Genetic Algorithm with Migration on Topology Conserving Maps

Optimization problems depending on external variables (parameters) are treated with the help of a Kohonen network extended by a genetic algorithm (GA). The optimal solution is assumed to have continuous dependence on the external variables. The GA was generalized to organize individuals into subpopulations, which were allocated in the space of the external variables in an optimal fashion by Kohonen digitization. Individuals were allowed to breed within their own subpopulations and in neighboring ones (migration). To illustrate the strength of the modified GA the optimal control of a simulated robot-arm is treated: a falling ping-pong ball has to be caught by a bat without bouncing. It is shown that the simultaneous optimization problem (for different values of the external parameter) can be solved successfully, and that migration can considerably reduce computation time.