Finding the right cutting planes for the TSP
ACM Journal of Experimental Algorithmics(2000)
摘要
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.
更多查看译文
关键词
optimal answer,question empirically,integer programming formulation,dimensional euclidean instance,salesman problem,combinatorial optimization,large improvement,simplest tsp formulation,cutting plane,linear program,performance,experimentation,minimum cut,algorithms,traveling salesman problem,large instance,linear programming relaxation,lower bound
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要