Editing Crossover (evolutionary algorithm) (section)

=== Further crossover operators for permutations ===
Over time, a large number of crossover operators for permutations have been proposed, so the following list is only a small selection. For more information, the reader is referred to the literature.<ref name=":0" /><ref name=":5" /><ref name=":3" /><ref name=":2" />

# cycle crossover (CX)<ref>{{Citation |last1=Oliver |first1=I.M. |last2=Smith |first2=D.J. |last3=Holland |first3=J. |title=A study of permutation crossover operators on the travelling salesman problem |work=Proceedings of the Second International Conference on Genetic Algorithms and Their Applications (ICGA) |date=1987 |publisher=Lawrence Erlbaum Associates |editor-last=Grefenstette |editor-first=John J. |isbn=978-0-8058-0158-3 |location=Hillsdale, N.J. |pages=224–230 |language=en }}</ref><ref name=":3" />
# order-based crossover (OX2)<ref name=":5" /><ref name=":4">{{Cite book |last=Syswerda |first=Gilbert |title=Handbook of genetic algorithms |date=1991 |publisher=Van Nostrand Reinhold |isbn=0-442-00173-8 |editor-last=Davis |editor-first=Lawrence |location=New York |pages=332–349 |language=en |chapter=Schedule Optimization Using Genetic Algorithms |oclc=23081440 }}</ref>
# position-based crossover (POS)<ref name=":5" /><ref name=":4" />
# edge recombination<ref>{{Citation |last1=Whitley |first1=Darrell |last2=Starkweather |first2=Timothy |last3=Fuquay |first3=D'Ann |title=Scheduling Problems and Traveling Salesmen: The Genetic Edge Recombination Operator |date=1989 |work=Proceedings of the 3rd International Conference on Genetic Algorithms (ICGA) |pages=133–140 |editor-last=Schaffer |editor-first=J.D. |place=San Francisco |publisher=Morgan Kaufmann |isbn=1558600663 }}</ref><ref name=":3" />
# voting recombination (VR)<ref name=":2" />
# alternating-positions crossover (AP)<ref name=":2" />
# maximal preservative crossover (MPX)<ref name=":5" /><ref>{{Citation |last1=Dzubera |first1=John |title=Advanced correlation analysis of operators for the traveling salesman problem |date=1994 |url=http://link.springer.com/10.1007/3-540-58484-6_251 |work=Parallel Problem Solving from Nature — PPSN III |volume=866 |pages=68–77 |editor-last=Davidor |editor-first=Yuval |place=Berlin, Heidelberg |publisher=Springer |doi=10.1007/3-540-58484-6_251 |isbn=978-3-540-58484-1 |access-date=2023-01-15 |last2=Whitley |first2=Darrell |editor2-last=Schwefel |editor2-first=Hans-Paul |editor3-last=Männer |editor3-first=Reinhard|url-access=subscription }}</ref>
# merge crossover (MX)<ref name=":5" /><ref>{{Citation |last1=Blanton |first1=Joe L. |last2=Wainwright |first2=Roger L. |title=Multiple Vehicle Routing with Time and Capacity Constraints Using Genetic Algorithms |date=1993 |work=Proceedings of the 5th International Conference on Genetic Algorithms (ICGA) |pages=452–459 |editor-last=Forrest |editor-first=Stephanie |place=San Francisco |publisher=Morgan Kaufmann |isbn=978-1-55860-299-1 }}</ref>
# sequential constructive crossover operator (SCX)<ref>{{cite thesis |last=Ahmed |first=Zakir Hussain |date=2000 |title=Sequential Constructive Sampling and Related approaches to Combinatorial Optimization |type=PhD |publisher=Tezpur University, India }}</ref>

The usual approach to solving TSP-like problems by genetic or, more generally, evolutionary algorithms, presented earlier, is either to [[Genotypic and phenotypic repair|repair]] illegal descendants or to adjust the operators appropriately so that illegal offspring do not arise in the first place. Alternatively, Riazi suggests the use of a double chromosome representation, which avoids illegal offspring.<ref>{{cite journal |last1=Riazi |first1=Amin |title=Genetic algorithm and a double-chromosome implementation to the traveling salesman problem |journal=SN Applied Sciences |date=14 October 2019 |volume=1 |issue=11 |doi=10.1007/s42452-019-1469-1|doi-access= }}</ref>