General Lower Bounds for the Running Time of Evolutionary Algorithms

We present a new method for proving lower bounds in evolutionary computation based on fitness-level arguments and an additional condition on transition probabilities between fitness levels. The method yields exact or near-exact lower bounds for LO, OneMax, and all functions with a unique optimum. All lower bounds hold for every evolutionary algorithm that only uses standard mutation as variation operator.

[1]  Xin Yao,et al.  Time complexity of evolutionary algorithms for combinatorial optimization: A decade of results , 2007, Int. J. Autom. Comput..

[2]  Benjamin Doerr,et al.  Multiplicative Drift Analysis , 2010, GECCO '10.

[3]  Benjamin Doerr,et al.  Drift analysis and linear functions revisited , 2010, IEEE Congress on Evolutionary Computation.

[4]  Per Kristian Lehre,et al.  Black-Box Search by Unbiased Variation , 2010, GECCO '10.

[5]  Simon M. Lucas,et al.  Parallel Problem Solving from Nature - PPSN X, 10th International Conference Dortmund, Germany, September 13-17, 2008, Proceedings , 2008, PPSN.

[6]  Thomas Jansen,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 Upper and Lower Bounds for Randomized Search Heuristics in Black-Box Optimization , 2004 .

[7]  Xin Yao,et al.  Evolutionary Optimization , 2002 .

[8]  Xin Yao,et al.  A study of drift analysis for estimating computation time of evolutionary algorithms , 2004, Natural Computing.

[9]  Thomas Jansen,et al.  On the analysis of the (1+1) evolutionary algorithm , 2002, Theor. Comput. Sci..

[10]  Mahmoud Fouz,et al.  Quasirandom evolutionary algorithms , 2010, GECCO '10.

[11]  Thomas Jansen,et al.  Analysis of an Asymmetric Mutation Operator , 2010, Evolutionary Computation.

[12]  Pietro Simone Oliveto,et al.  Erratum: Simplified Drift Analysis for Proving Lower Bounds in Evolutionary Computation , 2008, PPSN.

[13]  Pietro Simone Oliveto,et al.  Simplified Drift Analysis for Proving Lower Bounds in Evolutionary Computation , 2008, Algorithmica.

[14]  Ingo Wegener,et al.  Methods for the Analysis of Evolutionary Algorithms on Pseudo-Boolean Functions , 2003 .