A branch-and-cut algorithm for the Multiple Steiner TSP with Order constraints

Borne, Sylvie; Mahjoub, Ali Ridha; Taktak, Raouia

doi:10.1016/j.endm.2013.05.129

Cited by 12 publications

(7 citation statements)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…() and Fleischmann (), where its NP‐hardness is also proved. The Steiner TSP is specially suitable to model network design (Borne et al., ), package delivery (Zhang et al., , ), and routing (Letchford et al., ) problems. All of them are typically modeled using sparse graphs.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

A GRASP heuristic using path‐relinking and restarts for the Steiner traveling salesman problem

Interian

Ribeiro

2017

Int Trans Operational Res

View full text Add to dashboard Cite

The traveling salesman problem (TSP) is one of the most studied problems in combinatorial optimization. Given a set of nodes and the distances between them, it consists in finding the shortest route that visits each node exactly once and returns to the first. Nevertheless, more flexible and applicable formulations of this problem exist and can be considered. The Steiner TSP (STSP) is a variant of the TSP that assumes that only a given subset of nodes must be visited by the shortest route, eventually visiting some nodes and edges more than once. In this paper, we adapt some classical TSP constructive heuristics and neighborhood structures to the STSP variant. In particular, we propose a reduced 2‐opt neighborhood and we show that it leads to better results in smaller computation times. Computational results with an implementation of a GRASP heuristic using path‐relinking and restarts are reported. In addition, ten large test instances are generated. All instances and their best‐known solutions are made available for download and benchmarking purposes.

show abstract

Section: Introductionmentioning

confidence: 99%

“…A network design problem consisting of multiple Steiner TSPs with order constraints is studied in Borne et al. (), using an integer linear programming formulation and a branch‐and‐cut algorithm. An extension of the STSP in which the edge traversal costs are stochastic and correlated is studied in Letchford and Nasiri ().…”

Section: Introductionmentioning

confidence: 99%

A GRASP heuristic using path‐relinking and restarts for the Steiner traveling salesman problem

Interian

Ribeiro

2017

Int Trans Operational Res

View full text Add to dashboard Cite

show abstract

“…In the past two decades the mTSP received great attention, and various approaches have been proposed to solve the problem. For this we may refer branch-and-cut (Borne et al 2013), Cuckoo search (Ouaarab et al 2013), Firefly algorithm (Ma et al 2014), and Neural network (Hsu et al 1991). The main goal is to minimize the total travelling cost of the above problem that is often formulated as assignment based integer linear programming (Bektas 2006).…”

Section: Introductionmentioning

confidence: 99%

A genetic ant colony optimization based algorithm for solid multiple travelling salesmen problem in fuzzy rough environment

Changdar

Pal

Mahapatra³

2016

Soft Comput

View full text Add to dashboard Cite

In this paper, a genetic-ant colony optimization algorithm has been presented to solve a solid multiple Travelling Salesmen Problem (mTSP) in fuzzy rough environment. In solid mTSP, a set of nodes (locations/cities) are given, and each of the cities must be visited exactly once by the salesmen such that all of them start and finish at a depot using different conveyance facility. A solid mTSP is an extension of mTSP where the travellers use different conveyance facilities for travelling from one city to another. To solve an mTSP, a hybrid algorithm has been developed based on the concept of two algorithms, namely genetic algorithm (GA) and ant colony optimization (ACO) based algorithm. Each salesman selects his/her route using ACO and the routes of different salesmen (to construct a complete solution) are controlled by the GA. Here, a set of simple ACO characteristics have further been modified by incorporating a special feature namely 'refinement'. In this paper, we have utilized cyclic crossover and two-point's mutation in the proposed algorithm to solve the problem. The travelling cost is considered as imprecise in nature (fuzzy-rough) and is reduced to its approximate Communicated by V. Loia. B Chiranjit Changdar chiranjit_changdar@yahoo.co.in Rajat Kumar Pal crisp using fuzzy-rough expectation. Computational results with different data sets are presented and some sensitivity analysis has also been made.

show abstract

“…In practice, subset TSP is typically more interesting than TSP: it is often that the set of vertices we want to visit in a graph is much smaller than the whole vertex set. Indeed, subset TSP has been studied extensively in operational research since 1985 [21,51,11,55,43,56] under a different name -Steiner TSP problem. Arora, Grigni, Karger, Klein and Woloszyn [4] observed that subset TSP in planar graphs generalizes the well-studied TSP in Euclidean plane.…”

Section: Introductionmentioning

confidence: 99%

A PTAS for subset TSP in minor-free graphs

Le¹

2020

Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms

View full text Add to dashboard Cite

We give the first PTAS for the subset Traveling Salesperson Problem (TSP) in H-minorfree graphs. This resolves a long standing open problem in a long line of work on designing PTASes for TSP in minor-closed families initiated by Grigni, Koutsoupias and Papadimitriou in FOCS'95. The main technical ingredient in our PTAS is a construction of a nearly light subset (1 + )-spanner for any given edge-weighted H-minor-free graph. This construction is based on a necessary and sufficient condition given by sparse spanner oracles: light subset spanners exist if and only if sparse spanner oracles exist. This relationship allows us to obtain two new results: • An (1 + )-spanner with lightness O( −d+2 ) for any doubling metric of constant dimension d. This improves the earlier lightness bound −O(d) obtained by Borradaile, Le and Wulff-Nilsen [15].

show abstract

A branch-and-cut algorithm for the Multiple Steiner TSP with Order constraints

Cited by 12 publications

References 3 publications

A GRASP heuristic using path‐relinking and restarts for the Steiner traveling salesman problem

A GRASP heuristic using path‐relinking and restarts for the Steiner traveling salesman problem

A genetic ant colony optimization based algorithm for solid multiple travelling salesmen problem in fuzzy rough environment

A PTAS for subset TSP in minor-free graphs

Contact Info

Product

Resources

About