On the Choice of the Parent Population Size

Storch, Tobias

doi:10.1162/evco.2008.16.4.557

Cited by 35 publications

(12 citation statements)

References 16 publications

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“…Sometimes, even smaller changes to the population size can have a large impact on the runtime. Storch (2008) described a class of problems where reducing the offspring population size by one leads to an exponential increase in the runtime, assuming the EA uses a specific diversity mechanism. Witt (2008) analysed the runtime of an EA without a diversity mechanism, showing that the runtime can improve from exponential to polynomial when the population size is increased by a constant factor.…”

Section: Introductionmentioning

confidence: 99%

On the Effect of Populations in Evolutionary Multi-Objective Optimisation

Giel

Lehre

2010

Evolutionary Computation

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Multi-objective evolutionary algorithms (MOEAs) have become increasingly popular as multi-objective problem solving techniques. An important open problem is to understand the role of populations in MOEAs. We present two simple bi-objective problems which emphasise when populations are needed. Rigorous runtime analysis points out an exponential runtime gap between the population-based algorithm simple evolutionary multi-objective optimiser (SEMO) and several single individual-based algorithms on this problem. This means that among the algorithms considered, only the population-based MOEA is successful and all other algorithms fail.

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Section: Introductionmentioning

confidence: 99%

On the Effect of Populations in Evolutionary Multi-Objective Optimisation

Giel

Lehre

2010

Evolutionary Computation

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“…Note that these results are far from trivial, in fact, their proofs span several pages in [20]. Similar analyses on how the (µ+1) EA solves the OneMax problem, also technically highly demanding, have been conducted by Storch [27] and Witt [29]; results on how the (1, λ) EA optimizes OneMax were given by Jägersküpper and Storch [19] as well as Rowe and Sudholt [26].…”

Section: Population-based Eamentioning

confidence: 71%

How the (1+λ) evolutionary algorithm optimizes linear functions

Doerr

Künnemann

2013

Proceedings of the 15th Annual Conference on Genetic and Evolutionary Computation

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We analyze how the (1 + λ) evolutionary algorithm (EA) optimizes linear pseudo-Boolean functions. We prove that it finds the optimum of any linear function within an expected number of O( 1 λ n log n + n) iterations. We also show that this bound is sharp for some functions, e.g., the binary value function. Hence unlike for the (1 + 1) EA, for the (1 + λ) EA different linear functions may have run-times of different asymptotic order. The proof of our upper bound heavily relies on a number of classic and recent drift analysis methods. In particular, we show how to analyze a process displaying different types of drifts in different phases. Our work corrects a wrongfully claimed better asymptotic runtime in an earlier work [12].

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“…The (µ+1) EA with genotype diversity [14,16] is shown as Algorithm 1. Definition 1 extends the mutation operator mut r to support a finite alphabet as in [3,5]; for r = 1, it is equivalent to the standard mutation operator of the (1+1) EA.…”

Section: Preliminariesmentioning

confidence: 99%

MMAS Versus Population-Based EA on a Family of Dynamic Fitness Functions

Lissovoi

Witt

2015

Algorithmica

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We study the behavior of a population-based EA and the Max-Min Ant System (MMAS) on a family of deterministically-changing fitness functions, where, in order to find the global optimum, the algorithms have to find specific local optima within each of a series of phases. In particular, we prove that a (2+1) EA with genotype diversity is able to find the global optimum of the Maze function, previously considered by Kötzing and Molter (PPSN 2012, 113-122), in polynomial time. This is then generalized to a hierarchy result stating that for every µ, a (µ+1) EA with genotype diversity is able to track a Maze function extended over a finite alphabet of µ symbols, whereas population size µ − 1 is not sufficient. Furthermore, we show that MMAS does not require additional modifications to track the optimum of the finitealphabet Maze functions, and, using a novel drift statement to simplify the analysis, reduce the required phase length of the Maze function.

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On the Choice of the Parent Population Size

Cited by 35 publications

References 16 publications

On the Effect of Populations in Evolutionary Multi-Objective Optimisation

On the Effect of Populations in Evolutionary Multi-Objective Optimisation

How the (1+λ) evolutionary algorithm optimizes linear functions

MMAS Versus Population-Based EA on a Family of Dynamic Fitness Functions

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