A reaction network arises when a set of reactants (chromosomes, chemicals, economic goods, or the like) recombine at specified rates to produce other reactants in the set. When the reactants are characterized in terms of “reactive regions” (schemata, active sites, building blocks), reaction networks can be modeled by classic stochastic urn models. The corresponding Markov processes are specified by matrices that, for realistic problems, are small enough to allow standard matrix operations and Monte Carlo estimates of important properties of the trajectory of the process, such as the expected time to first occurrence of some designated reactant.

Building blocks are a ubiquitous feature at all levels of human understanding, from perception through science and innovation. Genetic algorithms are designed to exploit this prevalence. A new, more robust class of genetic algorithms, cohort genetic algorithms (cGA's), provides substantial advantages in exploring search spaces for building blocks while exploiting building blocks already found. To test these capabilities, a new, general class of test functions, the hyperplane-defined functions (hdf's), has been designed. Hdf's offer the means of tracing the origin of each advance in performance; at the same time hdf's are resistant to reverse engineering, so that algorithms cannot be designed to take advantage of the characteristics of particular examples.