To overcome this, we may try a more generous neighborhood, for instance 3-change, consisting of tours that differ on up to three edges. And indeed, the preceding bad case gets fixed:

But there is a downside, in that the size of a neighborhood becomes O (n³), making each iteration more expensive. Moreover, there may still be suboptimal local minima, although fewer than before. To avoid these, we would have to go up to 4-change, or higher.

In this manner, efficiency and quality often turn out to be competing considerations in a local search. Efficiency demands neighborhoods that can be searched quickly, but smaller neighborhoods can increase the abundance of low-quality local optima. The appropriate compromise is typically determined by experimentation.