Discrete Set Handling - Differential Evolution: A Topic for Global Permutation-Based Combinatorial Optimization - page 174

In[26]:= Table Random Integer, 1, NP , i, 3

3, 6, 8

Out[26]=

Fig. 7.12. Random values

SelectOther active : Module ,
rand 0, 0, 0 ;
While rand 1 rand 2 rand 1 rand 3 rand 2
rand 3 active rand 1 active rand 2
active rand 3 , rand Table Random Integer, 1, NP , i, 3 ;
Return rand

Fig. 7.13. SelectOther function

SelectOther active : Module rand 0, 0, 0, 0, 0 , allvals ,
While allvals Append rand, active ;
Length allvals Length Union allvals ,
rand Table Random Integer, 1, NP , i, 5 ;
Return rand

Fig. 7.14. SelectOther compressed function

In[29]:= SelectOther 1

2, 8, 3 Out[29]=

Fig. 7.15. Three random indexes

This command returns the initial population of individuals with the structure Cost-
Value,parameter1,parameter2,..,parameterNP. NP is a size of the population.
Canonical version of the DE is based on the selection of the three (or more based on
DE version) randomly chosen individuals from the population. Random selection, or
more precisely, random selection of three pointers, can be done by command Table in
Fig 7.12.
The random values selects pointers to three individuals of NP . To avoid the possibil-
ity that two or more will be the same, SelectOther function is used. Its argument active
is a pointer to the actively selected individual

− parent. SelectOther function is shown

in Fig 7.13.
SelectOther function can also be given in a compressed form as in Fig 7.14.
Counters are used for selection of three different individuals

from NP individuals. Fig 7.15 shows three individuals selected from the first solution
(parent). Note that all these individuals differ from the first one (position 3).
Till this point, the initial population has been initialized and three individuals have
been randomly selected from the population. In the following step, the function Se-
lectOther is applied to the entire population at once. Mathematica language allows
parallel

{ 1 , 2 ,.., NP } and { i , 3 }

like programming, which is visible throughout of the code. This is also the
case of the following command of function MapIndexed whichisusedtoapply Selec-
tOther on all individuals, so that the virtual population of pointers (randomly selected

−