A Tabu Search Heuristic Based on k-Diamonds for the Weighted Feedback Vertex Set Problem

Carrabs, Francesco; Cerulli, Raffaele; Gentili, Monica; Parlato, Gennaro

doi:10.1007/978-3-642-21527-8_66

Cited by 8 publications

(16 citation statements)

References 18 publications

(19 reference statements)

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“…d). Finally, let us define the k ‐diamond graphs . Definition A weighted k‐diamond

{scriptD}_{R, z} = (V_{R}, E_{R}, w)

, where

k \geq 1, R = {r_{1}, r_{2}, \dots, r_{k}}

and

z \in V_{R}

, is an undirected and vertex weighted graph where (i) each vertex

v \in V_{R}

is included in a simple path between exactly one of the k apices

r_{i} \in R

and the vertex z and (ii)

{scriptD}_{R, z} [V_{R} ∖ {z}]

is a forest with k connected components .…”

Section: Definitions and Notationsmentioning

confidence: 99%

“…b). The WFVS problem can be solved in linear time on the k ‐diamond graphs using the dynamic programming (DP) algorithm provided in .…”

Section: A Memetic Approach: Basic Componentsmentioning

confidence: 99%

“…As we will see in Section , the introduction of FLS procedure and the criterion used by MA to invoke the two local search, makes our algorithm much more effective than the ITS metaheuristic that uses only the BLS local search.…”

Section: The Memetic Algorithmmentioning

confidence: 99%

“…For the cases that are not known to be polynomially solvable, there have been intensive efforts on approximation algorithms whereas very few heuristics are proposed in the literature for the WFVS. To the best of our knowledge, for the FVS problem a GRASP procedure and a simulated annealing algorithm are introduced whereas two metaheuristics XTS and ITS are proposed for the WFVS. The tabu search XTS is based on the “eXploring Tabu Search” schema .…”

Section: Introductionmentioning

confidence: 99%

“…This open question is solved in where a linear time procedure is proposed. The authors embedded this procedure into an iterative tabu search ITS for the WFVS problem .…”

Section: Introductionmentioning

confidence: 99%

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A memetic algorithm for the weighted feedback vertex set problem

2014

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Given an undirected and vertex weighted graph G = (V , E , w ), the Weighted Feedback Vertex Set Problem consists of finding the subset F ⊆ V of vertices, with minimum weight, whose removal results in an acyclic graph. Finding the minimum feedback vertex set in a graph is an important combinatorial problem that has a variety of real applications. In this article, we introduce a memetic algorithm for this problem. We propose an efficient greedy procedure that quickly generates chromosomes with specific characteristics and a wise application of recent local search procedures based on k -diamonds. Computational results show that the proposed algorithm outperforms the effectiveness of two other metaheuristics recently proposed in the literature for this problem.

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“…d). Finally, let us define the k ‐diamond graphs . Definition A weighted k‐diamond

{scriptD}_{R, z} = (V_{R}, E_{R}, w)

, where

k \geq 1, R = {r_{1}, r_{2}, \dots, r_{k}}

and

z \in V_{R}

, is an undirected and vertex weighted graph where (i) each vertex

v \in V_{R}

is included in a simple path between exactly one of the k apices

r_{i} \in R

and the vertex z and (ii)

{scriptD}_{R, z} [V_{R} ∖ {z}]

is a forest with k connected components .…”

Section: Definitions and Notationsmentioning

confidence: 99%

“…b). The WFVS problem can be solved in linear time on the k ‐diamond graphs using the dynamic programming (DP) algorithm provided in .…”

Section: A Memetic Approach: Basic Componentsmentioning

confidence: 99%

Section: The Memetic Algorithmmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

“…This open question is solved in where a linear time procedure is proposed. The authors embedded this procedure into an iterative tabu search ITS for the WFVS problem .…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations