Inequality's Arrow: The Role of Greed and Order in Genetic Algorithms

Moderated greedy search is based on the idea that it is helpful for greedy search algorithms to make non-optimal choices “once in a while.” This notion can be made precise by using the majorizationtheoretic approach to greedy algorithms. Majorization is the study of pre-orderings induced by doubly stochastic matrices. A majorization operator when applied to a distribution makes it “less unequal,” where inequality is defined with respect to a very wide class of measures known as Schur-convex functions. It is shown that proportional selection, point crossover and point mutations are all majorization operators. It is also shown that with respect to the majorization-theoretic definition, the standard GA is a moderated greedy algorithm. Some consequences of this result are discussed.