# Evolutionary Algorithms for Vertex Cover

@inproceedings{Evans1998EvolutionaryAF, title={Evolutionary Algorithms for Vertex Cover}, author={Isaac K. Evans}, booktitle={Evolutionary Programming}, year={1998} }

This paper reports work investigating various evolutionary approaches to vertex cover (VC), a well-known NP-Hard optimization problem. Central to each of the algorithms is a novel encoding scheme for VC and related problems that treats each chromosome as a binary decision diagram. As a result, the encoding allows only a (guaranteed optimal) subset of feasible solutions. The encoding also incorporates features of a powerful traditional heuristic for VC that allow initial evolutionary algorithm…

## 33 Citations

A Hybrid Genetic Algorithm for Minimum Vertex Cover Problem

- Computer ScienceIICAI
- 2003

It is demonstrated that when local optimization technique is added to genetic algorithm to form HGA, it gives near to optimal solution speedy, and new heuristic vertex crossover operator (HVX) is developed especially for MVCP, which converges faster to the global optimal solution.

Analyses of Simple Hybrid Algorithms for the Vertex Cover Problem

- Computer Science, MathematicsEvolutionary Computation
- 2009

This paper makes a first step into the rigorous analysis of such combinations for combinatorial optimization problems, the subject of which is the vertex cover problem for which several approximation algorithms have been proposed.

The Applicability of Genetic algorithm to Vertex Cover

- Mathematics, Computer Science
- 2015

The future scope of this work intends to apply Diploid Genetic Algorithms to the problem to incorporate robustness into the proposed algorithm.

Analysis of the $(1+1)$-EA for Finding Approximate Solutions to Vertex Cover Problems

- Computer ScienceIEEE Transactions on Evolutionary Computation
- 2009

A theoretical analysis that explains empirical results is presented concerning the random local search algorithm and the (1+1)-EA and a lower bound for the worst case approximation ratio, slightly less than two, is proved.

On improving approximate solutions by evolutionary algorithms

- Computer Science2007 IEEE Congress on Evolutionary Computation
- 2007

The aim of this paper is to make a first step into the rigorous analysis of such combinations for combinatorial optimization problems, the subject of which is the vertex cover problem for which several approximation algorithms have been proposed.

The COMPSET Algorithm for Subset Selection

- Computer ScienceIJCAI
- 2005

Preliminary results on complex SAT, Max Clique, 0/1 Multidimensional Knapsack and Vertex Cover problems show that COMPSET improves the efficient stochastic hill climbing and tabu search algorithms by up to two orders of magnitudes.

A local search method based on edge age strategy for minimum vertex cover problem in massive graphs

- Computer ScienceExpert Syst. Appl.
- 2021

A Stochastic Local Search Approach to Vertex Cover

- Computer ScienceKI
- 2007

This work introduces a novel stochastic local search algorithm for the vertex cover problem and evaluates its performance on the commonly used DIMACS benchmarks for the related clique problem, finding that its approach is competitive with the current best stochastically local search algorithms for finding cliques.

Combining Edge Weight and Vertex Weight for Minimum Vertex Cover Problem

- Computer ScienceFAW
- 2014

VEWLS is presented, which is the first time to combine two weighting schemes for the MVC problem, and outperforms NuMVC, the state-of-the-art local search algorithm for MVC, on 73% and 68% of the instances, respectively.

On the applicability of Diploid Genetic Algorithms in Vertex Cover Problem

- Computer ScienceCSI Transactions on ICT
- 2016

This work presents a novel approach to solve the Vertex Cover Problem using Diploid Genetic Algorithm using the capacity of producing better results as compared to Simple Genetic Algorithms.

## References

SHOWING 1-10 OF 18 REFERENCES

An evolutionary heuristic for the maximum independent set problem

- Computer ScienceProceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence
- 1994

The results clearly indicate that genetic algorithms can be successfully used as heuristics for finding good approximative solutions for this highly constrained optimization problem.

Optimized Crossover for the Independent Set Problem

- Computer ScienceOper. Res.
- 1997

A knowledge-based crossover mechanism for genetic algorithms that exploits the structure of the solution rather than its coding, and yields one of the best heuristics for the independent set problem in terms of robustness and time performance.

A practical method for computing vertex covers for large graphs

- Computer Science[Proceedings] 1992 IEEE International Symposium on Circuits and Systems
- 1992

Empirical data indicate that PDI consistently outperforms other reported vertex cover heuristics, including those that require orders of magnitude greater execution time.

A Greedy Randomized Adaptive Search Procedure for Maximum Independent Set

- MathematicsOper. Res.
- 1994

Computational results indicate that the heuristic frequently finds the optimal or expected optimal solution in a fraction of the time required by implementations of simulated annealing, tabu search, and an exact partial enumeration method.

A Local-Ratio Theorem for Approximating the Weighted Vertex Cover Problem

- Mathematics, Computer ScienceWG
- 1983

Enhanced genetic algorithms in constrained search spaces with emphasis in parallel environments

- Computer Science
- 1993

This thesis investigates methods to enhance the performance of the Genetic Algorithms in these search spaces both theoretically and in application domains and results show that the Parallel Genetic Al algorithm is indeed more efficient that the sequential Genetic Algorithm in its search.

A genetic learning strategy in constrained search spaces

- Computer ScienceProceedings of the Twenty-Fifth Hawaii International Conference on System Sciences
- 1992

A randomized validation procedure to limit the genetic search to feasible regions of the search space is described and analysis of the effect of the validation procedure on genetic optimization is presented.

Approximation Algorithms for NP-Hard Problems

- Computer ScienceSIGA
- 1997

This book reviews the design techniques for approximation algorithms and the developments in this area since its inception about three decades ago and the "closeness" to optimum that is achievable in polynomial time.

An Inherently Parallel Method for Heuristic Problem-Solving: Part II-Example Applications

- BusinessIEEE Trans. Parallel Distributed Syst.
- 1995

The results of an empirical study of 90 example instances of these problems indicate that PDI consistently out-performs previously published heuristics for the vertex cover problem, and can typically generate solutions within a few percent of optimal for flow-shop and job-shop problems.

Embracing premature convergence: the Hypergamous Parallel Genetic Algorithm

- Computer Science1998 IEEE International Conference on Evolutionary Computation Proceedings. IEEE World Congress on Computational Intelligence (Cat. No.98TH8360)
- 1998

An alternative genetic algorithm that uses only recombination as its global search operator, the Hypergamous Parallel Genetic Algorithm (HPGA) embraces premature convergence as exponential-like convergence to some (probabilistic) local optimum.