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Lower bounding procedure for the Asymmetric Quadratic Traveling Salesman Problem

Borzou Rostami(brostami***at***mathematik.tu-dortmund.de)
Federico Malucelli(federico.malucelli***at***polimi.it)
Pietro Belotti(pietrobelotti***at***fico.com)
Stefano Gualandi(stefano.gualandi***at***gmail.com)

Abstract: In this paper we consider the Asymmetric Quadratic Traveling Salesman Problem. Given a directed graph and a function that maps every pair of consecutive arcs to a cost, the problem consists in finding a cycle that visits every vertex exactly once and such that the sum of the costs is minimum. We propose an extended Linear Programming formulation that has a variable for each cycle in the graph. Since the number of cycles is exponential in the graph size, we propose a column generation approach. We compare the bounds resulting from this new formulation with those obtained by some linearization techniques for 0-1 quadratic optimization or specifically proposed for the QTSP. Computational results on some set of benchmarks used in the literature show that the column generation approach is very promising.

Keywords: Traveling salesman, Quadratic Traveling Salesman Problem, Column Generation, Lower bound, Cycle cover

Category 1: Combinatorial Optimization

Category 2: Nonlinear Optimization (Quadratic Programming )

Category 3: Integer Programming ((Mixed) Integer Linear Programming )

Citation:

Download: [PDF]

Entry Submitted: 02/04/2015
Entry Accepted: 02/07/2015
Entry Last Modified: 02/04/2015

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