A class of lifted path and flow-based formulations for the asymmetric traveling salesman problem with and without precedence constraints

Sherali, Hanif D.; Sarin, Subhash C.; Tsai, Pei-Fang

doi:10.1016/j.disopt.2005.10.004

Cited by 36 publications

(28 citation statements)

References 10 publications

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“…The results for the SD (see Sherali and Driscoll (2002)) and SST formulations were obtained by Sherali et al (2006), using a Dell Workstation PWS 650 Double 2,5 GHZ CPU with the AMPL (Vs. 8.1) and CPLEX MIP Solver (V.s 9,0). The results for the well known multicommodity flow (MCF) formulation were obtained by Oncan et al (2009), using a Pentium IV 3GHZ CPU with the CPLEX BARRIER Solver (Vs. 9.0) The results obtained from our computational experiment show that the All-k model produces quite good gaps for the cumulative version as well as the pure time-dependent version of the ATSP.…”

Section: Computational Resultsmentioning

confidence: 99%

Natural and extended formulations for the Time-Dependent Traveling Salesman Problem

Godinho

Gouveia

Pesneau

2014

Discrete Applied Mathematics

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In this paper we present a new formulation for the Time-Dependent Travelling Salesman Problem (TDTSP). We start by reviewing well known natural formulations with some emphasis on the formulation by Picard and Queyranne (1978). The main feature of this formulation is that it uses, as a subproblem, an exact description of the n-circuit problem. Then, we present a new formulation that uses more variables and is based on using, for each node, a stronger subproblem, namely a ncircuit subproblem with the additional constraint that the corresponding node is not repeated in the circuit. Although the new model has more variables and constraints than the original PQ model, the results given from our computational experiments show that the linear programming relaxation of the new model gives, for many of the instances tested, gaps that are close to zero. Thus, the new model is worth investigating for solving TDTSP instances. We have also provided a complete characterization of the feasible set of the corresponding linear programming relaxation in the space of the variables of the PQ model. This characterization permits us to suggest alternative methods of using the proposed formulations.

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Section: Computational Resultsmentioning

confidence: 99%

Natural and extended formulations for the Time-Dependent Traveling Salesman Problem

Godinho

Gouveia

Pesneau

2014

Discrete Applied Mathematics

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“…This technique is a generic strategy for constructing tight polyhedral relaxations of the feasible set of 0-1 mixed integer linear programs ( [37], [38], [39]). During the last few years, it has been successfully applied to derive tightened compact formulations for the asymmetric traveling salesman (see [40] and [41]). Research into this exciting direction is recommended for future studies.…”

Section: Discussionmentioning

confidence: 99%

The Steiner Tree Problem with Delays: A compact formulation and reduction procedures

Leggieri

Haouari

Triki

2014

Discrete Applied Mathematics

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This paper investigates the Steiner Tree Problem with Delays (STPD), a variation of the classical Steiner Tree problem that arises in multicast routing. We present a polynomial-size formulation for this challenging NP-hard problem. The LP relaxation of this formulation is enhanced through the derivation of new lifted Miller-Tucker-Zemlin subtour elimination constraints. Furthermore, we present several preprocessing techniques for both reducing the problem size and tightening the LP relaxation. Finally, we describe an effective hybrid heuristic, that combines optimization and intuitive techniques. We report the results of extensive computational experiments on instances with up to 1000 nodes. These results attest to the efficacy of the combination of the enhanced formulation, reduction techniques, and heuristic.

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“…Godinho et al [2011] pointed out that variables t k ij can be interpreted in the same way as the flow variables w k ij used in formulation CLAUS. Öncan et al [2009] showed that the LP relaxation of SST is stronger than those of MCF+, whereas Sherali et al [2006] proved that the LP relaxation of SST is stronger than that of L1ATSPxy.…”

Section: Review Of Polynomial Formulationsmentioning

confidence: 99%

“…An analysis of all the formulations involving variables x ij and v ij (or d ij ) can be found in Gouveia and Pesneau [2006]. Sherali et al [2006] proposed several polynomial formulations. Here, we present formulation SST (therein ATSP6) only, which uses (n − 1) 3 nonnegative continuous variables t k ij , i, j, k = 2, .…”

Section: Review Of Polynomial Formulationsmentioning

confidence: 99%

Exact algorithms for different classes of vehicle routing problems

Roberti¹

2012

4OR-Q J Oper Res

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A class of lifted path and flow-based formulations for the asymmetric traveling salesman problem with and without precedence constraints

Cited by 36 publications

References 10 publications

Natural and extended formulations for the Time-Dependent Traveling Salesman Problem

Natural and extended formulations for the Time-Dependent Traveling Salesman Problem

The Steiner Tree Problem with Delays: A compact formulation and reduction procedures

Exact algorithms for different classes of vehicle routing problems

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