ABSTRACT
This paper introduces an easy to use technique for deriving upper bounds on the expected runtime of non-elitist population-based evolutionary algorithms (EAs). Applications of the technique show how the efficiency of EAs is critically dependant on having a sufficiently strong selective pressure. Parameter settings that ensure sufficient selective pressure on commonly considered benchmark functions are derived for the most popular selection mechanisms. Together with a recent technique for deriving lower bounds, this paper contributes to a much-needed analytical tool-box for the analysis of evolutionary algorithms with populations.
- T. Chen, J. He, G. Sun, G. Chen, and X. Yao. A new approach for analyzing average time complexity of population-based evolutionary algorithms on unimodal problems. IEEE Trans. on Systems, Man, and Cybernetics, Part B: Cybernetics, 39(5):1092--1106, Oct. 2009. Google ScholarDigital Library
- T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein. Introduction to Algorithms. McGraw Hill, New York, NY, 2nd edition, 2001. Google ScholarDigital Library
- S. Droste, T. Jansen, and I. Wegener. On the analysis of the (1Google Scholar
- 1) Evolutionary Algorithm. Theoretical Computer Science, 276:51--81, 2002. Google ScholarDigital Library
- D. E. Goldberg and K. Deb. A comparative analysis of selection schemes used in genetic algorithms. In Foundations of Genetic Algorithms, pages 69--93. Morgan Kaufmann, 1991.Google Scholar
- E. Happ, D. Johannsen, C. Klein, and F. Neumann. Rigorous analyses of fitness-proportional selection for optimizing linear functions. In Proc. of the 10th annual conference on Genetic and evolutionary computation (GECCO 2008), pages 953--960, New York, NY, USA, 2008. ACM. Google ScholarDigital Library
- J. He and X. Yao. Drift analysis and average time complexity of evolutionary algorithms. Artificial Intelligence, 127(1):57--85, March 2001. Google ScholarDigital Library
- W. Hoeffding. Probability inequalities for sums of bounded random variables. Journal of the American Statistical Association, 58(301):13--30, 1963.Google ScholarCross Ref
- T. Kötzing, F. Neumann, D. Sudholt, and M. Wagner. Simple max-min ant systems and the optimization of linear pseudo-boolean functions. To appear in Proc. of Foundations of Genetic Algorithms (FOGA 2011), 2011. Google ScholarDigital Library
- J. Lässig and D. Sudholt. General scheme for analyzing running times of parallel evolutionary algorithms. In Proc. of the 11th international conference on Parallel problem solving from nature: Part I, (PPSN 2010), pages 234--243, Berlin, Heidelberg, 2010. Springer-Verlag. Google ScholarDigital Library
- P. K. Lehre. Negative drift in populations. In Proc. of the 11th international conference on Parallel problem solving from nature: Part I, (PPSN 2010), pages 244--253, Berlin, Heidelberg, 2010. Springer-Verlag. Google ScholarDigital Library
- P. K. Lehre and X. Yao. On the impact of mutation-selection balance on the runtime of evolutionary algorithms. To appear in IEEE Trans. on Evolutionary Computation, 2011.Google Scholar
- F. Neumann, P. S. Oliveto, and C. Witt. Theoretical analysis of fitness-proportional selection: landscapes and efficiency. In Proc. of the 11th Annual conference on Genetic and evolutionary computation (GECCO 2009), pages 835--842, New York, NY, USA, 2009. ACM. Google ScholarDigital Library
- P. S. Oliveto, J. He, and X. Yao. Time complexity of evolutionary algorithms for combinatorial optimization: A decade of results. Intl. Journal of Automation and Computing, 4(1):100--106, 2007.Google Scholar
- D. Sudholt. General lower bounds for the running time of evolutionary algorithms. In Proc. of the 11th international conference on Parallel problem solving from nature: Part I, (PPSN 2010), pages 124--133, Berlin, Heidelberg, 2010. Springer-Verlag. Google ScholarDigital Library
- I. Wegener and C. Witt. On the analysis of a simple evolutionary algorithm on quadratic pseudo-boolean functions. Journal of Discrete Algorithms, 3(1):61--78, 2005.Google ScholarCross Ref
- C. Witt. Runtime Analysis of the (μGoogle Scholar
- $1$) EA on Simple Pseudo-Boolean Functions. Evolutionary Computation, 14(1):65--86, 2006. Google ScholarDigital Library
Index Terms
Fitness-levels for non-elitist populations
Recommendations
Non-elitist evolutionary algorithms excel in fitness landscapes with sparse deceptive regions and dense valleys
GECCO '21: Proceedings of the Genetic and Evolutionary Computation ConferenceIt is largely unknown how the runtime of evolutionary algorithms depends on fitness landscape characteristics for broad classes of problems. Runtime guarantees for complex and multi-modal problems where EAs are typically applied are rarely available.
We ...
Towards a Runtime Comparison of Natural and Artificial Evolution
Evolutionary algorithms (EAs) form a popular optimisation paradigm inspired by natural evolution. In recent years the field of evolutionary computation has developed a rigorous analytical theory to analyse the runtimes of EAs on many illustrative ...
Refined upper bounds on the expected runtime of non-elitist populations from fitness-levels
GECCO '14: Proceedings of the 2014 Annual Conference on Genetic and Evolutionary ComputationRecently, an easy-to-use fitness-level technique was introduced to prove upper bounds on the expected runtime of randomised search heuristics with non-elitist populations and unary variation operators. Following this work, we present a new and much more ...
Comments