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A comparative study of three evolutionary algorithms incorporating different amounts of domain knowledge for node covering problem
 IEEE TRANSACTIONS ON SYSTEMS, MAN, AND CYBERNETICS, PART C
, 2005
"... This paper compares three different evolutionary algorithms for solving the node covering problem: EAI relies on the definition of the problem only without using any domain knowledge, while EAII and EAIII employ extra heuristic knowledge. In theory, it is proven that all three algorithms can find ..."
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Cited by 11 (6 self)
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This paper compares three different evolutionary algorithms for solving the node covering problem: EAI relies on the definition of the problem only without using any domain knowledge, while EAII and EAIII employ extra heuristic knowledge. In theory, it is proven that all three algorithms can find an optimal solution in finite generations and find a feasible solution efficiently; but none of them can find the optimal solution efficiently for all instances of the problem. Through experiments, it is observed that all three algorithms can find a feasible solution efficiently, and the algorithms with extra heuristic knowledge can find better approximation solutions; but none of them can find the optimal solution to the first instance efficiently. This paper shows that heuristic knowledge is helpful for evolutionary algorithms to find good approximation solutions, but it contributes little to search the optimal solution for some instances.
A stochastic local search approach to vertex cover
 In Proceedings of the 30th German Conference on Artificial Intelligence (KI
, 2007
"... Abstract. We introduce a novel stochastic local search algorithm for the vertex cover problem. Compared to current exhaustive search techniques, our algorithm achieves excellent performance on a suite of problems drawn from the field of biology. We also evaluate our performance on the commonly used ..."
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Cited by 11 (0 self)
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Abstract. We introduce a novel stochastic local search algorithm for the vertex cover problem. Compared to current exhaustive search techniques, our algorithm achieves excellent performance on a suite of problems drawn from the field of biology. We also evaluate our performance on the commonly used DIMACS benchmarks for the related clique problem, finding that our approach is competitive with the current best stochastic local search algorithm for finding cliques. On three very large problem instances, our algorithm establishes new records in solution quality. 1
Analysis of the (1 + 1)EA for Finding Approximate Solutions to Vertex Cover Problems
, 2009
"... Vertex cover is one of the best known NPHard combinatorial optimization problems. Experimental work has claimed that evolutionary algorithms (EAs) perform fairly well for the problem and can compete with problemspecific ones. A theoretical analysis that explains these empirical results is presente ..."
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Cited by 8 (4 self)
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Vertex cover is one of the best known NPHard combinatorial optimization problems. Experimental work has claimed that evolutionary algorithms (EAs) perform fairly well for the problem and can compete with problemspecific 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 problemspecific 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 stateoftheart 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.
Analyses of Simple Hybrid Algorithms for the Vertex Cover Problem
, 2008
"... Hybrid methods are very popular for solving problems from combinatorial optimization. In contrast to this the theoretical understanding of the interplay of different optimization methods is rare. In this paper, we make a first step into the rigorous analysis of such combinations for combinatorial op ..."
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Cited by 4 (1 self)
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Hybrid methods are very popular for solving problems from combinatorial optimization. In contrast to this the theoretical understanding of the interplay of different optimization methods is rare. In this paper, we make a first step into the rigorous analysis of such combinations for combinatorial optimization problems. The subject of our analyses is the vertex cover problem for which several approximation algorithms have been proposed. We point out specific instances where solutions can (or cannot) be improved by the search process of a simple evolutionary algorithm in expected polynomial time.
A Hybrid Genetic Algorithm for Minimum Vertex Cover Problem
 In Prasad, B. (Ed.), The First Indian International Conference on Artificial Intelligence
, 2003
"... Minimum vertex cover problem (MVCP) is an NPhard problem and it has numerous real life applications. This paper presents hybrid genetic algorithm (HGA) to solve MVCP efficiently. In this paper we have demonstrated that when local optimization technique is added to genetic algorithm to form HGA, it ..."
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Cited by 4 (0 self)
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Minimum vertex cover problem (MVCP) is an NPhard problem and it has numerous real life applications. This paper presents hybrid genetic algorithm (HGA) to solve MVCP efficiently. In this paper we have demonstrated that when local optimization technique is added to genetic algorithm to form HGA, it gives near to optimal solution speedy. We have developed new heuristic vertex crossover operator (HVX) especially for MVCP, which converges faster to the global optimal solution. HVX gives far better results compared to classical crossover operators. We have also studied the effect of mutation on optimal solution in MVCP.
Computer and Biomedical
"... Abstract — Minimum vertex cover problem is an NPHard problem with the aim of finding minimum number of vertices to cover graph. In this paper, a learning automaton based algorithm is proposed to find minimum vertex cover in graph. In the proposed algorithm, each vertex of graph is equipped with a l ..."
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Abstract — Minimum vertex cover problem is an NPHard problem with the aim of finding minimum number of vertices to cover graph. In this paper, a learning automaton based algorithm is proposed to find minimum vertex cover in graph. In the proposed algorithm, each vertex of graph is equipped with a learning automaton that has two actions in the candidate or noncandidate of the corresponding vertex cover set. Due to characteristics of learning automata, this algorithm significantly reduces the number of covering vertices of graph. The proposed algorithm based on learning automata iteratively minimize the candidate vertex cover through the update its action probability. As the proposed algorithm proceeds, a candidate solution nears to optimal solution of the minimum vertex cover problem. In order to evaluate the proposed algorithm, several experiments conducted on DIMACS dataset which compared to conventional methods. Experimental results show the major superiority of the proposed algorithm over the other methods.
The Centre of Excellence for Research in Computational Intelligence and Applications
"... This paper compares three different evolutionary algorithms for solving the node covering problem: EAI relies on the definition of the problem only without using any domain knowledge, while EAII and EAIII employ extra heuristic knowledge for the problem. It is proven in theory all three evolution ..."
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This paper compares three different evolutionary algorithms for solving the node covering problem: EAI relies on the definition of the problem only without using any domain knowledge, while EAII and EAIII employ extra heuristic knowledge for the problem. It is proven in theory all three evolutionary algorithms can find the optimal solution in a finite computation time, find a feasible solution efficiently, but none of them can find the optimal solution efficiently for all instances of the problem. Through experiments, it is found that all three evolutionary algorithms can find a feasible solution efficiently, and evolutionary algorithms with extra heuristic knowledge can find good approximation solutions; but none of them can find the optimal solution to the first instance efficiently. It is shown in this paper that heuristic knowledge is helpful for evolutionary algorithms to find good approximation solutions, but for some instances, it contributes little to finding the optimal solution. I.