scholarly journals Improving Local Search for Minimum Weight Vertex Cover by Dynamic Strategies

2018 ◽  
Author(s):  
Shaowei Cai ◽  
Wenying Hou ◽  
Jinkun Lin ◽  
Yuanjie Li
Keyword(s):  
Local Search ◽  
Real World ◽  
Heuristic Algorithms ◽  
Minimum Weight ◽  
Vertex Cover ◽  
Independent Set ◽  
Map Labeling ◽  
Massive Graphs ◽  
Real World Problem ◽  
Np Hardness

The minimum weight vertex cover (MWVC) problem is an important combinatorial optimization problem with various real-world applications. Due to its NP hardness, most works on solving MWVC focus on heuristic algorithms that can return a good quality solution in reasonable time. In this work, we propose two dynamic strategies that adjust the behavior of the algorithm during search, which are used to improve a state of the art local search for MWVC named FastWVC, resulting in two local search algorithms called DynWVC1 and DynWVC2. Previous MWVC algorithms are evaluated on graphs with random or hand crafted weights. In this work, we evaluate the algorithms on the vertex weighted graphs that obtained from an important real world problem, the map labeling problem. Experiments show that our algorithm obtains better results than previous algorithms for MWVC and maximum weight independent set (MWIS) on these real world instances. We also test our algorithms on massive graphs studied in previous works, and show significant improvements there.

scholarly journals Finding A Small Vertex Cover in Massive Sparse Graphs: Construct, Local Search, and Preprocess

2017 ◽  
Vol 59 ◽  
pp. 463-494 ◽  
Author(s):  
Shaowei Cai ◽  
Jinkun Lin ◽  
Chuan Luo
Keyword(s):  
Local Search ◽  
Real World ◽  
Large Scale ◽  
Heuristic Algorithms ◽  
Search Algorithm ◽  
Vertex Cover ◽  
Search Algorithms ◽  
Theory And Practice ◽  
Sparse Graphs ◽  
Massive Graphs

The problem of finding a minimum vertex cover (MinVC) in a graph is a well known NP-hard combinatorial optimization problem of great importance in theory and practice. Due to its NP-hardness, there has been much interest in developing heuristic algorithms for finding a small vertex cover in reasonable time. Previously, heuristic algorithms for MinVC have focused on solving graphs of relatively small size, and they are not suitable for solving massive graphs as they usually have high-complexity heuristics. This paper explores techniques for solving MinVC in very large scale real-world graphs, including a construction algorithm, a local search algorithm and a preprocessing algorithm. Both the construction and search algorithms are based on low-complexity heuristics, and we combine them to develop a heuristic algorithm for MinVC called FastVC. Experimental results on a broad range of real-world massive graphs show that, our algorithms are very fast and have better performance than previous heuristic algorithms for MinVC. We also develop a preprocessing algorithm to simplify graphs for MinVC algorithms. By applying the preprocessing algorithm to local search algorithms, we obtain two efficient MinVC solvers called NuMVC2+p and FastVC2+p, which show further improvement on the massive graphs.

scholarly journals A Fast Local Search Algorithm for Minimum Weight Dominating Set Problem on Massive Graphs

2018 ◽  
Author(s):  
Yiyuan Wang ◽  
Shaowei Cai ◽  
Jiejiang Chen ◽  
Minghao Yin
Keyword(s):  
Local Search ◽  
Real World ◽  
Search Algorithm ◽  
Dominating Set ◽  
Minimum Weight ◽  
Local Search Algorithm ◽  
Massive Graphs ◽  
Configuration Checking ◽  
Dominating Set Problem ◽  
Short Time

The minimum weight dominating set (MWDS) problem is NP-hard and also important in many applications. Recent heuristic MWDS algorithms can hardly solve massive real world graphs effectively. In this paper, we design a fast local search algorithm called FastMWDS for the MWDS problem, which aims to obtain a good solution on massive graphs within a short time. In this novel local search framework, we propose two ideas to make it effective. Firstly, we design a new fast construction procedure with four reduction rules to cut down the size of massive graphs. Secondly, we propose the three-valued two-level configuration checking strategy to improve local search, which is interestingly a variant of configuration checking (CC) with two levels and multiple values. Experiment results on a broad range of massive real world graphs show that FastMWDS finds much better solutions than state of the art MWDS algorithms.

Towards faster local search for minimum weight vertex cover on massive graphs

2019 ◽  
Vol 471 ◽  
pp. 64-79 ◽  
Author(s):  
Shaowei Cai ◽  
Yuanjie Li ◽  
Wenying Hou ◽  
Haoran Wang
Keyword(s):  
Local Search ◽  
Minimum Weight ◽  
Vertex Cover ◽  
Massive Graphs

scholarly journals Ground station scheduling optimization for a model of a real-world problem instance

2021 ◽  
Author(s):  
Bryce Wildish
Keyword(s):  
Real World ◽  
Heuristic Algorithms ◽  
Complex Problem ◽  
Initial Guess ◽  
Fine Tuning ◽  
Problem Instance ◽  
Ground Station ◽  
Real World Problem ◽  
Crucial Component ◽  
Orbiting Spacecraft

Effective scheduling of communication windows between orbiting spacecraft and ground stations is a crucial component of efficiently using spacecraft resources. In all but the most trivial cases, this forces the operator to choose a subset of the potentially available access windows such that they can achieve the best possible usage of their hardware and other resources. This is a complex problem not normally solvable analytically, and as a result the standard approach is to apply heuristic algorithms which take an initial guess at a solution and improve upon it in order to increase its quality. Various such algorithms exist, with some being in common practice for this particular problem. This thesis covers the application of several of the most commonly-used algorithms on a problem instance. Additionally, a real-world problem instance is used, and the resultant practical constraints are addressed when applying the heuristics and fine-tuning them for this application.

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.

scholarly journals Ground station scheduling optimization for a model of a real-world problem instance

2021 ◽  
Author(s):  
Bryce Wildish
Keyword(s):  
Real World ◽  
Heuristic Algorithms ◽  
Complex Problem ◽  
Initial Guess ◽  
Fine Tuning ◽  
Problem Instance ◽  
Ground Station ◽  
Real World Problem ◽  
Crucial Component ◽  
Orbiting Spacecraft

Effective scheduling of communication windows between orbiting spacecraft and ground stations is a crucial component of efficiently using spacecraft resources. In all but the most trivial cases, this forces the operator to choose a subset of the potentially available access windows such that they can achieve the best possible usage of their hardware and other resources. This is a complex problem not normally solvable analytically, and as a result the standard approach is to apply heuristic algorithms which take an initial guess at a solution and improve upon it in order to increase its quality. Various such algorithms exist, with some being in common practice for this particular problem. This thesis covers the application of several of the most commonly-used algorithms on a problem instance. Additionally, a real-world problem instance is used, and the resultant practical constraints are addressed when applying the heuristics and fine-tuning them for this application.

scholarly journals Local Search with Noisy Strategy for Minimum Vertex Cover in Massive Graphs

2016 ◽  
pp. 283-294 ◽  
Author(s):  
Zongjie Ma ◽  
Yi Fan ◽  
Kaile Su ◽  
Chengqian Li ◽  
Abdul Sattar
Keyword(s):  
Local Search ◽  
Vertex Cover ◽  
Massive Graphs

scholarly journals Feature Construction for Meta-heuristic Algorithm Recommendation of Capacitated Vehicle Routing Problems

2021 ◽  
Vol 1 (1) ◽  
pp. 1-28
Author(s):  
Hao Jiang ◽  
Yuhang Wang ◽  
Ye Tian ◽  
Xingyi Zhang ◽  
Jianhua Xiao
Keyword(s):  
Local Search ◽  
Vehicle Routing ◽  
Real World ◽  
Heuristic Algorithms ◽  
Image Features ◽  
Vehicle Routing Problems ◽  
Customer Demand ◽  
Routing Problems ◽  
Basic Features ◽  
Capacitated Vehicle

The algorithm recommendation is attracting increasing attention in solving real-world capacitated vehicle routing problems (CVRPs), due to the fact that existing meta-heuristic algorithms often show different performances on different CVRPs. To effectively perform algorithm recommendation for CVRPs, it becomes vital to extract suitable features to characterize the CVRPs accurately. To this end, in this article three groups of penetrating features are proposed to capture the characteristics of CVRPs. The first group consists of some basic features of CVRPs, where several features are suggested to capture the distribution of customer demand, the relationship between customer demand and vehicle capacity, besides some common attributes widely used in CVRPs. The second group is composed of the features extracted from some CVRP solutions generated by local search, where in addition to the feasible and better solutions, the worse solutions and the distribution of travel cost are also used to measure the sensitivity of CVRPs to local search operations. The third group is made up of image features obtained by depicting CVRP instances through images, which is first introduced by us to enhance the generalization of algorithm recommendation. Furthermore, based on the three groups of features, an algorithm recommendation method called ARM-I is built on the basis of a KNN classifier to recommend suitable algorithm for CVRPs. Experimental results on several selected benchmarks demonstrate the effectiveness of the designed features. More interestingly, the proposed ARM-I shows high generalization on real-world instances.

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