A restricted Lagrangean approach to the traveling salesman problem

@article{Balas1981ARL,
  title={A restricted Lagrangean approach to the traveling salesman problem},
  author={Egon Balas and Nicos Christofides},
  journal={Math. Program.},
  year={1981},
  volume={21},
  pages={19-46}
}
We describe an algorithm for the asymmetric traveling salesman problem (TSP) using a new, restricted Lagrangean relaxation based on the assignment problem (AP). The Lagrange multipliers are constrained so as to guarantee the continued optimality of the initial AP solution, thus eliminating the need for repeatedly solving AP in the process of computing multipliers. We give several polynomially bounded procedures for generating valid inequalities and taking them into the Lagrangean function with… CONTINUE READING
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