GRASP with path-relinking

Resende, Maurício G. C.; Ribeiro, Celso C.

doi:10.1007/978-1-4939-6530-4_9

Cited by 3 publications

(2 citation statements)

References 64 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In a subsequent work, Ribeiro et al [203] implemented a hybrid GRASP multi‐start heuristic in which solutions are generated using the MST‐based heuristics from Poggi de Aragão and Werneck [179]. They also employed neighborhood search heuristics, and reduction tests from Duin and Volgenant [74] and Uchoa et al [225] as a preprocessing, and path‐relinking [201] as a postprocessing procedure.…”

Section: Heuristicsmentioning

confidence: 99%

Solving Steiner trees: Recent advances, challenges, and perspectives

Ljubić

2020

Networks

View full text Add to dashboard Cite

The Steiner tree problem (STP) in graphs is one of the most studied problems in combinatorial optimization. Since its inception in 1970, numerous articles published in the journal Networks have stimulated new theoretical and computational studies on Steiner trees: from approximation algorithms, heuristics, metaheuristics, all the way to exact algorithms based on (mixed) integer linear programming, fixed parameter tractability, or combinatorial branch‐and‐bounds. The pervasive applicability and relevance of Steiner trees have been reinforced by the recent 11th DIMACS Implementation Challenge in 2014 and the PACE 2018 Challenge. This article provides an overview of the rich developments from the last three decades for the STP in graphs and highlights the most recent computational studies for some of its closely related variants.

show abstract

Section: Heuristicsmentioning

confidence: 99%

Solving Steiner trees: Recent advances, challenges, and perspectives

Ljubić

2020

Networks

View full text Add to dashboard Cite

show abstract

“…The VNS algorithm has been shown to perform well in various problems. Its applications include the max-cut combinatorial problem [17,18], the scheduling problem [19,20], the layouting problem [21], the vehicle routing problem [22], and the multiprocessor scheduling problem with communication delays [23]. It has, also, been used to tune proportional-integral-derivative controllers in cyber-physical systems [24].…”

Section: Introductionmentioning

confidence: 99%

Constructing the Neighborhood Structure of VNS Based on Binomial Distribution for Solving QUBO Problems

Pambudi

Kawamura

2022

Algorithms

View full text Add to dashboard Cite

The quadratic unconstrained binary optimization (QUBO) problem is categorized as an NP-hard combinatorial optimization problem. The variable neighborhood search (VNS) algorithm is one of the leading algorithms used to solve QUBO problems. As neighborhood structure change is the central concept in the VNS algorithm, the design of the neighborhood structure is crucial. This paper presents a modified VNS algorithm called “B-VNS”, which can be used to solve QUBO problems. A binomial trial was used to construct the neighborhood structure, and this was used with the aim of reducing computation time. The B-VNS and VNS algorithms were tested on standard QUBO problems from Glover and Beasley, on standard max-cut problems from Helmberg–Rendl, and on those proposed by Burer, Monteiro, and Zhang. Finally, Mann–Whitney tests were conducted using α=0.05, to statistically compare the performance of the two algorithms. It was shown that the B-VNS and VNS algorithms are able to provide good solutions, but the B-VNS algorithm runs substantially faster. Furthermore, the B-VNS algorithm performed the best in all of the max-cut problems, regardless of problem size, and it performed the best in QUBO problems, with sizes less than 500. The results suggest that the use of binomial distribution, to construct the neighborhood structure, has the potential for further development.

show abstract