2}^k, \ldots, X_{i, N}^k) is the kth-iteration
for the ith-individual. X is updated via the rule
X_{i, j}^{k+1} = X_{i, j}^k + I(X^k){i,j} + RandomWalk{i,j}^k
The intensity function I(X) should be monotonic
The optimization stops either because the number of iterations has been
reached or because the stationary function value limit has been reached.
The current implementation extends the normal Firefly Algorithm with a
differential evolution (DE) optimizer according to:
Afnizanfaizal Abdullah, et al. "A New Hybrid Firefly Algorithm for Complex
and Nonlinear Problem". Volume 151 of the series Advances in Intelligent and
Soft Computing pp 673-680, 2012.
http://link.springer.com/chapter/10.1007%2F978-3-642-28765-7_81
In effect this implementation provides a fully fledged DE global optimizer
as well. The Firefly Algorithm was easy to combine with DE because it already
contained a step where the current solutions are sorted. The population is
then divided into two subpopulations based on their order. The subpopulation
with the best results are updated via the firefly algorithm. The worse
subpopulation is updated via the DE operator:
Y^{k+1} = X_{best}^k + F(X_{r1}^k - X_{r2}^k)
and
X_{i,j}^{k+1} = if R_{i,j} <= CR Y_{i,j}^{k+1}
if R_{i,j} > CR X_{i,j}^{k+1}
Where CR is the crossover constant, and R is a random uniformly distributed
number
The main process is as follows:
M individuals are used to explore the N-dimensional parameter space X_{i}^k = (X_{i, 1}^k, X_{i, 2}^k, \ldots, X_{i, N}^k) is the kth-iteration for the ith-individual. X is updated via the rule X_{i, j}^{k+1} = X_{i, j}^k + I(X^k){i,j} + RandomWalk{i,j}^k
The intensity function I(X) should be monotonic The optimization stops either because the number of iterations has been reached or because the stationary function value limit has been reached.
The current implementation extends the normal Firefly Algorithm with a differential evolution (DE) optimizer according to: Afnizanfaizal Abdullah, et al. "A New Hybrid Firefly Algorithm for Complex and Nonlinear Problem". Volume 151 of the series Advances in Intelligent and Soft Computing pp 673-680, 2012. http://link.springer.com/chapter/10.1007%2F978-3-642-28765-7_81
In effect this implementation provides a fully fledged DE global optimizer as well. The Firefly Algorithm was easy to combine with DE because it already contained a step where the current solutions are sorted. The population is then divided into two subpopulations based on their order. The subpopulation with the best results are updated via the firefly algorithm. The worse subpopulation is updated via the DE operator: Y^{k+1} = X_{best}^k + F(X_{r1}^k - X_{r2}^k) and X_{i,j}^{k+1} = if R_{i,j} <= CR Y_{i,j}^{k+1} if R_{i,j} > CR X_{i,j}^{k+1} Where CR is the crossover constant, and R is a random uniformly distributed number