Convergence analysis of a segmentation algorithm for the evolutionary training of neural networks

In contrast to standard genetic algorithms with generational reproduction, we adopt the viewpoint of the reactor algorithm (Dittrich & Banzhaf, 1998). which is similar to steady-state genetic algorithms, but without ranking. This permits an analysis similar to Eigen's (1971) molecular evolution model. From this viewpoint, we consider combining segments from different populations into one genotype at every time-step, which can be regarded as many-parent combinations with fined crossover points, and is comparable to cooperative evolution (Potter & De Jong, 2000). We present fired-point analysis and phase portraits of the competitive dynamics, with the result that only the first-order (single parent) replicators exhibit global optimisation. A segmentation algorithm is developed that theoretically ensures convergence to the global optimum while Peeping the cooperative or reactor aspect for a better exploration of the search space. The algorithm creates different population islands for such cases of competition that otherwise cannot be solved correctly by the population dynamics. The population islands have different segmentation boundaries, which are generated by combining wed converged components into new segments. This gives first-order replicators that have the appropriate dynamical properties to compete with new solutions. Furthermore, the population islands communicate information about what solution strings have been found already, so new ones can be favoured. strings that have converged on any island Pre taken as the characterisaton of a fitness peak and disallowed afterwards to enforce diversity. This has been found to be successful in the simulation of an evolving neural network. We also present a simulation example where the genotypes on different islands have converged differently. A perspective from this research is to recombine budding blocks explicitly from the different islands, each time the populations converge.