Design and Management of Complex Technical Processes and Systems by Means of Computational Intelligence Methods Real Royal Road Functions — Where Crossover Provably Is Essential Real Royal Road Functions — Where Crossover Provably Is Essential *

Mutation and crossover are the main search operators of different variants of evolutionary algorithms. Despite the many discussions on the importance of crossover nobody has proved rigorously for some explicitly defined fitness functions fn : {0, 1} n → R that a genetic algorithm with crossover (but without idealization) can optimize fn in expected polynomial time while all evolution strategies based only on mutation (and selection) need expected exponential time. Here such functions and proofs are presented. For some functions one-point crossover is appropriate while for others uniform crossover is the right choice.