Forward Backward Transformation - Differential Evolution: A Topic for Global Permutation-Based Combinatorial Optimization - page 41

2. Conversion
a) Discrete to Floating Conversion : This conversion schema transforms the parent
solution into the required continuous solution.
b) DE Strategy : The DE strategy transforms the parent solution into the child
solution using its inbuilt crossover and mutation schemas.
c) Floating to Discrete Conversion : This conversion schema transforms the con-
tinuous child solution into a discrete solution.
3. Mutation
a) Relative Mutation Schema : Formulates the child solution into the discrete so-
lution of unique values.
4. Improvement Strategy
a) Mutation : Standard mutation is applied to obtain a better solution.
b) Insertion : Uses a two-point cascade to obtain a better solution.
5. Local Search
a) Local Search : 2 Opt local search is used to explore the neighborhood of the
solution.

3.4.1 Repairment

In order to repair the solutions, each solution is initially vetted. Vetting requires the res-
olution of two parameters: firstly to check for any bound offending values, and secondly
for repeating values in the solution. If a solution is detected to have violated a bound, it
is dragged to the offending boundary.

Input : D
Array Solution , ViolateVal , MissingVal
int Counter
for (int i = 0; i < D ; i ++) {
for (int j = 0; j < D ; j ++) {
if ( i == Solution [ j ]) {
Counter ++;

}

if ( Counter > 1) {
int Index = 0;
for (int j = 0; j < D ; j ++) {
if ( i = Solution [ j ])

{

Index ++
if ( Index > 1) {
ViolateVal Append

← }

j ;

}}}
if ( Counter == 0)

{
MissingVal Append

←

i ; }

Counter = 0;
}

Fig. 3.3. Pseudocode for replication detection