3-opt, 4-opt, and the 2.5-opt variant of the traveling salesman problem each have instances requiring exponentially many improving local-search iterations under every pivot rule.
Smoothed analysis of the 2- opt algorithm for the general TSP
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A near-complete resolution of the exponential-time complexity of k-opt for the traveling salesman problem
3-opt, 4-opt, and the 2.5-opt variant of the traveling salesman problem each have instances requiring exponentially many improving local-search iterations under every pivot rule.