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Author Levine, Matthew S.
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©2000
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Computer programming, programs & data
Subject Keyword Algorithms ♦ Combinatorial optimization ♦ Cutting plane ♦ Experimentation ♦ Minimum cut ♦ Performance ♦ Traveling salesman problem
Abstract Given an instance of the Traveling Salesman Problem (TSP), a reasonable way to get a lower bound on the optimal answer is to solve a linear programming relaxation of an integer programming formulation of the problem. These linear programs typically have an exponential number of constraints, but in theory they can be solved efficiently with the ellipsoid method as long as we have an algorithm that can take a solution and either declare it feasible or find a violated constraint. In practice, it is often the case that many constraints are violated, which raises the question of how to choose among them so as to improve performance. For the simplest TSP formulation it is possible to efficiently find all the violated constraints, which gives us a good chance to try to answer this question empirically. Looking at random two dimensional Euclidean instances and the large instances from TSPLIB, we ran experiments to evaluate several strategies for picking among the violated constraints. We found some information about which constraints to prefer, which resulted in modest gains, but were unable to get large improvements in performance.
ISSN 10846654
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2000-12-01
Publisher Place New York
e-ISSN 10846654
Journal Journal of Experimental Algorithmics (JEA)
Volume Number 5

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Source: ACM Digital Library