Kalman-extended genetic algorithm for search in nonstationary environments with noisy fitness evaluations

In basic genetic algorithm (GA) applications, the fitness of a solution takes a value that is certain and unchanging. This formulation does not work for ongoing searches for better solutions in a nonstationary environment in which expected solution fitness changes with time in unpredictable ways, or for fitness evaluations corrupted by noise. In such cases, the estimated fitness has an associated uncertainty. The uncertainties due to environmental changes (process noise) and to noisy evaluations (observation noise) can be reduced, at least temporarily, by re-evaluating existing solutions. The Kalman formulation provides a formal mechanism for treating uncertainty in GA. It provides the mechanics for determining the estimated fitness and uncertainty when a new solution is generated and evaluated for the first time. It also provides the mechanics for updating the estimated fitness and uncertainty after an existing solution is re-evaluated and for increasing the uncertainty with the passage of time. A Kalman-extended GA (KGA) is developed to determine when to generate a new individual, and when to re-evaluate an existing one and which to re-evaluate. This KGA is applied to the problem of maintaining a network configuration with minimized message loss, with mobile nodes and stochastic transmission. As the nodes move, the optimal network changes, but information contained within the population of solutions allows efficient discovery of better-adapted solutions. The sensitivity of the KGA to several control parameters is explored.