Error analysis of elitist randomized search heuristics

Chen, Yu; He, Jifeng; Xie, Chengwang

doi:10.1016/j.swevo.2021.100875

Cited by 4 publications

(6 citation statements)

References 42 publications

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“…Dongwen Li et al [44] proposed a combined model based on RSM-XGBoost and KF algorithm to study the remaining life prediction problem of an aircraft engine, and solved the noise influence problem by adding a Carr filter to achieve higher life prediction accuracy. Cong Wang et al [45] worked on analyzing the elite RSH by estimating the desired approximation error. Based on the distribution of non-zero elements in the Markov chain transfer matrix, the search process of the elite RSH was classified into three categories, and a general framework for estimating the approximation error, called error analysis, was proposed.…”

Section: Diagnostic Methods Accuracymentioning

confidence: 99%

Fault Diagnosis Strategy Based on BOA-ResNet18 Method for Motor Bearing Signals with Simulated Hydrogen Refueling Station Operating Noise

Liu,

Chen,

Chen

et al. 2023

Applied Sciences

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The harsh working environment of hydrogen refueling stations often causes equipment failure and is vulnerable to mechanical noise during monitoring. This limits the accuracy of equipment monitoring, ultimately decreasing efficiency. To address this issue, this paper presents a motor bearing vibration signal diagnosis method that employs a Bayesian optimization (BOA) residual neural network (ResNet). The industrial noise signal of the hydrogenation station is simulated and then combined with the motor bearing signal. The resulting one-dimensional bearing signal is processed and transformed into a two-dimensional signal using Fast Fourier Transform (FFT). Afterwards, the signal is segmented using the sliding window translation method to enhance the data volume. After comparing signal feature extraction and classification results from various convolutional neural network models, ResNet18 yields the best classification accuracy, achieving a training accuracy of 89.50% with the shortest computation time. Afterwards, the hyperparameters of ResNet18 such as InitialLearnRate, Momentum, and L2Regularization Parameter are optimized using the Bayesian optimization algorithm. The experiment findings demonstrate a diagnostic accuracy of 99.31% for the original signal model, while the accuracy for the bearing signal, with simulated industrial noise from the hydrogenation station, can reach over 92%.

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Section: Diagnostic Methods Accuracymentioning

confidence: 99%

Fault Diagnosis Strategy Based on BOA-ResNet18 Method for Motor Bearing Signals with Simulated Hydrogen Refueling Station Operating Noise

Liu,

Chen,

Chen

et al. 2023

Applied Sciences

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“…Nallaperuma et al [42] considered the well-known traveling salesperson problem (TSP) and derived the lower bounds of the expected fitness gain for a specified number of generations. Based on the Markov chain model of RSHs, Wang et al [29] constructed a general framework of FBA, by which they found the analytic expression of approximation error instead of asymptotic results of expected fitness values. Doerr et al [43] built a bridge between runtime analysis and FBA, by which a huge body of work and a large collection of tools for the analysis of the expected optimization time could meet the new challenges introduced by the new fixed-budget perspective.…”

Section: Fixed-budget Analysis and Approximation Errormentioning

confidence: 99%

“…Due to this reason, optimization time is seldom used in computer simulation for evaluating the performance of EAs, and their performance is evaluated after running finite generations by solution quality such as the mean and median of the fitness value or approximation error [26]. In theory, solution quality can be measured for a given iteration budget by the expected fitness value [27] or approximation error [28,29], which contributes to the analysis framework named fixed-budget analysis (FBA). An FBA on immune-inspired hypermutations led to theoretical results that are very different from those of runtime analysis but consistent with the empirical results, which demonstrates that the perspective of fixed-budget computations provides valuable information and additional insights for the performance of randomized search heuristics [30].…”

Section: Introductionmentioning

confidence: 99%

Influence of Binomial Crossover on Approximation Error of Evolutionary Algorithms

Chen

Zou

2022

Mathematics

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Although differential evolution (DE) algorithms perform well on a large variety of complicated optimization problems, only a few theoretical studies are focused on the working principle of DE algorithms. To make the first attempt to reveal the function of binomial crossover, this paper aims to answer whether it can reduce the approximation error of evolutionary algorithms. By investigating the expected approximation error and the probability of not finding the optimum, we conduct a case study comparing two evolutionary algorithms with and without binomial crossover on two classical benchmark problems: OneMax and Deceptive. It is proven that using binomial crossover leads to the dominance of transition matrices. As a result, the algorithm with binomial crossover asymptotically outperforms that without crossover on both OneMax and Deceptive, and outperforms on OneMax, however, not on Deceptive. Furthermore, an adaptive parameter strategy is proposed which can strengthen the superiority of binomial crossover on Deceptive.

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“…One can get full information of RSHs from the transition Matrix R, however, it does not display performances of RSHs in an intuitive way. Thus, we take the expected approximation error (EAE) and the tail probability (TP) as the evaluate metrics for performance comparison of RSHs [21], [22].…”

Section: Performance Metricsmentioning

confidence: 99%

“…For the OneMax problem,outperformance of the (1 + 1)EA C over the (1 + 1)EA and (1 + 1)EA CM is based on the following lemma [22].…”

Section: Influence Of the Binomial Crossover On Performances On The O...mentioning

confidence: 99%

Influence of Binomial Crossover on Approximation Error of Evolutionary Algorithms

He¹,

Chen²,

Zou³

2021

Preprint

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Unlike other metaheuristics, differential Evolution (DE) employs a crossover operation filtering variables to be mutated, which contributes to its successful applications in a variety of complicated optimization problems. However, the underlying working principles of the crossover operation is not yet fully understood. In this paper, we try to reveal influence of the binomial crossover by performing theoretical comparison between the (1 + 1)EA and its variants, the (1 + 1)EAC and the (1 + 1)EACM . Generally, introduction of the binomial crossover contributes to enhancement of the exploration ability as well as degradation of the exploitation ability, and under some conditions, leads to the dominance of transition matrix for binary optimization problems. As a result, both the (1 + 1)EAC and the (1 + 1)EACM outperform the (1 + 1)EA on the unimodal OneMax problem, but do not always dominate it on the Deceptive problem. Finally, we perform exploration analysis by investigating probabilities to transfer from non-optimal statuses to the optimal status of the Deceptive problem, inspired by which adaptive strategies are proposed to improve the ability of global exploration. It suggests that incorporation of the binomial crossover could be a feasible strategy to improve performances of randomized search heuristics.

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Error analysis of elitist randomized search heuristics

Cited by 4 publications

References 42 publications

Fault Diagnosis Strategy Based on BOA-ResNet18 Method for Motor Bearing Signals with Simulated Hydrogen Refueling Station Operating Noise

Fault Diagnosis Strategy Based on BOA-ResNet18 Method for Motor Bearing Signals with Simulated Hydrogen Refueling Station Operating Noise

Influence of Binomial Crossover on Approximation Error of Evolutionary Algorithms

Influence of Binomial Crossover on Approximation Error of Evolutionary Algorithms

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