A building-block royal road where crossover is provably essential

One of the most controversial yet enduring hypotheses about what genetic algorithms (GAs) are good for concerns the idea that GAs process building-blocks. More specifically, it has been suggested that crossover in GAs can assemble short low-order schemata of above average fitness (building blocks) to create higher-order higher-fitness schemata. However, there has been considerable difficulty in demonstrating this rigorously and intuitively. Here we provide a simple building-block function that a GA with twopoint crossover can solve on average in polynomial time, whereas an asexual population or mutation hill-climber cannot. Categories and Subject Descriptors I.2.8 [Artificial Inteligence]: Problem Solving, Search – heuristic methods; F.2.2 [Analysis of Algorithms and Problem Complexity]: Non-numerical Algorithms and Problems. General Terms Algorithms, Performance, Theory. Keywords Mutation, crossover, modularity, building block hypothesis, genetic algorithms theory, royal roads.

• Type: Conference
• Year: 2007
• Where: GECCO
• Authors: Richard A. Watson, Thomas Jansen
• Keywords: Building Block, GECCO 2007, Genetic Algorithms, Short Low-order Schemata