A new analysis method for evolutionary optimization of dynamic and noisy objective functions

Dang-Nhu, Raphaël; Dardinier, Thibault; Doerr, Benjamin; Izacard, Gautier; Nogneng, Dorian

doi:10.1145/3205455.3205563

Cited by 34 publications

(17 citation statements)

References 13 publications

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“…The goal of OM is maximizing the number of 1s in a solution, while the goal of LO is maximizing the number of continuous 1s from the first bit in a solution. Runtime analysis for the two problems under various noise models [15][16][17][18][19][20] showed that only if the noise level is low, (1+1)-EA can quickly find the optimum. For instance, onebit noise is a frequently-used noise model in theoretical analysis.…”

Section: Introductionmentioning

confidence: 99%

“…For OM of size n under onebit noise, the expected runtime (ERT) of (1+1)-EA is superpolynomial if p = ω(log n/n). There are also some studies concerning the effectiveness of various strategies to tackle noise, e.g., threshold selection [19,21,22], populations [16,18,20,23,24], and sampling [25][26][27]. For instance, if µ = Θ(log n), the ERT of (µ + 1)-EA optimizing OM under onebit noise is polynomial for any p ∈ [0, 1] (note that p denotes the noise probability).…”

Section: Introductionmentioning

confidence: 99%

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On the robustness of median sampling in noisy evolutionary optimization

Bian

Qian

et al. 2021

Sci. China Inf. Sci.

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Evolutionary algorithms (EAs) are a sort of nature-inspired metaheuristics, which have wide applications in various practical optimization problems. In these problems, objective evaluations are usually inaccurate, because noise is almost inevitable in real world, and it is a crucial issue to weaken the negative effect caused by noise. Sampling is a popular strategy, which evaluates the objective a couple of times, and employs the mean of these evaluation results as an estimate of the objective value. In this work, we introduce a novel sampling method, median sampling, into EAs, and illustrate its properties and usefulness theoretically by solving OneMax, the problem of maximizing the number of 1s in a bit string. Instead of the mean, median sampling employs the median of the evaluation results as an estimate. Through rigorous theoretical analysis on OneMax under the commonly used onebit noise, we show that median sampling reduces the expected runtime exponentially. Next, through two special noise models, we show that when the 2-quantile of the noisy fitness increases with the true fitness, median sampling can be better than mean sampling; otherwise, it may fail and mean sampling can be better. The results may guide us to employ median sampling properly in practical applications.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the robustness of median sampling in noisy evolutionary optimization

Bian

Qian

et al. 2021

Sci. China Inf. Sci.

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“…The studies show that the (1+1)-EA is efficient, i.e., it can find an optimal solution in polynomial running time, only under low noise levels. Later studies mainly proved the robustness of different strategies against noise, including using populations [3,9,10,11,12], sampling [4,13] and threshold selection [14]. There is also a sequence of papers analyzing the running time of the compact genetic algorithm [15] and a simple ant colony optimization algorithm [16,17,18,19] solving noisy problems, including OneMax as well as the combinatorial optimization problem, single destination shortest paths.…”

Section: Introductionmentioning

confidence: 99%

Running Time Analysis of the (1+1)-EA for Robust Linear Optimization

Bian¹,

Qian²,

Tang³

2019

Preprint

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Evolutionary algorithms (EAs) have found many successful real-world applications, where the optimization problems are often subject to a wide range of uncertainties. To understand the practical behaviors of EAs theoretically, there are a series of efforts devoted to analyzing the running time of EAs for optimization under uncertainties. Existing studies mainly focus on noisy and dynamic optimization, while another common type of uncertain optimization, i.e., robust optimization, has been rarely touched. In this paper, we analyze the expected running time of the (1+1)-EA solving robust linear optimization problems (i.e., linear problems under robust scenarios) with a cardinality constraint . Two common robust scenarios, i.e., deletion-robust and worst-case, are considered. Particularly, we derive tight ranges of the robust parameter or budget allowing the (1+1)-EA to find an optimal solution in polynomial running time, which disclose the potential of EAs for robust optimization.

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“…The presence of noise further increases the randomness of optimization, and only a few results on noisy evolutionary optimization have been reported. The (1+1)-EA algorithm, which uses population size 1 and mutation only, was first studied on the OneMax and LeadingOnes problems under various noise models [6,10,14,19,27,30]. OneMax and LeadingOnes are two benchmark pseudo-Boolean problems, widely used in theoretical analyses of EAs, whose goals are to maximize the number of 1-bits of a solution and the number of consecutive 1-bits counting from the left of a solution, respectively.…”

Section: Introductionmentioning

confidence: 99%

“…Later studies mainly investigated the robustness of different strategies against noise, including using populations [9,10,19,24,30], sampling [25,26,28] and threshold selection [27]. For example, the (µ + 1)-EA with µ = Θ(log n) can solve OneMax in polynomial time even if the probability of one-bit noise reaches 1.…”

Section: Introductionmentioning

confidence: 99%

On the Robustness of Median Sampling in Noisy Evolutionary Optimization

Bian¹,

Qian

2019

Preprint

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In real-world optimization tasks, the objective (i.e., fitness) function evaluation is often disturbed by noise due to a wide range of uncertainties. Evolutionary algorithms (EAs) have been widely applied to tackle noisy optimization, where reducing the negative effect of noise is a crucial issue. One popular strategy to cope with noise is sampling, which evaluates the fitness multiple times and uses the sample average to approximate the true fitness. In this paper, we introduce median sampling as a noise handling strategy into EAs, which uses the median of the multiple evaluations to approximate the true fitness instead of the mean. We theoretically show that median sampling can reduce the expected running time of EAs from exponential to polynomial by considering the (1+1)-EA on OneMax under the commonly used one-bit noise. We also compare mean sampling with median sampling by considering two specific noise models, suggesting that when the 2-quantile of the noisy fitness increases with the true fitness, median sampling can be a better choice. The results provide us with some guidance to employ median sampling efficiently in practice.

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A new analysis method for evolutionary optimization of dynamic and noisy objective functions

Cited by 34 publications

References 13 publications

On the robustness of median sampling in noisy evolutionary optimization

On the robustness of median sampling in noisy evolutionary optimization

Running Time Analysis of the (1+1)-EA for Robust Linear Optimization

On the Robustness of Median Sampling in Noisy Evolutionary Optimization

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