Combinatorial optimization: algorithms and complexity
Combinatorial optimization: algorithms and complexity
The time complexity of maximum matching by simulated annealing
Journal of the ACM (JACM)
Randomized algorithms
Finite Markov chain results in evolutionary computation: a tour d'horizon
Fundamenta Informaticae
Improved approximation algorithms for the vertex cover problem in graphs and hypergraphs
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
Drift analysis and average time complexity of evolutionary algorithms
Artificial Intelligence
Evolutionary Optimization
On the analysis of the (1+ 1) evolutionary algorithm
Theoretical Computer Science
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Introduction to Algorithms
On the Optimization of Unimodal Functions with the (1 + 1) Evolutionary Algorithm
PPSN V Proceedings of the 5th International Conference on Parallel Problem Solving from Nature
Evolutionary Algorithms and the Maximum Matching Problem
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
Evolutionary Algorithms for Vertex Cover
EP '98 Proceedings of the 7th International Conference on Evolutionary Programming VII
Towards an analytic framework for analysing the computation time of evolutionary algorithms
Artificial Intelligence
A study of drift analysis for estimating computation time of evolutionary algorithms
Natural Computing: an international journal
Journal of Computer Science and Technology
Randomized local search, evolutionary algorithms, and the minimum spanning tree problem
Theoretical Computer Science
Approximating covering problems by randomized search heuristics using multi-objective models
Proceedings of the 9th annual conference on Genetic and evolutionary computation
Finding large cliques in sparse semi-random graphs by simple randomized search heuristics
Theoretical Computer Science
Worst-case and average-case approximations by simple randomized search heuristics
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
IEEE Transactions on Systems, Man, and Cybernetics, Part C: Applications and Reviews
IEEE Transactions on Evolutionary Computation
On the effectiveness of crossover for migration in parallel evolutionary algorithms
Proceedings of the 13th annual conference on Genetic and evolutionary computation
On the analysis of the immune-inspired B-cell algorithm for the vertex cover problem
ICARIS'11 Proceedings of the 10th international conference on Artificial immune systems
On the approximation ability of evolutionary optimization with application to minimum set cover
Artificial Intelligence
Diversity Guided Evolutionary Programming: A novel approach for continuous optimization
Applied Soft Computing
A large population size can be unhelpful in evolutionary algorithms
Theoretical Computer Science
The use of tail inequalities on the probable computational time of randomized search heuristics
Theoretical Computer Science
Unpacking and understanding evolutionary algorithms
WCCI'12 Proceedings of the 2012 World Congress conference on Advances in Computational Intelligence
Approximating vertex cover using edge-based representations
Proceedings of the twelfth workshop on Foundations of genetic algorithms XII
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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Vertex cover is one of the best known NP-Hard combinatorial optimization problems. Experimental work has claimed that evolutionary algorithms (EAs) perform fairly well for the problem and can compete with problem-specific ones. A theoretical analysis that explains these empirical results is presented concerning the random local search algorithm and the (1 + 1)-EA. Since it is not expected that an algorithm can solve the vertex cover problem in polynomial time, a worst case approximation analysis is carried out for the two considered algorithms and comparisons with the best known problem-specific ones are presented. By studying instance classes of the problem, general results are derived. Although arbitrarily bad approximation ratios of the (1 + 1)-EA can be proved for a bipartite instance class, the same algorithm can quickly find the minimum cover of the graph when a restart strategy is used. Instance classes where multiple runs cannot considerably improve the performance of the (1 + 1)-EA are considered and the characteristics of the graphs that make the optimization task hard for the algorithm are investigated and highlighted. An instance class is designed to prove that the (1 + 1)-EA cannot guarantee better solutions than the state-of-the-art algorithm for vertex cover if worst cases are considered. In particular, a lower bound for the worst case approximation ratio, slightly less than two, is proved. Nevertheless, there are subclasses of the vertex cover problem for which the (1 + 1)-EA is efficient. It is proved that if the vertex degree is at most two, then the algorithm can solve the problem in polynomial time.