Editing Selection (evolutionary algorithm) (section)

==== Linear rank selection ====
Linear ranking, which goes back to Baker,<ref>{{Citation |last=Baker |first=James E. |title=Adaptive Selection Methods for Genetic Algorithms |date=1985 |work=Conf. Proc. of the 1st Int. Conf. on Genetic Algorithms and Their Applications (ICGA)  |pages=101–111 |editor-last=Grefenstette |editor-first=John J. |place=Hillsdale, New. Jersey |publisher=L. Erlbaum Associates |isbn=0-8058-0426-9 }}</ref><ref>{{Citation |last=Baker |first=James E. |title=Reducing Bias and Inefficiency in the Selection Algorithm |date=1987 |work=Conf. Proc. of the 2nd Int. Conf. on Genetic Algorithms and Their Applications (ICGA)  |pages=14–21 |editor-last=Grefenstette |editor-first=John J. |place=Hillsdale, New. Jersey |publisher=L. Erlbaum Associates |isbn=0-8058-0158-8 }}</ref> is often used.<ref name=":0" /><ref name=":1" /><ref>{{Citation |last1=Hoffmeister |first1=Frank |title=Genetic Algorithms and evolution strategies: Similarities and differences |date=1991 |work=Parallel Problem Solving from Nature |volume=496 |pages=455–469 |editor-last=Schwefel |editor-first=Hans-Paul |url= |access-date= |place=Berlin, Heidelberg |publisher=Springer-Verlag |language=en |doi=10.1007/bfb0029787 |isbn=978-3-540-54148-6 |last2=Bäck |first2=Thomas |editor2-last=Männer |editor2-first=Reinhard}}</ref> It allows the selection pressure to be set by the parameter <math>sp </math>, which can take values between 1.0 (no selection pressure) and 2.0 (high selection pressure). The probability <math>P </math> for <math>n</math> rank positions <math>R_i </math> is obtained as follows:
:<math>P(R_i) =\frac{1}{n}\Bigl(sp-(2sp-2)\frac{i-1}{n-1}\Bigr) \quad \quad  1\leq i \leq n ,\quad 1 \leq sp \leq 2 \quad \mathsf{with} \quad P(R_i) \ge 0, \quad \sum_{i=1}^nP(R_i)=1 </math>

Another definition for the probability <math>P</math> for rank positions <math>i</math> is:<ref name=selist>{{cite journal |last1=Jannoud |first1=Ismael |last2=Jaradat |first2=Yousef |last3=Masoud |first3=Mohammad Z. |last4=Manasrah |first4=Ahmad |last5=Alia |first5=Mohammad |title=The Role of Genetic Algorithm Selection Operators in Extending WSN Stability Period: A Comparative Study |journal=Electronics |date=22 December 2021 |volume=11 |issue=1 |pages=28 |doi=10.3390/electronics11010028|doi-access=free }}</ref>
:<math>P(i) =\frac{2*(n-i+1)}{n*(n+1)}</math>