In this work a co-evolutionary approach is used in conjunction with Genetic Programming operators in order to find certain transition rules for two-step discrete dynamical systems. This issue is similar to the well-known artificial-ant problem. We seek the dynamic system to produce a trajectory leading from given initial values to a maximum of a given spatial functional.This problem is recast into the framework of input-output relations for controllers, and the optimization is performed on program trees describing input filters and finite state machines incorporated by these controllers simultaneously. In the context of Genetic Programming there is always a set of test cases which has to be maintained for the evaluation of program trees. These test cases are subject to evolution here, too, so we employ a so-called host-parasitoid model in order to evolve optimizing dynamical systems.Reinterpreting these systems as algorithms for finding the maximum of a functional under constraints, we have derived a paradigm for the automatic generation of adapted optimization algorithms via optimal control. We provide numerical examples generated by the GP-system MathEvEco. These examples refer to key properties of the resulting strategies and they include statistical evidence showing that for this problem of system identification the co-evolutionary approach is superior to standard Genetic Programming.
An Algebraic Framework to Represent Finite State Machines in Single-Layer Recurrent Neural Networks
