Information Technology Reference
In-Depth Information
candidate solutions are represented by chromosomes based on floating-point numbers.
In the mutation process of a DE algorithm, the weighted difference between two ran-
domly selected population members is added to a third member to generate a mutated
solution. Then, a crossover operator follows to combine the mutated solution with the
target solution so as to generate a trial solution. Thereafter, a selection operator is ap-
plied to compare the fitness function value of both competing solutions, namely, target
and trial solutions to determine who can survive for the next generation. Since DE
was first introduced to solve the Chebychev polynomial fitting problem by Storn &
Price [31], it has been successfully applied in a variety of applications that can be found
in Corne et. al [5], Lampinen [19], Babu & Onwubolu [1]; and Price et al. [22].
Currently, there are several variants of DE algorithms. We follow the DE/rand/1/bin
scheme of Storn & Price [31] with the inclusion of SPV rule in the algorithm. Pseu-
docode of the DE algorithm is given in Fig 6.1.
Initialize parameters
Initialize the target population individuals
Find the tour of the target population individuals
Evaluate the target population individuals
Apply local search to the target population individuals (Optional)
Do { Obtain the mutant population individuals
Obtain the trial population individuals
Find the tour of trial population individuals
Evaluate the trial population individuals
Do selection between the target and trial population individuals
Apply local search to the target population individuals (Optional)
} While (Not Termination)
Fig. 6.1. DE Algorithm with Local Search
The basic elements of DE algorithm are summarized as follows:
Target individual: X i
denotes the i th
individual in the population at generation t and
is defined as X i = x i 1 , x i 2 ,..., x in ,where x ij is the parameter value of the i th individual
with respect to the j th dimension ( j = 1 , 2 ,..., m ).
Mutant individual: V i
denotes the i th individual in the population at generation t and
is defined as V i = v i 1 , v i 2 ,..., v in ,where v ij is the parameter value of the i th individual
with respect to the j th dimension ( j = 1 , 2 ,..., m ).
Trial individual: U i
denotes the i th
individual in the population at generation t and is
defined as U i = u i 1 , u i 2 ,..., u in ,where u ij is the parameter value of the i th
individual
with respect to the j th dimension ( j = 1 , 2 ,..., m ).
Target population: X k is the set of NP individuals in the target population at generation
t , i.e., X k = X 1 , X 2 ,..., X NP .
Search WWH ::




Custom Search