The ( p , L , s , B ) Distribution : A Selection Scheme For Ranked Populations

A bilinear selection scheme for ranked populations is presented. The deVelopment of the selection scheme is motivated by the desire for a generationally dependant selection mechanism that can be adjusted in an intuitive manner. The selection mechanism is dehned by a four parameter (p, l, c, B) bilinear cumulative probabiliry distribution. Expressions for the mean and variance of the proposed bilinear distrrbution are developed along with expressions for takeover time. The mean and variance equations derived for the proposed bilinear distribution are equated with those for tournament selection for tournament sizes ranging from 2 to 10. It is shown that simple superposition of the proposed bilinear disbibution allows one to approximate more complex cumulative probability distributions in an efficient manner. Expressions for the mean and variance for two superimposed bilinear distributions are provided. The resulting multil inear selection mechanism (pi, l i , c;, B;,1), is shown to be efficient to program and allows for uncoupled contol of the section pressure and selection variance in a dynamic and intuitive maruler.