Efficient separation routines for the symmetric traveling salesman problem I: general tools and comb separation

Efficient separation routines for the symmetric traveling salesman problem II: separating multi handle inequalities

Mathematical Programming Approaches to the Traveling Salesman Problem

The Traveling Salesman Problem or TSP is a fundamental andwell-known problem in combinatorial optimisation. At present, the mostsuccessful algorithms for solving large-scale instances of the TSP to proven(near-)optimality are based on integer programming. This entry introducesthe main theoretical and algorithmic tools involved. Topics covered include:formulations of the TSP,...

Computing with Domino-Parity Inequalities for the Traveling Salesman Problem (TSP)

W describe methods for implementing separation algorithms for domino-parity inequalities for the symmetric traveling salesman problem. These inequalities were introduced by Letchford (2000), who showed that the separation problem can be solved in polynomial time when the support graph of the LP solution is planar. In our study we deal with the problem of how to use this algorithm in the general...

Implementing Domino-Parity Inequalities for the Traveling Salesman Problem

We describe an implementation of Letchford’s domino-parity inequalities for the (symmetric) traveling salesman problem. The implementation includes pruning methods to restrict the search for dominoes, a parallelization of the main domino-building step, heuristics to obtain planar-support graphs, a set of safe-shrinking routines, a random-walk heuristic to extract additional violated constraints...

Solving the Traveling Salesman Problem by an Efficient Hybrid Metaheuristic Algorithm

The traveling salesman problem (TSP) is the problem of finding the shortest tour through all the nodes that a salesman has to visit. The TSP is probably the most famous and extensively studied problem in the field of combinatorial optimization. Because this problem is an NP-hard problem, practical large-scale instances cannot be solved by exact algorithms within acceptable computational times. ...