Discrete Set Handling - Differential Evolution: A Topic for Global Permutation-Based Combinatorial Optimization - page 178

ExpForm nmbr : PaddedForm nmbr, 6, 5 , ExponentFunction 1& ,
NumberFormat 1 " E " 3& , NumberSigns " ", " " ;
BestInd pop : Module best, ind, str ,
best Position , Min 1 1 & Transpose pop 1 ;
ind pop best ;
str "Best individual is on position " ToString best
" with cost value " ToString ExpForm ind 1 " and
parameters " ToString ind 2 ;
Print str ;
Return Flatten best, ind ,1
BestInd np

Best individual is on position 7 with cost
value 3.41433 E 2 and parameters 297.175, 150.458
7, 341.433, 297.175, 150.458
Fig. 7.25. Best individual from population

NewPop Pop : MapThread If 1 1 2 1 , 1, 2 &,
Pop, CostFunction 1 , 1 & Flatten
MapIndexed CheckInterval 1, 2 &, 1 ,1 &
Flatten Table If Cr Random , Pop i, 2, j ,
1 i, j , i, NP , j, Dim & F 1 1, 2
1 2, 2 1 3, 2 & Pop 1 & MapIndexed
SelectOther 2 1 &, Pop ,1

Fig. 7.26. Compressed DE form

Repair Sol : Module Temp, MissingValue, Solution, Pos, Size ,
Solution Sol; Size Length Solution ;
MissingValue RandomRelist Complement Range Size , Solution ;
Pos & Position Solution, Range Size ;

Drop Solution, & Pos Solution Sort Flatten MapIndexed

Drop 1, 1 &, 1 & MapIndexed RandomRelist 1 &, &
Join Temp & 1 & Range Length 1 & Flatten
Position Flatten Dimensions Temp Flatten Pos &

Range Size , ? 1 & , Greater ;

Pos Sort Pos, Less ;
MapThread Solution Insert Solution, 1, 2 &, MissingValue, Pos
Return Solution

Fig. 7.27. Repair routine

The Repair function is broken down and explained in-depth. The initial process is
to find all the missing values in the solution. Since this is a permutative solution, each
value is exist only once in the solution. Therefore it stands to reason that if there are
more than one single value in the solution, then some values will be missing.

The function:
MissingValue = RandomRelist[Complement[Range[Size] , Solution]]; finds the missing
values in the solution.