Local Optima in Graph Partitioning

We now have a reasonable local search procedure, and we could just stop here. But there is still a lot of room for improvement in terms of the quality of the solutions produced, The search space includes some local optima that are quite far from the global solution. Here's one which has cost 2.

This local optima is bad. What can be done about such suboptimal solutions? We could expand the neighborhood size to allow two swaps at a time, but this particular bad instance would still stubbornly resist. Instead, let's look at some other generic schemes for improving local search procedures.