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 and 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 and De Jong, 2000). We present fixed-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 keeping 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 blends have different segmentation boundaries which are generated by combining well converged components into new segments. This gives first-order replicators that have the appropriate dynamical properties to compete with new solutions.