Lower tolerance-based Branch and Bound algorithms for the ATSP

Authors:
Remco Germs;Boris Goldengorin;Marcel Turkensteen
Affiliations:
Faculty of Economics and Business, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands;Faculty of Economics and Business, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands and Department of Applied Mathematics and Informatics, The Higher School of Economics, ...;CORAL, Department of Business Studies, Aarhus School of Business and Social Sciences, Aarhus University, Fuglesangs Alle 4, 8210 Aarhus V, Denmark
Venue:
Computers and Operations Research
Year:
2012

Citing 10
Cited 2

Exact solution of large-scale, asymmetric traveling salesman problems

ACM Transactions on Mathematical Software (TOMS)
Computers and Intractability: A Guide to the Theory of NP-Completeness

Computers and Intractability: A Guide to the Theory of NP-Completeness
The Asymmetric Traveling Salesman Problem: Algorithms, Instance Generators, and Tests

ALENEX '01 Revised Papers from the Third International Workshop on Algorithm Engineering and Experimentation
Sensitivity analysis for shortest path problems and maximum capacity path problems in undirected graphs

Mathematical Programming: Series A and B
Graph theory: An algorithmic approach (Computer science and applied mathematics)

Graph theory: An algorithmic approach (Computer science and applied mathematics)
Cut-and-solve: An iterative search strategy for combinatorial optimization problems

Artificial Intelligence
Some basics on tolerances

AAIM'06 Proceedings of the Second international conference on Algorithmic Aspects in Information and Management
Tolerance based algorithms for the ATSP

WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Branching rules revisited

Operations Research Letters
Improving the Hungarian assignment algorithm

Operations Research Letters

The effect of the asymmetry of road transportation networks on the traveling salesman problem

Computers and Operations Research
A backbone based TSP heuristic for large instances

Journal of Heuristics

Quantified Score

Hi-index	0.01

Visualization

Abstract

In this paper, we develop a new tolerance-based Branch and Bound algorithm for solving NP-hard problems. In particular, we consider the asymmetric traveling salesman problem (ATSP), an NP-hard problem with large practical relevance. The main algorithmic contribution is our lower bounding strategy that uses the expected costs of including arcs in the solution to the assignment problem relaxation of the ATSP, the so-called lower tolerance values. The computation of the lower bound requires the calculation of a large set of lower tolerances. We apply and adapt a finding from [23] that makes it possible to compute all lower tolerance values efficiently. Computational results show that our Branch and Bound algorithm exhibits very good performance in comparison with state-of-the-art algorithms, in particular for difficult clustered ATSP instances.