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 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 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 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.

scholarly journals A Matheuristic Approach Combining Local Search and Mathematical Programming

2016 ◽  
Vol 2016 ◽  
pp. 1-7 ◽  
Author(s):  
Carolina Lagos ◽  
Guillermo Guerrero ◽  
Enrique Cabrera ◽  
Stefanie Niklander ◽  
Franklin Johnson ◽  
...  
Keyword(s):  
Mathematical Programming ◽  
Local Search ◽  
Large Scale ◽  
Search Algorithm ◽  
Facility Location Problem ◽  
Specific Information ◽  
Local Search Algorithm ◽  
Capacitated Facility Location Problem ◽  
Capacitated Facility Location ◽  
Installation Cost

A novel matheuristic approach is presented and tested on a well-known optimisation problem, namely, capacitated facility location problem (CFLP). The algorithm combines local search and mathematical programming. While the local search algorithm is used to select a subset of promising facilities, mathematical programming strategies are used to solve the subproblem to optimality. Proposed local search is influenced by instance-specific information such as installation cost and the distance between customers and facilities. The algorithm is tested on large instances of the CFLP, where neither local search nor mathematical programming is able to find good quality solutions within acceptable computational times. Our approach is shown to be a very competitive alternative to solve large-scale instances for the CFLP.

scholarly journals Circumspect descent prevails in solving random constraint satisfaction problems

2008 ◽  
Vol 105 (40) ◽  
pp. 15253-15257 ◽  
Author(s):  
Mikko Alava ◽  
John Ardelius ◽  
Erik Aurell ◽  
Petteri Kaski ◽  
Supriya Krishnamurthy ◽  
...  
Keyword(s):  
Local Search ◽  
Linear Time ◽  
Search Algorithm ◽  
Solution Space ◽  
Search Algorithms ◽  
Constraint Satisfaction Problems ◽  
Problem Instance ◽  
Stochastic Local Search ◽  
Local Search Algorithms ◽  
Local Energy Minimum

We study the performance of stochastic local search algorithms for random instances of the K-satisfiability (K-SAT) problem. We present a stochastic local search algorithm, ChainSAT, which moves in the energy landscape of a problem instance by never going upwards in energy. ChainSAT is a focused algorithm in the sense that it focuses on variables occurring in unsatisfied clauses. We show by extensive numerical investigations that ChainSAT and other focused algorithms solve large K-SAT instances almost surely in linear time, up to high clause-to-variable ratios α; for example, for K = 4 we observe linear-time performance well beyond the recently postulated clustering and condensation transitions in the solution space. The performance of ChainSAT is a surprise given that by design the algorithm gets trapped into the first local energy minimum it encounters, yet no such minima are encountered. We also study the geometry of the solution space as accessed by stochastic local search algorithms.

scholarly journals Two-goal Local Search and Inference Rules for Minimum Dominating Set

2020 ◽  
Author(s):  
Shaowei Cai ◽  
Wenying Hou ◽  
Yiyuan Wang ◽  
Chuan Luo ◽  
Qingwei Lin
Keyword(s):  
Local Search ◽  
Search Algorithm ◽  
Dominating Set ◽  
Inference Rules ◽  
Local Search Algorithm ◽  
Minimum Dominating Set ◽  
Massive Graphs ◽  
Construction Procedure ◽  
Almost All ◽  
Main Ideas

Minimum dominating set (MinDS) is a canonical NP-hard combinatorial optimization problem with applications. For large and hard instances one must resort to heuristic approaches to obtain good solutions within reasonable time. This paper develops an efficient local search algorithm for MinDS, which has two main ideas. The first one is a novel local search framework, while the second is a construction procedure with inference rules. Our algorithm named FastDS is evaluated on 4 standard benchmarks and 3 massive graphs benchmarks. FastDS obtains the best performance for almost all benchmarks, and obtains better solutions than state-of-the-art algorithms on massive graphs.

scholarly journals Effective Heuristic Algorithms Solving the Jobshop Scheduling Problem with Release Dates

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1221
Author(s):  
Tao Ren ◽  
Yan Zhang ◽  
Shuenn-Ren Cheng ◽  
Chin-Chia Wu ◽  
Meng Zhang ◽  
...  
Keyword(s):  
Differential Evolution ◽  
Large Scale ◽  
Manufacturing Industry ◽  
Heuristic Algorithms ◽  
Search Algorithm ◽  
Optimal Schedule ◽  
Differential Evolution Algorithm ◽  
Developed Countries ◽  
Productivity Level ◽  
Jobshop Scheduling

Manufacturing industry reflects a country’s productivity level and occupies an important share in the national economy of developed countries in the world. Jobshop scheduling (JSS) model originates from modern manufacturing, in which a number of tasks are executed individually on a series of processors following their preset processing routes. This study addresses a JSS problem with the criterion of minimizing total quadratic completion time (TQCT), where each task is available at its own release date. Constructive heuristic and meta-heuristic algorithms are introduced to handle different scale instances as the problem is NP-hard. Given that the shortest-processing-time (SPT)-based heuristic and dense scheduling rule are effective for the TQCT criterion and the JSS problem, respectively, an innovative heuristic combining SPT and dense scheduling rule is put forward to provide feasible solutions for large-scale instances. A preemptive single-machine-based lower bound is designed to estimate the optimal schedule and reveal the performance of the heuristic. Differential evolution algorithm is a global search algorithm on the basis of population, which has the advantages of simple structure, strong robustness, fast convergence, and easy implementation. Therefore, a hybrid discrete differential evolution (HDDE) algorithm is presented to obtain near-optimal solutions for medium-scale instances, where multi-point insertion and a local search scheme enhance the quality of final solutions. The superiority of the HDDE algorithm is highlighted by contrast experiments with population-based meta-heuristics, i.e., ant colony optimization (ACO), particle swarm optimization (PSO) and genetic algorithm (GA). Average gaps 45.62, 63.38 and 188.46 between HDDE with ACO, PSO and GA, respectively, are demonstrated by the numerical results with benchmark data, which reveals the domination of the proposed HDDE algorithm.

scholarly journals Local Search with Dynamic-Threshold Configuration Checking and Incremental Neighborhood Updating for Maximum k-plex Problem

2020 ◽  
Vol 34 (03) ◽  
pp. 2343-2350 ◽  
Author(s):  
Peilin Chen ◽  
Hai Wan ◽  
Shaowei Cai ◽  
Jia Li ◽  
Haicheng Chen
Keyword(s):  
Local Search ◽  
Search Algorithm ◽  
Promising Result ◽  
Dynamic Threshold ◽  
Local Search Algorithm ◽  
Local Search Algorithms ◽  
Worst Case ◽  
Massive Graphs ◽  
Configuration Checking ◽  
Novel Strategy

The Maximum k-plex Problem is an important combinatorial optimization problem with increasingly wide applications. In this paper, we propose a novel strategy, named Dynamic-threshold Configuration Checking (DCC), to reduce the cycling problem of local search. Due to the complicated neighborhood relations, all the previous local search algorithms for this problem spend a large amount of time in identifying feasible neighbors in each step. To further improve the performance on dense and challenging instances, we propose Double-attributes Incremental Neighborhood Updating (DINU) scheme which reduces the worst-case time complexity per iteration from O(|V|⋅ΔG) to O(k · Δ‾G). Based on DCC strategy and DINU scheme, we develop a local search algorithm named DCCplex. According to the experiment result, DCCplex shows promising result on DIMACS and BHOSLIB benchmark as well as real-world massive graphs. Especially, DCCplex updates the lower bound of the maximum k-plex for most dense and challenging instances.

scholarly journals A Variable Neighborhood Walksat-Based Algorithm for MAX-SAT Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-11 ◽  
Author(s):  
Noureddine Bouhmala
Keyword(s):  
Local Search ◽  
Optimization Problems ◽  
Search Algorithm ◽  
Search Algorithms ◽  
Boolean Formula ◽  
Local Search Algorithms ◽  
Neighborhood Structure ◽  
Np Complete ◽  
Max Sat ◽  
Almost All

The simplicity of the maximum satisfiability problem (MAX-SAT) combined with its applicability in many areas of artificial intelligence and computing science made it one of the fundamental optimization problems. This NP-complete problem refers to the task of finding a variable assignment that satisfies the maximum number of clauses (or the sum of weights of satisfied clauses) in a Boolean formula. The Walksat algorithm is considered to be the main skeleton underlying almost all local search algorithms for MAX-SAT. Most local search algorithms including Walksat rely on the 1-flip neighborhood structure. This paper introduces a variable neighborhood walksat-based algorithm. The neighborhood structure can be combined easily using any local search algorithm. Its effectiveness is compared with existing algorithms using 1-flip neighborhood structure and solvers such as CCLS and Optimax from the eighth MAX-SAT evaluation.

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