A tabu search scheme for abstract problems, with applications to the computation of fixed points

We present a general tabu search iterative algorithm to solve abstract problems on metric spaces. At each iteration, if the current solution turns out to be unacceptable then a neighborhood of unacceptable solutions is determined and excluded for further exploration, in such a way that, under mild assumptions, an acceptable solution is asymptotically reached. Thus our algorithm makes a crucial use of memory to avoid visiting unacceptable solutions more than once. We also present a specialization of our general method to the computation of fixed points.