New tighter polynomial length formulations for the asymmetric traveling salesman problem with and without precedence constraints

Sarin, Subhash C.; Sherali, Hanif D.; Bhootra, Ajay

doi:10.1016/j.orl.2004.03.007

Cited by 71 publications

(32 citation statements)

References 11 publications

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“…The Multiple Traveling Salesman Problem (mTSP) is a generalization of the Traveling Salesman Problem (TSP) in which more than one salesman is allowed [21,22]. Given a set of cities, and m salesmen, the objective of is to determine a tour for each salesman such that, starting from the same base city, each salesman visits at least one city and returns to the base city so as to minimize the total cost.…”

Section: Multiple Traveling Salesman Problemmentioning

confidence: 99%

Multi-robot Task Allocation: A Review of the State-of-the-Art

Khamis

Hussein

Elmogy

2015

Studies in Computational Intelligence

333

193

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Multi-robot systems (MRS) are a group of robots that are designed aiming to perform some collective behavior. By this collective behavior, some goals that are impossible for a single robot to achieve become feasible and attainable. There are several foreseen benefits of MRS compared to single robot systems such as the increased ability to resolve task complexity, increasing performance, reliability and simplicity in design. These benefits have attracted many researchers from academia and industry to investigate how to design and develop robust versatile MRS by solving a number of challenging problems such as complex task allocation, group formation, cooperative object detection and tracking, communication relaying and self-organization to name just a few. One of the most challenging problems of MRS is how to optimally assign a set of robots to a set of tasks in such a way that optimizes the overall system performance subject to a set of constraints. This problem is known as Multi-robot Task Allocation (MRTA) problem. MRTA is a complex problem especially when it comes to heterogeneous unreliable robots equipped with different capabilities that are required to perform various tasks with different requirements and constraints in an optimal way. This chapter provides a comprehensive review on challenging aspects of MRTA problem, recent approaches to tackle this problem and the future directions.

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Section: Multiple Traveling Salesman Problemmentioning

confidence: 99%

Multi-robot Task Allocation: A Review of the State-of-the-Art

Khamis

Hussein

Elmogy

2015

Studies in Computational Intelligence

333

193

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“…The MTZ formulation for the ATSP (minimize (1) subject to (2,3,5,7,8,10,11)) is enhanced by the addition of new constraints derived in this section. The constraints account for ordering of boundary nodes as well as all intermediate nodes in the salesman tour.…”

Section: Enhancement Of the Mtz Formulationmentioning

confidence: 99%

“…On the other hand the researchers seek to tighten the polyhedral representation of the initial ATSP formulation to use the best bounds produced by the linear programming relaxation of the initial formulation that guides branching decisions, regardless of the run-time actions taken by the MIP optimizers. There exists an extensive literature on the MTZ constraints, e.g., [4][5][6][7][8]. For a recent overview, see [9].…”

Section: Introductionmentioning

confidence: 99%

A note on the Miller-Tucker-Zemlin model for the asymmetric traveling salesman problem

Sawik¹

2016

Bulletin of the Polish Academy of Sciences Technical Sciences

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Abstract. An enhancement of the Miller-Tucker-Zemlin (MTZ) model for the asymmetric traveling salesman problem is presented by introducing additional constraints to the initial formulation. The constraints account for ordering of boundary nodes as well as all successive nodes in the salesman tour. The enhanced MTZ subtour elimination constraints are computationally compared with the basic MTZ constraints and the version of MTZ lifted by Desrochers and Laporte. The proposed enhancement shows improved performance on a number of asymmetric TSPLIB instances.

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“…Sarin et al [2005] studied the asymmetric traveling salesman problem with and without precedence constraints and proposed five polynomial formulations (therein ATSPxy, L1ATSPxy, SL1ATSPxy, L2ATSPxy and ML1ATSPxy) for the ATSP, whose LP relaxations are stronger than that of RMTZ. Moreover, Sarin et al [2005] showed that the LP relaxation of L1ATSPxy is stronger than that of SL1ATSPxy whose LP relaxation is stronger than that of ATSPxy; the LP relaxations of L1ATSPxy and L2ATSPxy are also stronger than those of formulations L1RMTZ and L2RMTZ by Gouveia and Pires [1999], respectively.…”

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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New tighter polynomial length formulations for the asymmetric traveling salesman problem with and without precedence constraints

Cited by 71 publications

References 11 publications

Multi-robot Task Allocation: A Review of the State-of-the-Art

Multi-robot Task Allocation: A Review of the State-of-the-Art

A note on the Miller-Tucker-Zemlin model for the asymmetric traveling salesman problem

Exact algorithms for different classes of vehicle routing problems

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