On improving approximate solutions by evolutionary algorithms

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. 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 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.

[1]  Ingo Wegener,et al.  Maximum cardinality matchings on trees by randomized local search , 2006, GECCO '06.

[2]  Isaac K. Evans,et al.  Evolutionary Algorithms for Vertex Cover , 1998, Evolutionary Programming.

[3]  Raúl Hector Gallard,et al.  Genetic algorithms + Data structure = Evolution programs , Zbigniew Michalewicz , 1999 .

[4]  Ingo Wegener,et al.  Evolutionary Algorithms and the Maximum Matching Problem , 2003, STACS.

[5]  Carsten Witt,et al.  UNIVERSITY OF DORTMUND REIHE COMPUTATIONAL INTELLIGENCE COLLABORATIVE RESEARCH CENTER 531 Design and Management of Complex Technical Processes and Systems by means of Computational Intelligence Methods Worst-Case and Average-Case Approximations by Simple Randomized Search Heuristics , 2004 .

[6]  Ingo Wegener,et al.  On the Optimization of Monotone Polynomials by Simple Randomized Search Heuristics , 2005, Combinatorics, Probability and Computing.

[7]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[8]  David K. Smith.  Theory of Linear and Integer Programming , 1987 .

[9]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[10]  The Centre of Excellence for Research in Computational Intelligence and Applications , .

[11]  Frank Neumann.  Expected Runtimes of a Simple Evolutionary Algorithm for the Multi-objective Minimum Spanning Tree Problem , 2004, PPSN.

[12]  Frank Neumann,et al.  Randomized Local Search, Evolutionary Algorithms, and the Minimum Spanning Tree Problem , 2004, GECCO.

[13]  Frank Neumann,et al.  Speeding Up Evolutionary Algorithms Through Restricted Mutation Operators , 2006, PPSN.

[14]  Zbigniew Michalewicz,et al.  Genetic Algorithms + Data Structures = Evolution Programs , 1996, Springer Berlin Heidelberg.

[15]  Kenneth Steiglitz,et al.  Combinatorial Optimization: Algorithms and Complexity , 1981 .

[16]  Xin Yao,et al.  A comparative study of three evolutionary algorithms incorporating different amounts of domain knowledge for node covering problem , 2005, IEEE Trans. Syst. Man Cybern. Part C.

[17]  Dirk Sudholt.  Local Search in Evolutionary Algorithms: The Impact of the Local Search Frequency , 2006, ISAAC.

[18]  Ingo Wegener,et al.  Randomized local search, evolutionary algorithms, and the minimum spanning tree problem , 2004, Theor. Comput. Sci..

[19]  Carsten Witt,et al.  Approximating Covering Problems by Randomized Search Heuristics Using Multi-Objective Models , 2007, Evolutionary Computation.

[20]  Fred W. Glover,et al.  Tabu Search , 1997, Handbook of Heuristics.

[21]  Ingo Wegener,et al.  The analysis of evolutionary algorithms on sorting and shortest paths problems , 2004, J. Math. Model. Algorithms.

[22]  D. E. Goldberg,et al.  Genetic Algorithms in Search , 1989 .

[23]  Frank Neumann,et al.  A Relation-Algebraic View on Evolutionary Algorithms for Some Graph Problems , 2006, EvoCOP.

[24]  R. J. Dakin,et al.  A tree-search algorithm for mixed integer programming problems , 1965, Comput. J..

[25]  Dirk Sudholt,et al.  On the analysis of the (1+1) memetic algorithm , 2006, GECCO.

[26]  Frank Neumann.  Expected runtimes of evolutionary algorithms for the Eulerian cycle problem , 2004, IEEE Congress on Evolutionary Computation.