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Fixed-Parameter Evolutionary Algorithms and the Vertex Cover Problem

Stefan Kratsch, Frank Neumann
2012 Algorithmica  
This shows that evolutionary algorithms are randomized fixed-parameter tractable algorithms for the vertex cover problem.  ...  In this paper, we consider multi-objective evolutionary algorithms for the Vertex Cover problem in the context of parameterized complexity.  ...  A well known fixed-parameter tractable problem is the (standard) parameterized Vertex Cover problem.  ... 
doi:10.1007/s00453-012-9660-4 fatcat:56bdeczbjngepjerigh6aazksa

Fixed-parameter evolutionary algorithms and the vertex cover problem

Stefan Kratsch, Frank Neumann
2009 Proceedings of the 11th Annual conference on Genetic and evolutionary computation - GECCO '09  
This shows that evolutionary algorithms are randomized fixed-parameter tractable algorithms for the vertex cover problem.  ...  In this paper, we consider multi-objective evolutionary algorithms for the Vertex Cover problem in the context of parameterized complexity.  ...  A well known fixed-parameter tractable problem is the (standard) parameterized Vertex Cover problem.  ... 
doi:10.1145/1569901.1569943 dblp:conf/gecco/KratschN09 fatcat:7vznjwygmnghdea3snatlcp4ju

Guest Editorial: Special Issue on Parameterized and Exact Computation, Part II

Venkatesh Raman, Saket Saurabh
2013 Algorithmica  
The paper 'Fixed-parameter evolutionary algorithms and the vertex cover problem' adopts a parameterized view to analyze the expected behavior of evolutionary algorithms.  ...  While some of the papers in this volume supplement the ones in the first volume in the sub areas of kernelization and improved fixed-parameter algorithms for graph modification problems, most others complement  ...  The papers 'Proper interval vertex deletion' and 'Fast polynomial space algorithms using inclusion-exclusion' give improved fixed-parameter algorithms for some graph problems.  ... 
doi:10.1007/s00453-013-9744-9 fatcat:j2ya4p5u7zcvlgvxwotywr7f34

Preface to the Special Issue on Theory of Genetic and Evolutionary Computation

Anne Auger, Per Kristian Lehre
2021 Algorithmica  
We thank all authors for their submission, the reviewers for their time in providing thorough reviews and the Algorithmica team including Ming-Yang Kao for their support and patience.  ...  Anne Auger and Per Kristian Lehre Paris and Birmingham, October 2020  ...  algorithms for the Weighted Vertex Cover Problem.  ... 
doi:10.1007/s00453-021-00803-0 fatcat:ct6pffzfojepfay2jfhu2yb3j4

The Applicability of Genetic algorithm to Vertex Cover

Harsh Bhasin, Mohammad Amini
2015 International Journal of Computer Applications  
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 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.  ...  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] .  ... 
doi:10.5120/ijca2015905785 fatcat:zbv7b2nl7jb4loo26kbb6ri5ha

Evolutionary Search of Thresholds for Robust Feature Set Selection: Application to the Analysis of Microarray Data [chapter]

Carlos Cotta, Christian Sloper, Pablo Moscato
2004 Lecture Notes in Computer Science  
We address this problem using an evolutionary algorithm that learns the appropriate value of the thresholds. The empirical evaluation shows that robust subset of genes can be obtained.  ...  We deal with two important problems in pattern recognition that arise in the analysis of large datasets.  ...  We thank Mike Fellows and Luke Mathieson for useful discussions, and Evosolve (UK Registered Charity No. 1083684) for supporting previous work.  ... 
doi:10.1007/978-3-540-24653-4_3 fatcat:ko6th4a2unhflny53ac4vuksom

Focused Jump-and-Repair Constraint Handling for Fixed-Parameter Tractable Graph Problems [article]

Luke Branson, Andrew M. Sutton
2022 arXiv   pre-print
For the latter two problems, this constitutes the first parameterized result for any evolutionary algorithm.  ...  This leads to an exponential (in k) improvement over the best-known parameterized bound for evolutionary algorithms on VertexCover.  ...  A problem L is fixed-parameter tractable if (x, k) ∈ L can be decided in time g(k)|x| O( Applying parameterized complexity analysis to the run time analysis of evolutionary algorithms is useful when one  ... 
arXiv:2203.13877v1 fatcat:enp5zk66avf4zorl7f7yamzc2m

Hybrid evolutionary algorithms on minimum vertex cover for random graphs

Martin Pelikan, Rajiv Kalapala, Alexander K. Hartmann
2007 Proceedings of the 9th annual conference on Genetic and evolutionary computation - GECCO '07  
The results indicate that BB is significantly outperformed by all the other tested methods, which is expected as BB is a complete search algorithm and minimum vertex cover is an NP-complete problem.  ...  Keywords Minimum vertex cover, hierarchical BOA, genetic algorithm, simulated annealing, branch and bound.  ...  The purpose of this paper is to compare several simple and advanced evolutionary algorithms on an extensive set of minimum vertex cover problem instances.  ... 
doi:10.1145/1276958.1277073 dblp:conf/gecco/PelikanKH07 fatcat:j5usjs7bkzgrri7hilxamdy3ce

Evolutionary Computation based Optimization Technique For Minimum Vertex Cover

Shet Reshma Prakash Shet Reshma Prakash
2018 International Journal of Computer Science Engineering and Information Technology Research  
Minimum Vertex Cover (MVC) is a classical problem of graph theory and belongs to the class of NP-Complete, hence finding the approximate solution is much more efficient compared to the exact solution.  ...  In this paper, the proposed solution is designed to find the approximate solution of Minimum Vertex Cover problem for the un-weighted graph.  ...  Vertex Cover problem belongs to the field of graph theory and it is a collection of a set of vertices which covers all edges of the graph.  ... 
doi:10.24247/ijcseitrjun201810 fatcat:lt3glrw2yrhpnkfs2eq7326cvm

Parameterized Complexity Analysis of Randomized Search Heuristics [chapter]

Frank Neumann, Andrew M. Sutton
2019 Natural Computing Series  
We outline the main results and proof techniques for a collection of randomized search heuristics tasked to solve NP-hard combinatorial optimization problems such as finding a minimum vertex cover in a  ...  This chapter compiles a number of results that apply the theory of parameterized algorithmics to the running-time analysis of randomized search heuristics such as evolutionary algorithms.  ...  This shows that the problem-specific mutation operator of Algorithm 2 makes the difference between a fixed-parameter evolutionary algorithm and an evolutionary algorithm that cannot compute an optimal  ... 
doi:10.1007/978-3-030-29414-4_4 fatcat:toerkmrhizeg3euqilecmdhbyi

A fast and robust heuristic algorithm for the minimum weight vertex cover problem

Yang Wang, Zhipeng Lu, Abraham P. Punnen
2021 IEEE Access  
INDEX TERMS Hybrid evolutionary algorithm, metaheuristics, minimum weight vertex cover problem, solution-based tabu search.  ...  The minimum weight vertex cover problem (MWVCP) is a fundamental combinatorial optimization problem with various real-world applications.  ...  In this paper, we investigate this line of reasoning to develop an effective and robust algorithm to solve the weighted vertex cover problem.  ... 
doi:10.1109/access.2021.3051741 fatcat:hnglpzdeavaqxk2bzgsqn4u52i

The bi-objective covering tour problem

Nicolas Jozefowiez, Frédéric Semet, El-Ghazali Talbi
2007 Computers & Operations Research  
We propose a two-phase cooperative strategy that combines a multi-objective evolutionary algorithm with a branch-and-cut algorithm initially designed to solve a single-objective covering tour problem.  ...  The paper discusses the definition and solution of a bi-objective routing problem, namely the bi-objective covering tour problem.  ...  Acknowledgements This work was partially supported by the Nord-Pas-de-Calais region. This support is gratefully acknowledged. Thanks are also due to the referees for their valuable comments.  ... 
doi:10.1016/j.cor.2005.07.022 fatcat:o5pppjlqgfhm7jrfrxay7nkwzm

Parameterized Analysis of Multi-objective Evolutionary Algorithms and the Weighted Vertex Cover Problem

Mojgan Pourhassan, Feng Shi, Frank Neumann
2019 Evolutionary Computation  
Evolutionary multiobjective optimization for the classical vertex cover problem has been analysed in Kratsch and Neumann (2013) in the context of parameterized complexity analysis.  ...  Using an alternative mutation operator introduced in Kratsch and Neumann (2013), we provide a fixed parameter evolutionary algorithm with respect to OPT, the cost of an optimal solution for the problem  ...  Acknowledgments This research has been supported by Australian Research Council grants DP140103400 and DP160102401, and National Natural Science Foundation of China grant 61802441.  ... 
doi:10.1162/evco_a_00255 pmid:31012735 fatcat:j5qodxbdbjbdbli5ilbqmddhhu

Fixed Parameter Evolutionary Algorithms and Maximum Leaf Spanning Trees: A Matter of Mutation [chapter]

Stefan Kratsch, Per Kristian Lehre, Frank Neumann, Pietro Simone Oliveto
2010 Parallel Problem Solving from Nature, PPSN XI  
We investigate the NP-hard problem of computing a spanning tree that has a maximal number of leaves by evolutionary algorithms in the context of fixed parameter tractability (FPT) where the maximum number  ...  Evolutionary algorithms have been shown to be very successful for a wide range of NP-hard combinatorial optimization problems.  ...  In [6] , it has been shown that there are fixed parameter evolutionary algorithms for the vertex cover problem.  ... 
doi:10.1007/978-3-642-15844-5_21 dblp:conf/ppsn/KratschLNO10 fatcat:byxjfluezzgydcmzdrxqmcskda

Graph Partitioning for Independent Sets [article]

Sebastian Lamm and Peter Sanders and Christian Schulz
2015 arXiv   pre-print
Computing maximum independent sets in graphs is an important problem in computer science. In this paper, we develop an evolutionary algorithm to tackle the problem.  ...  The core innovations of the algorithm are very natural combine operations based on graph partitioning and local search algorithms.  ...  Acknowledgements We would like to thank Renato Werneck for providing us the source code of the local search algorithms presented in Andrade et al. [1] .  ... 
arXiv:1502.01687v1 fatcat:yiqqcuglbzfyxmiypqo4m633b4
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