On the effect of populations in evolutionary multi-objective optimization

Giel, Oliver; Lehre, Per Kristian

doi:10.1145/1143997.1144114

Cited by 27 publications

(19 citation statements)

References 14 publications

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“…The previous theorem is generalized by the Global Gambler's Theorem below which on its own is a specialization of a variant of the Drift Theorem found in [3].…”

Section: Theorem 2 (Local Gambler's Ruin)mentioning

confidence: 99%

Rigorous analyses of fitness-proportional selection for optimizing linear functions

Happ

Johannsen

Klein

et al. 2008

Proceedings of the 10th Annual Conference on Genetic and Evolutionary Computation

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Rigorous runtime analyses of evolutionary algorithms (EAs) mainly investigate algorithms that use elitist selection methods. Two algorithms commonly studied are Randomized Local Search (RLS) and the (1+1) EA and it is well known that both optimize any linear pseudo-Boolean function on n bits within an expected number of O(n log n) fitness evaluations.In this paper, we analyze variants of these algorithms that use fitness proportional selection.A well-known method in analyzing the local changes in the solutions of RLS is a reduction to the gambler's ruin problem. We extend this method in order to analyze the global changes imposed by the (1+1) EA. By applying this new technique we show that with high probability using fitness proportional selection leads to an exponential optimization time for any linear pseudo-Boolean function with non-zero weights. Even worse, all solutions of the algorithms during an exponential number of fitness evaluations differ with high probability in linearly many bits from the optimal solution.Our theoretical studies are complemented by experimental investigations which confirm the asymptotic results on realistic input sizes.

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“…The previous theorem is generalized by the Global Gambler's Theorem below which on its own is a specialization of a variant of the Drift Theorem found in [3].…”

Section: Theorem 2 (Local Gambler's Ruin)mentioning

confidence: 99%

Rigorous analyses of fitness-proportional selection for optimizing linear functions

Happ

Johannsen

Klein

et al. 2008

Proceedings of the 10th Annual Conference on Genetic and Evolutionary Computation

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“…Even more important, it quickly became one of the most powerful tools for both proving upper and lower bounds on the expected optimization times of evolutionary algorithms. For example, see [HY04,GW03,GL06,HJKN08,NOW09,OW].…”

Section: Introductionmentioning

confidence: 99%

Multiplicative Drift Analysis

2012

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In this work, we introduce multiplicative drift analysis as a suitable way to analyze the runtime of randomized search heuristics such as evolutionary algorithms.We give a multiplicative version of the classical drift theorem. This allows easier analyses in those settings where the optimization progress is roughly proportional to the current distance to the optimum.To display the strength of this tool, we regard the classical problem how the (1+1) Evolutionary Algorithm optimizes an arbitrary linear pseudo-Boolean function. Here, we first give a relatively simple proof for the fact that any linear function is optimized in expected time O(n log n), where n is the length of the bit string. Afterwards, we show that in fact any such function is optimized in expected time at most (1 + o(1))1.39en ln(n), again using multiplicative drift analysis. We also prove a corresponding lower bound of (1 − o(1))en ln(n) which actually holds for all functions with a unique global optimum.We further demonstrate how our drift theorem immediately gives natural proofs (with better constants) for the best known runtime bounds for the (1+1) Evolutionary Algorithm on combinatorial problems like finding minimum spanning trees, shortest paths, or Euler tours. * Carola Winzen is a recipient of the Google Europe Fellowship in Randomized Algorithms, and this work is supported in part by this Google Fellowship.

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“…Many approaches to the evolution of cooperative behavior in non-biological systems involve multilevel selection, the theory that selection acts not only on the individual directly, but also indirectly through the groups that it is a member of [8]. Researchers in evolutionary computation have used various forms of multilevel selection to accurately diagnose malignancy in cancer [24] and improve runtime performance of multi-objective evolutionary algorithms [9]. Additionally, genetic programming has been used to design communications protocols for autonomic systems, where individuals in the population were different protocols [23].…”

Section: Related Workmentioning

confidence: 99%

Cooperative network construction using digital germlines

Knoester

McKinley

Ofria

2008

Proceedings of the 10th Annual Conference on Genetic and Evolutionary Computation

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This paper describes a study in the evolution of cooperative behavior, specifically the construction of communication networks, through digital evolution and multilevel selection. In digital evolution, a population of self-replicating computer programs exists in a user-defined computational environment and is subject to instruction-level mutations and natural selection. Multilevel selection links the survival of the individual to the survival of its group, thus encouraging cooperation. The results of experiments using the Avida digital evolution platform demonstrate that populations of digital organisms are capable of constructing communication networks, and that these networks can exhibit desired properties depending on the selective pressures used. We also show that the use of a digital germline can significantly improve evolvability of cooperation.

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On the effect of populations in evolutionary multi-objective optimization

Cited by 27 publications

References 14 publications

Rigorous analyses of fitness-proportional selection for optimizing linear functions

Rigorous analyses of fitness-proportional selection for optimizing linear functions

Multiplicative Drift Analysis

Cooperative network construction using digital germlines

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