Although some studies have achieved good optimization results when solving noisy mul-tiobjective optimization problems (NMOPs), these studies require considerable computa-tional resources to reduce the impact of noise...
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Although some studies have achieved good optimization results when solving noisy mul-tiobjective optimization problems (NMOPs), these studies require considerable computa-tional resources to reduce the impact of noise on evolutionary algorithms. Inspired by the universal approximation theorem, we use a radial basis network (RBN) to estimate the noise-free fitness and embed it into the classical multiobjective algorithm NSGA-II to solve NMOPs, called RBN-NSGA-II. Specifically, the averaged fitness after individual resam-pling is used as the training sample of the RBN, and then, the trained RBN is used to sim-ulate the fitness functions and estimate the noise-free fitness. Also, to better simulate the shape of the fitness functions, the RBN is adaptively updated based on its estimated error, and its training samples are gradually increased based on the population distribution in the search space. Experimental results demonstrate that RBN-NSGA-II markedly improves the optimization speed while maintaining good search ability compared with six state-of-the-art algorithms, which is important in practical noisyoptimization scenarios.(c) 2022 Elsevier Inc. All rights reserved.
This paper proposes and evaluates an indicator based and noise-aware dominance operator for evolutionary algorithms to solve the multiobjectiveoptimization problems (MOPs) that contain noise in their objective functi...
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ISBN:
(纸本)9781479954315
This paper proposes and evaluates an indicator based and noise-aware dominance operator for evolutionary algorithms to solve the multiobjectiveoptimization problems (MOPs) that contain noise in their objective functions. The proposed operator, U(R)2(-)dominance operator is designed with (1) a quality indicator, called R2 indicator, which quantifies the goodness of a given solution candidate (individual) and (2) a non-parametric (i.e., distribution-free) statistical significance test called the Mann Whitney U-test. The U-R2-dominance operator takes samples of given two individuals in the objective space, calculates the R2 indicator value for each sample, estimates the impacts of noise on the R2 values with a U-test, and determines which individual is statistically superior/inferior. Experimental results show that it operates reliably in noisy MOPs and outperforms existing noise aware dominance operators particularly when many outliers exist under asymmetric noise distributions.
Optimizing a field-scale in-situ leaching (ISL) of uranium system under uncertainty in sandstone reservoirs by simulation-optimization (SO) models is a challenging problem, often referred to as a noisyoptimization pr...
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Optimizing a field-scale in-situ leaching (ISL) of uranium system under uncertainty in sandstone reservoirs by simulation-optimization (SO) models is a challenging problem, often referred to as a noisyoptimization problem. The practical utility of classic stochastic optimization methods has been limited, particularly when addressing subsurface spatial heterogeneity and sophisticated reactive transport modeling (RTM). A traditional method of handling uncertainty in optimization is accomplished by the Monte Carlo sampling strategy to discover reliable optimal solutions, but such an optimization process is generally redundant and computationally prohibitive for the ISL design problem. Here, this study intends to incorporate a novel noise-handling strategy into a multiobjective evolutionary algorithm, along with using a deep learning-based proxy model to substitute the timeconsuming simulation model. By doing so, the recurrent residual U-Net model is constructed as an alternative to RTM simulator for predicting spatiotemporal uranium recovery concentrations, and a k-Nearest-Neighbor averaging (kNN-averaging) denoising technique is introduced to deal with the uncertainty associated with the objectives in optimization. We then demonstrate the performance of the proposed methodology through the field-scale ISL design problem in northeastern China. Comparative results indicate that the proposed approach is of robust operation and efficient performance in finding optimal solutions to the noisy multiobjective optimization problems in terms of both convergence and diversity. The study provides a novel, computationally efficient approach to assist multiobjective decision-making processes for ISL system design under multiple uncertainties.
In the context of noisy Multi-Objective optimization, dealing with uncertainties requires the decision maker to define some preferences about how to handle them, through some statistics (e.g., mean, median) to be used...
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ISBN:
(纸本)9783319107622;9783319107615
In the context of noisy Multi-Objective optimization, dealing with uncertainties requires the decision maker to define some preferences about how to handle them, through some statistics (e.g., mean, median) to be used to evaluate the qualities of the solutions, and define the corresponding Pareto set. Approximating these statistics requires repeated samplings of the population, drastically increasing the overall computational cost. To tackle this issue, this paper proposes to directly estimate the probability of each individual to be selected, using some Hoeffding races to dynamically assign the estimation budget during the selection step. The proposed racing approach is validated against static budget approaches with NSGA-II on noisy versions of the ZDT benchmark functions.
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