Fixed Set Search Applied to the Minimum Weighted Vertex Cover Problem

2019 ◽  
pp. 490-504 ◽  
Author(s):  
Raka Jovanovic ◽  
Stefan Voß
Keyword(s):  
Vertex Cover ◽  
Vertex Cover Problem ◽  
Fixed Set ◽  
Weighted Vertex ◽  
Cover Problem

scholarly journals Parameterized Analysis of Multiobjective Evolutionary Algorithms and the Weighted Vertex Cover Problem

2019 ◽  
Vol 27 (4) ◽  
pp. 559-575
Author(s):  
Mojgan Pourhassan ◽  
Feng Shi ◽  
Frank Neumann
Keyword(s):  
Evolutionary Algorithm ◽  
Complexity Analysis ◽  
Minimum Weight ◽  
Vertex Cover ◽  
Optimal Solution ◽  
Population Based ◽  
Mutation Operator ◽  
Vertex Cover Problem ◽  
Weighted Vertex ◽  
Cover Problem

Evolutionary multiobjective optimization for the classical vertex cover problem has been analysed in Kratsch and Neumann ( 2013 ) in the context of parameterized complexity analysis. This article extends the analysis to the weighted vertex cover problem in which integer weights are assigned to the vertices and the goal is to find a vertex cover of minimum weight. Using an alternative mutation operator introduced in Kratsch and Neumann ( 2013 ), we provide a fixed parameter evolutionary algorithm with respect to [Formula: see text], the cost of an optimal solution for the problem. Moreover, we present a multiobjective evolutionary algorithm with standard mutation operator that keeps the population size in a polynomial order by means of a proper diversity mechanism, and therefore, manages to find a 2-approximation in expected polynomial time. We also introduce a population-based evolutionary algorithm which finds a [Formula: see text]-approximation in expected time [Formula: see text].

scholarly journals Crown reductions for the Minimum Weighted Vertex Cover problem

2008 ◽  
Vol 156 (3) ◽  
pp. 292-312 ◽  
Author(s):  
Miroslav Chlebík ◽  
Janka Chlebíková
Keyword(s):  
Vertex Cover ◽  
Vertex Cover Problem ◽  
Weighted Vertex ◽  
Cover Problem

NuMWVC: A novel local search for minimum weighted vertex cover problem

2019 ◽  
Vol 71 (9) ◽  
pp. 1498-1509 ◽  
Author(s):  
Ruizhi Li ◽  
Shuli Hu ◽  
Shaowei Cai ◽  
Jian Gao ◽  
Yiyuan Wang ◽  
...  
Keyword(s):  
Local Search ◽  
Vertex Cover ◽  
Vertex Cover Problem ◽  
Weighted Vertex ◽  
Cover Problem

An efficient local search framework for the minimum weighted vertex cover problem

2016 ◽  
Vol 372 ◽  
pp. 428-445 ◽  
Author(s):  
Ruizhi Li ◽  
Shuli Hu ◽  
Haochen Zhang ◽  
Minghao Yin
Keyword(s):  
Local Search ◽  
Vertex Cover ◽  
Vertex Cover Problem ◽  
Weighted Vertex ◽  
Cover Problem

scholarly journals Multi-Objective Neighborhood Search Algorithm Based on Decomposition for Multi-Objective Minimum Weighted Vertex Cover Problem

2019 ◽  
Vol 11 (13) ◽  
pp. 3634
Author(s):  
Shuli Hu ◽  
Xiaoli Wu ◽  
Huan Liu ◽  
Yiyuan Wang ◽  
Ruizhi Li ◽  
...  
Keyword(s):  
Search Algorithm ◽  
Vertex Cover ◽  
Score Function ◽  
Search Space ◽  
Single Type ◽  
Neighborhood Search ◽  
Multi Objective ◽  
Vertex Cover Problem ◽  
Weighted Vertex ◽  
Cover Problem

The multi-objective minimum weighted vertex cover problem aims to minimize the sum of different single type weights simultaneously. In this paper, we focus on the bi-objective minimum weighted vertex cover and propose a multi-objective algorithm integrating iterated neighborhood search with decomposition technique to solve this problem. Initially, we adopt the decomposition method to divide the multi-objective problem into several scalar optimization sub-problems. Meanwhile, to find more possible optimal solutions, we design a mixed score function according to the problem feature, which is applied in initializing procedure and neighborhood search. During the neighborhood search, three operators ( A d d , D e l e t e , S w a p ) explore the search space effectively. We performed numerical experiments on many instances, and the results show the effectiveness of our new algorithm (combining decomposition and neighborhood search with mixed score) on several experimental metrics. We compared our experimental results with the classical multi-objective algorithm non-dominated sorting genetic algorithm II. It was obviously shown that our algorithm can provide much better results than the comparative algorithm considering the different metrics.

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