A local search algorithm with tabu strategy and perturbation mechanism for generalized vertex cover problem

2016 ◽  
Vol 28 (7) ◽  
pp. 1775-1785 ◽  
Author(s):  
Ruizhi Li ◽  
Shuli Hu ◽  
Yiyuan Wang ◽  
Minghao Yin
Keyword(s):  
Local Search ◽  
Search Algorithm ◽  
Vertex Cover ◽  
Local Search Algorithm ◽  
Vertex Cover Problem ◽  
Cover Problem

scholarly journals NuMVC: An Efficient Local Search Algorithm for Minimum Vertex Cover

2013 ◽  
Vol 46 ◽  
pp. 687-716 ◽  
Author(s):  
S. Cai ◽  
K. Su ◽  
C. Luo ◽  
A. Sattar
Keyword(s):  
Local Search ◽  
Heuristic Algorithms ◽  
State Of The Art ◽  
Search Algorithm ◽  
Vertex Cover ◽  
Experimental Studies ◽  
Maximum Clique ◽  
Local Search Algorithm ◽  
Two Stage ◽  
Edge Weighting

The Minimum Vertex Cover (MVC) problem is a prominent NP-hard combinatorial optimization problem of great importance in both theory and application. Local search has proved successful for this problem. However, there are two main drawbacks in state-of-the-art MVC local search algorithms. First, they select a pair of vertices to exchange simultaneously, which is time-consuming. Secondly, although using edge weighting techniques to diversify the search, these algorithms lack mechanisms for decreasing the weights. To address these issues, we propose two new strategies: two-stage exchange and edge weighting with forgetting. The two-stage exchange strategy selects two vertices to exchange separately and performs the exchange in two stages. The strategy of edge weighting with forgetting not only increases weights of uncovered edges, but also decreases some weights for each edge periodically. These two strategies are used in designing a new MVC local search algorithm, which is referred to as NuMVC. We conduct extensive experimental studies on the standard benchmarks, namely DIMACS and BHOSLIB. The experiment comparing NuMVC with state-of-the-art heuristic algorithms show that NuMVC is at least competitive with the nearest competitor namely PLS on the DIMACS benchmark, and clearly dominates all competitors on the BHOSLIB benchmark. Also, experimental results indicate that NuMVC finds an optimal solution much faster than the current best exact algorithm for Maximum Clique on random instances as well as some structured ones. Moreover, we study the effectiveness of the two strategies and the run-time behaviour through experimental analysis.

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

Two Local Search Algorithms for Partition Vertex Cover Problem

2016 ◽  
Vol 13 (1) ◽  
pp. 743-751 ◽  
Author(s):  
Yupeng Zhou ◽  
Haochen Zhang ◽  
Ruizhi Li ◽  
Jianan Wang
Keyword(s):  
Local Search ◽  
Vertex Cover ◽  
Search Algorithms ◽  
Local Search Algorithms ◽  
Vertex Cover Problem ◽  
Cover Problem

scholarly journals An Efficient Heuristic Algorithm for Solving Connected Vertex Cover Problem

2018 ◽  
Vol 2018 ◽  
pp. 1-10
Author(s):  
Yongfei Zhang ◽  
Jun Wu ◽  
Liming Zhang ◽  
Peng Zhao ◽  
Junping Zhou ◽  
...  
Keyword(s):  
Local Search ◽  
Vertex Cover ◽  
Cost Savings ◽  
Industrial Applications ◽  
Wavelength Assignment ◽  
Vertex Cover Problem ◽  
Connected Vertex Cover ◽  
Cover Problem ◽  
Comparison Algorithms ◽  
Connected Vertex

The connected vertex cover (CVC) problem, which has many important applications, is a variant of the vertex cover problem, such as wireless network design, routing, and wavelength assignment problem. A good algorithm for the problem can help us improve engineering efficiency, cost savings, and resources consumption in industrial applications. In this work, we present an efficient algorithm GRASP-CVC (Greedy Randomized Adaptive Search Procedure for Connected Vertex Cover) for CVC in general graphs. The algorithm has two main phases, i.e., construction phase and local search phase. In the construction phase, to construct a high quality feasible initial solution, we design a greedy function and a restricted candidate list. In the local search phase, the configuration checking strategy is adopted to decrease the cycling problem. The experimental results demonstrate that GRASP-CVC is better than other comparison algorithms in terms of effectivity and efficiency.

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

An efficient local search for partial vertex cover problem

2016 ◽  
Vol 30 (7) ◽  
pp. 2245-2256 ◽  
Author(s):  
Yupeng Zhou ◽  
Yiyuan Wang ◽  
Jian Gao ◽  
Na Luo ◽  
Jianan Wang
Keyword(s):  
Local Search ◽  
Vertex Cover ◽  
Vertex Cover Problem ◽  
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.

scholarly journals An Efficient Heuristic Algorithm for Solving Connected Vertex Cover Problem in Graph Theory

2018 ◽  
Author(s):  
Yongfei Zhang ◽  
Jun Wu ◽  
Liming Zhang ◽  
Peng Zhao ◽  
Junping Zhou ◽  
...  
Keyword(s):  
Local Search ◽  
Vertex Cover ◽  
Cost Savings ◽  
Industrial Applications ◽  
Wavelength Assignment ◽  
Vertex Cover Problem ◽  
Configuration Checking ◽  
Connected Vertex Cover ◽  
Cover Problem ◽  
Connected Vertex

The connected vertex cover (CVC) problem is a variant of the vertex cover problem, which has many important applications, such as wireless network design, routing and wavelength assignment problem, etc. A good algorithm for the problem can help us improve engineering efficiency, cost savings and resources in industrial applications. In this work, we present an efficient algorithm GRASP-CVC (Greedy Randomized Adaptive Search Procedure for Connected Vertex Cover) for CVC in general graphs. The algorithm has two main phases, i.e., construction phase and local search phase. To construct a high quality feasible initial solution, we design a greedy function and a restricted candidate list in the construction phase. The configuration checking strategy is adopted to decrease the cycling problem in the local search phase. The experimental results demonstrate that GRASP-CVC is competitive with the other competitive algorithm, which validate the effectivity and efficiency of our GRASP-CVC solver.

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