Further Extension of the TSP Assign Neighborhood

We introduce a new extension of Punnen’s exponential neighborhood for the traveling salesman problem (TSP). In contrast to an interesting generalization of Punnen’s neighborhood by De Franceschi, Fischetti and Toth (2005), our neighborhood is searchable in polynomial time, a feature that invites exploitation by heuristic and metaheuristic procedures for the TSP and related problems, including those of De Franceschi, Fischetti and Toth (2005) for the vehicle routing problem. Key words: traveling salesman problem; local search; exponential neighborhood; assign neighborhood Local search heuristics are among the main tools to compute near optimal solutions in large instances of combinatorial optimization problems in relatively short time. These heuristics include variants of both constructive search and improving local search, including more advanced metaheuristic variants such as tabu search, simulated annealing and genetic algorithms, among others. In most cases the neighborhoods used in these algorithms are of polynomial cardinality. One may ask whether it is possible to have exponential size neighborhood