Theoretical Aspects of Evolutionary Algorithms

  title={Theoretical Aspects of Evolutionary Algorithms},
  author={Ingo Wegener},
  • I. Wegener
  • Published in ICALP 8 July 2001
  • Computer Science
Randomized search heuristics like simulated annealing and evolutionary algorithms are applied successfully in many different situations. However, the theory on these algorithms is still in its infancy. Here it is discussed how and why such a theory should be developed. Afterwards, some fundamental results on evolutionary algorithms are presented in order to show how theoretical results on randomized search heuristics can be proved and how they contribute to the understanding of evolutionary… 
How to analyse evolutionary algorithms
The history of attempts to analyse evolutionary algorithms is described and then new methods for continuous as well as discrete search spaces are presented and discussed.
Theoretical Perspectives on Evolutionary Algorithms
This chapter is devoted to the presentation of some of these approaches to evolutionary computation theory, and the choice of which branches to cover is governed by the influence on current research in this area.
Metropolis Versus Simulated Annealing and the Black-Box-Complexity of Optimization Problems
Two fundamental results of this kind are presented to show how such a theory of randomized search heuristics can be developed.
Towards a Theory of Randomized Search Heuristics
A framework for a theory of randomized search heuristics is presented and it is discussed how randomized Search Heuristics can be delimited from other types of algorithms, which leads to the theory of black-box optimization.
Evolutionary Algorithms and the Maximum Matching Problem
It is proven that the evolutionary algorithm is a polynomial-time randomized approximation scheme (PRAS) for this optimization problem, although the algorithm does not employ the idea of augmenting paths.
Searching Randomly for Maximum Matchings
  • O. Giel, I. Wegener
  • Computer Science, Mathematics
    Electron. Colloquium Comput. Complex.
  • 2004
The main purpose is to develop methods for the analysis of general randomized search heuristics and to investigate when it is possible to “simulate randomly” clever optimization techniques and when this random search fails.
Evolutionary Algorithms , Randomized Local Search , and the Maximum Matching Problem ∗
The design and analysis of problem-specific algorithms for combinatorial optimization problems is a well-studied subject. It is accepted that randomization is a powerful concept for theoretically and
Algorithmic analysis of a basic evolutionary algorithm for continuous optimization
It turns out that, in the scenario considered, Gaussian mutations in combination with the 1/5-rule indeed ensure asymptotically optimal runtime; namely, Θ(n) steps/function evaluations are necessary and sufficient to halve the approximation error.
Upper and Lower Bounds for Randomized Search Heuristics in Black-Box Optimization
Lower bounds on the black-box complexity of problems are derived without complexity theoretical assumptions and are compared with upper bounds in this scenario.
Benefits of Sexual Reproduction in Evolutionary Computation
Theoretical and empirical results show substantial speedups for functions of unitation when combined with a fitness-invariant bit shuffling operator, and it is proved for small crossover probabilities that subsequent mutations create sufficient diversity, even for very small populations.


On the Analysis of Evolutionary Algorithms - A Proof That Crossover Really Can Help
This paper presents an example of an evolutionary algorithm using crossover and shows that it is essentially more efficient than evolutionary algorithms without crossover.
On the Expected Runtime and the Success Probability of Evolutionary Algorithms
It is shown that the most simple evolutionary algorithm optimizes each pseudo-boolean linear function in an expected time of O(n log n) and an example is shown where crossover decreases the expected runtime from superpolynomial to polynomial.
On the analysis of the (1+1) evolutionary algorithm
A step towards a theory on Evolutionary Algorithms, in particular, the so-called (1+1) evolutionary Algorithm, is performed and linear functions are proved to be optimized in expected time O(nlnn) but only mutation rates of size (1/n) can ensure this behavior.
When will a Genetic Algorithm Outperform Hill Climbing
An "idealized" genetic algorithm (IGA) is analyzed that is significantly faster than RMHC and that gives a lower bound for GA speed.
Genetic Algorithms in Search Optimization and Machine Learning
This book brings together the computer techniques, mathematical tools, and research results that will enable both students and practitioners to apply genetic algorithms to problems in many fields.
On the Choice of the Mutation Probability for the (1+1) EA
It is shown for a non-trivial example function that the most recommended choice for the mutation probability 1/n is by far not optimal, and a simple evolutionary algorithm with an extremely simple dynamic mutation probability scheme is suggested to overcome the difficulty of finding a proper setting.
On the Optimization of Unimodal Functions with the (1 + 1) Evolutionary Algorithm
It is shown that unimodal functions can be very difficult to be optimized for the (1+1) EA, and it is proved that a little modification in the selection method can lead to huge changes in the expected running time.
Evolution and optimum seeking
  • H. Schwefel
  • Engineering, Computer Science
    Sixth-generation computer technology series
  • 1995
Problems and Methods of Optimization Hill Climbing Strategies Random Strategies Evolution Strategies for Numerical Optimization Comparison of Direct Search Strategies for Parameter Optimization.
The royal road for genetic algorithms: Fitness landscapes and GA performance
An initial set of proposed feature classes are described, one such class (Royal Road) is described in detail, and some initial experimental results concerning the role of crossover and buildingblocks on landscapes constructed from features of this class are presented.
Analysis of recombinative algorithms on a non-separable building-block problem
  • R. Watson
  • Mathematics, Computer Science
  • 2000
An upper bound on the expected time for a recombinative algorithm to solve a nonseparable building-block problem by proving the existence of a path to the solution and calculating the time for each step on this path is given.