Theoretical analysis of a mutation-based evolutionary algorithm for a tracking problem in the lattice

Evolutionary algorithms are often applied for solving optimization problems that are too complex or different from classical problems so that the application of classical methods is difficult. One example are dynamic problems that change with time. An important class of dynamic problems is the class of tracking problems where an algorithm has to find an approximately optimal solution and insure an almost constant quality in spite of the changing problem. For the application of evolutionary algorithms to static optimization problems, the distribution of the optimization time and most often its expected value are most important. Adopting this perspective a simple tracking problem in the lattice is considered and the performance of a mutation-based evolutionary algorithm is evaluated. For the static case, asymptotically tight upper and lower bounds are proven. These results are applied to derive results on the tracking performance for different rates of change.