On the Brittleness of Evolutionary Algorithms

Jansen, Thomas

doi:10.1007/978-3-540-73482-6_4

Cited by 32 publications

(24 citation statements)

References 10 publications

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“…In fact, we are not aware of any other results apart from the Jansen's work [10] described above and [4], which shows for the (1 + 1) EA (i) that all monotonic functions are optimized in time O(n log n) when the mutation probability is c/n with c < 1 and (ii) that there are monotonic functions such that a mutation probability of at least 16/n results in an exponential runtime. This last result indicates that the class of monotonic functions is more complex than the one of linear functions-for the latter, [3] for the first time showed an optimization time of O(n log n) for all mutation rates c/n, c a constant.…”

Section: Related Resultsmentioning

confidence: 88%

“…For optimization processes with even more misleading selection decisions like Jansen's PO-EA, things are even worse. For example, it takes around three pages of impressive calculations in [10] to estimate the expected Hamming distance of the outcome of one mutation-selection cycle (it decreases by Θ(z 2 /n 2 ), where z is the number of zeros of the parent individual).…”

Section: Methods: Overcoming the Dependencies Imposed By The Mutationmentioning

confidence: 99%

“…Recall that the PO-EA accepts the worse among parent and offspring whenever there is no domination among the two. It was already noted in [10] that there is no monotonic function leading to the fitness landscape assumed by the PO-EA. We now argue that any monotonic function f leads to a considerable number of solutions x, y such that there is no domination between x and y, y is closer to the optimum than x, and f (y) > f (x).…”

Section: Extending the Po-ea Modelmentioning

confidence: 96%

“…As outlined in the introduction, we extend in this work the PO-EA algorithm introduced in Jansen's article [10] by allowing a general mutation probability c/n (determined by a parameter c > 0) and a degree q ∈ [0, 1] of pessimism, which is the probability that selection is done via the pessimistic PO selection of Jansen's PO-EA and not by the standard selection. See Algorithm 1 for the pseudo-code of this algorithm PO-EA(c, q).…”

Section: Algorithms Consideredmentioning

confidence: 98%

“…One interesting attempt towards understanding the optimization behavior of evolutionary methods on monotonic functions was made by Jansen [10], who suggested the following pessimistic version of the optimization process of the (1 + 1) EA on a monotonic function. In this process called partially ordered EA (PO-EA), a run of the (1+ 1) EA (with standard mutation probability 1/n) on a monotonic function is simulated.…”

Section: Introductionmentioning

confidence: 99%

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Monotonic functions in EC

Colin

Doerr

Férey

2014

Proceedings of the 2014 Annual Conference on Genetic and Evolutionary Computation

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To understand how evolutionary algorithms optimize the simple class of monotonic functions, Jansen (FOGA 2007) introduced the partially-ordered evolutionary algorithm (PO-EA) model and analyzed its runtime. The PO-EA is a pessimistic model of the true optimization process, hence performance guarantees for it immediately take over to the true optimization process.Based on the observation that Jansen's model leads to a process more pessimistic than what any monotonic function would, we extend his model by parameterizing the degree of pessimism. For all degrees of pessimism, and all mutation rates c/n, we give a precise runtime analysis of this process. For all degrees of pessimism lower than that of Jansen, we observe a Θ(n log n) runtime for the standard mutation probability of 1/n. However, we also observe a strange double-jump behavior in terms of the mutation probability. For all non-zero degrees of pessimism, there is a threshold c ∈ R such that (i) for mutation rates c /n with c < c we have a Θ(n log n) runtime, (ii) for the mutation rate c/n we have a runtime of Θ(n 3/2 ), and (iii) for mutation rates c /n with c > c we have an exponential runtime.To overcome the complicated interplay of mutation and selection in the PO-EA, by define artificial algorithms which provably (via a coupling argument) have the same asymptotic runtime, but allow a much easier computation of the drift towards the optimum.

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Section: Related Resultsmentioning

confidence: 88%

Section: Methods: Overcoming the Dependencies Imposed By The Mutationmentioning

confidence: 99%

Section: Extending the Po-ea Modelmentioning

confidence: 96%

Section: Algorithms Consideredmentioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

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