Fixed-Parameter Evolutionary Algorithms and the Vertex Cover Problem

Kratsch, Stefan; Neumann, Franz‐Josef

doi:10.1007/s00453-012-9660-4

Cited by 70 publications

(18 citation statements)

References 32 publications

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“…It facilitates the understanding of which features in an instance of a given problem makes the problem hard to solve. Parameterized runtime results have been obtained in the context of evolutionary computation for the vertex cover problem [9], the computation of maximum leaf spanning trees [8], the MAX-2-SAT problem [12], and the Euclidean TSP [13].…”

Section: Introductionmentioning

confidence: 99%

A Parameterized Runtime Analysis of Simple Evolutionary Algorithms for Makespan Scheduling

Sutton

Neumann

2012

Lecture Notes in Computer Science

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Abstract. We consider simple multi-start evolutionary algorithms applied to the classical NP-hard combinatorial optimization problem of Makespan Scheduling on two machines. We study the dependence of the runtime of this type of algorithm on three different key hardness parameters. By doing this, we provide further structural insights into the behavior of evolutionary algorithms for this classical problem.

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Section: Introductionmentioning

confidence: 99%

A Parameterized Runtime Analysis of Simple Evolutionary Algorithms for Makespan Scheduling

Sutton

Neumann

2012

Lecture Notes in Computer Science

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“…The problem has also been solved by fixed parameter evolutionary algorithm wherein the running time Θ( f(OPT)n c ), where c is a small constant [12].…”

Section: Literature Reviewmentioning

confidence: 99%

The Applicability of Genetic algorithm to Vertex Cover

Bhasin¹,

Amini²

2015

IJCA

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The Vertex Cover Problem calls for the selection of a set of vertices(V) in a way that all the edges of the graph, connected to those vertices constitute the set E of the given graph G= (V, E). The problem finds applications in various fields and is therefore, one of the most widely researched topics in NP Complete Problems. The problem is an NP Complete problem this work proposes a Genetic Algorithm based solution to handle the problem. The proposed algorithm has been implemented and tested for various graphs. These instances vary in the number of vertices and connectivity. The results are encouraging. This paper also explores the available techniques in order to put the things in the perspective. The future scope of this work intends to apply Diploid Genetic Algorithms to the problem to incorporate robustness into the proposed algorithm.

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“…Based on results for different kinds of pseudo-Boolean functions [12,18], results have been obtained for different kinds of combinatorial optimization problems [29]. Starting with some results for classical combinatorial optimization problems that are solvable in polynomial time such as the computation of minimum spanning trees [28] or maximum matchings [16], different results have been obtained for NP-hard problems [27,15,22,42]. Analyses discussing the use of crossover operators on problems with a bit string representation include [19,21].…”

Section: Introductionmentioning

confidence: 99%

More Effective Crossover Operators for the All-Pairs Shortest Path Problem

Doerr

Johannsen

Kötzing

et al. 2010

Parallel Problem Solving From Nature, PPSN XI

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The all-pairs shortest path problem is the first non-artificial problem for which it was shown that adding crossover can significantly speed up a mutation-only evolutionary algorithm. Recently, the analysis of this algorithm was refined and it was shown to have an expected optimization time (w. r. t. the number of fitness evaluations) of Θ(n 3.25 (log n) 0.25 ).In contrast to this simple algorithm, evolutionary algorithms used in practice usually employ refined recombination strategies in order to avoid the creation of infeasible offspring. We study extensions of the basic algorithm by two such concepts which are central in recombination, namely repair mechanisms and parent selection. We show that repairing infeasible offspring leads to an improved expected optimization time of O(n 3.2 (log n) 0.2 ). As a second part of our study we prove that choosing parents that guarantee feasible offspring results in an even better optimization time of O(n 3 log n).Both results show that already simple adjustments of the recombination operator can asymptotically improve the runtime of evolutionary algorithms. * This work greatly benefited from various discussions at the Dagstuhl seminar 08051 on Theory of Evolutionary Algorithms.

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Fixed-Parameter Evolutionary Algorithms and the Vertex Cover Problem

Cited by 70 publications

References 32 publications

A Parameterized Runtime Analysis of Simple Evolutionary Algorithms for Makespan Scheduling

A Parameterized Runtime Analysis of Simple Evolutionary Algorithms for Makespan Scheduling

The Applicability of Genetic algorithm to Vertex Cover

More Effective Crossover Operators for the All-Pairs Shortest Path Problem

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