Editing Crossover (evolutionary algorithm) (section)

=== Order crossover (OX1) ===
The order crossover goes back to Davis<ref name=":0" /> in its original form and is presented here in a slightly generalized version with more than two crossover points. It transfers information about the relative order from the second parent to the offspring. First, the number and position of the crossover points are determined randomly. The resulting gene sequences are then processed as described below:
{| 
|- 
| '''Procedure'''
|  &nbsp;
| '''''Example'''''
| &nbsp;
| '''''Example Chromosome'''''
|-
| colspan=5 | <hr style="background-color:black; height:2px;">
|- style="vertical-align: top; "
| style="width:38%;" | &nbsp;
| style="width:1%;"  | &nbsp;
| style="width:30%;" | ''Let be given two permutations of the same set.''
| style="width:1%;"  | &nbsp;
| style="width:30%;" | <math>P_0 = \left( A,B,C,D,E,F,G,H,I,J \right)</math> and <math>P_1 = \left( B,D,A,H,J,C,E,G,F,I \right)</math>
|-
| colspan=5 | <hr style="background-color:gray;">
|- style="vertical-align: top; "
| Randomly select gene segments in <math>P_0</math>.
| &nbsp;
| ''Here two segments from gene position 1 to 2 and from 6 to 8.''
| &nbsp;
| style="vertical-align: middle;" | <math>P_0 = \left( \underline {A,B},C,D,E,\underline {F,G,H},I,J \right)</math>
|-
| colspan=5 | <hr style="background-color:gray;">
|- style="vertical-align: top;"
| As a child permutation, a permutation is generated that contains the selected gene segments of <math>P_0</math> in the same position.
| &nbsp;
| ''The open positions are indicated by question marks.''
| &nbsp;
| style="vertical-align: middle;" | <math>P_C = \left( A,B,?,?,?,F,G,H,?,? \right)</math>
|-
| colspan=5 | <hr style="background-color:gray;">
|- style="vertical-align: top;"
| The remaining missing genes are now also transferred, but in the order in which they appear in <math>P_1</math>.
| &nbsp;
| ''The missing genes of <math>P_0</math> in the example are:''
| &nbsp;
| <math>P_\text{missing} = \left\{ C,D,E,I,J \right\}</math>
<math>P_{\text{in order from } P_1} = \left( D,J,C,E,I \right)</math>
|-
| colspan=5 | <hr style="background-color:gray;">
|- style="vertical-align: top;"
| This results in the completed child genome.
| &nbsp;
| ''The transferred genes are underlined:''
| &nbsp;
| <math>P_C = \left( A,B,\underline {D,J,C},F,G,H,\underline {E,I} \right)</math>
|-
| colspan=5 | <hr style="background-color:gray;">
|}

Among other things, order crossover is well suited for scheduling multiple workflows, when used in conjunction with 1- and n-point crossover.<ref>{{Citation |last1=Jakob |first1=Wilfried |title=Fast Multi-objective Scheduling of Jobs to Constrained Resources Using a Hybrid Evolutionary Algorithm |date=2008 |url=http://link.springer.com/10.1007/978-3-540-87700-4_102 |work=Parallel Problem Solving from Nature – PPSN X |volume=LNCS 5199 |pages=1031–1040 |editor-last=Rudolph |editor-first=Günter |place=Berlin, Heidelberg |publisher=Springer |doi=10.1007/978-3-540-87700-4_102 |isbn=978-3-540-87699-1 |access-date=2023-01-14 |last2=Quinte |first2=Alexander |last3=Stucky |first3=Karl-Uwe |last4=Süß |first4=Wolfgang |editor2-last=Jansen |editor2-first=Thomas |editor3-last=Beume |editor3-first=Nicola |editor4-last=Lucas |editor4-first=Simon|url-access=subscription }}</ref>