Chicano, F., Whitley D., & Alba E. (2012). Exact computation of the expectation curves for uniform crossover. (Soule, T., & Moore J. H., Ed.).Genetic and Evolutionary Computation Conference, GECCO'12, Philadelphia, PA, USA, July 7-11, 2012. 1301–1308.Uniform crossover is a popular operator used in genetic algorithms to combine two tentative solutions of a problem represented as binary strings. We use the Walsh decomposition of pseudo-Boolean functions and properties of Krawtchouk matrices to exactly compute the expected value for the fitness of a child generated by uniform crossover from two parent solutions. We prove that this expectation is a polynomial in , the probability of selecting the best-parent bit. We provide efficient algorithms to compute this polynomial for ONEMAX and MAX-kSAT problems, but the results also hold for domains such as NK-Landscapes.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech. Spanish Ministry of Science and Innovation and FEDER under contract TIN2011-28194 (the roadME project). Andalusian Government under contract P07-TIC-03044 (DIRICOM project)
