Multi-objective Optimization under Uncertain Objectives: Application to Engineering Design Problem

Villa, Céline; Lozinguez, Eric; Labayrade, Raphaël

doi:10.1007/978-3-642-37140-0_59

Cited by 14 publications

(9 citation statements)

References 20 publications

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“…3.3 Phase 3: determine promising robust solutions using MOO search strategy In this critical phase, promising robust solutions for the MRO problem can be identified (Step 7 in Figure 1) based on an approach suggested by Villa et al (2013). Compared with the grid point approach Chapman et al (2014a), their approach determines Pareto solutions using each alternate RS model.…”

Section: A Robust Multiobjective Mro Solution Approachmentioning

confidence: 99%

“…Thus, in this study, NSGA-II is selected to derive efficient solutions for varied mean-variance MRO problems. The suggested optimal parameter settings of NSGA-II (Sharma and Mukherjee, 2020), adopted in this study, are given in Table 2 with three responses and two controllable process variables are provided in Appendix C. Results indicate that the nondominated solution points identified by the Villa et al (2013) approach had a higher likelihood to appear in nondominated fronts. Thus, for a specific MRO problem in this study, the promising robust solutions are identified by solving equations ( 12)-( 15) for each alternate RS model.…”

Section: A Robust Multiobjective Mro Solution Approachmentioning

confidence: 99%

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A robust multiobjective solution approach for mean-variance optimisation of correlated multiple quality characteristics

Sharma

Mukherjee

Bera

et al. 2021

IJQRM

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PurposeThe primary objective of this study is to propose a robust multiobjective solution search approach for a mean-variance multiple correlated quality characteristics optimisation problem, so-called “multiple response optimisation (MRO) problem”. The solution approach needs to consider response surface (RS) model parameter uncertainties, response uncertainties, process setting sensitivity and response correlation strength to derive the robust solutions iteratively.Design/methodology/approachThis study adopts a new multiobjective solution search approach to determine robust solutions for a typical mean-variance MRO formulation. A fine-tuned, non-dominated sorting genetic algorithm-II (NSGA-II) is used to derive efficient multiobjective solutions for varied mean-variance MRO problems. The iterative search considers RS model uncertainties, process setting uncertainties and response correlation structure to derive efficient fronts. The final solutions are ranked based on two different multi-criteria decision-making (MCDM) techniques.FindingsFive different mean-variance MRO cases are selected from the literature to verify the efficacy of the proposed solution approach. Results derived from the proposed solution approach are compared and contrasted with the best solution(s) derived from other approaches suggested in the literature. Comparative results indicate significant superiorities of the top-ranked predicted robust solutions in nondominated frequency, closeness-to-target and response variabilities.Research limitations/implicationsThe solution approach depends on RS modelling and considers continuous search space.Practical implicationsIn this study, promising robust solutions are expected to be more suitable for implementation than point estimate-based MOO solutions for a real-life MRO problem.Originality/valueNo evidence of earlier research demonstrates the superiority of a MOO-based iterative solution search approach for mean-variance MRO problems by simultaneously considering model uncertainties, response correlation and process setting sensitivity.

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Section: A Robust Multiobjective Mro Solution Approachmentioning

confidence: 99%

Section: A Robust Multiobjective Mro Solution Approachmentioning

confidence: 99%

A robust multiobjective solution approach for mean-variance optimisation of correlated multiple quality characteristics

Sharma

Mukherjee

Bera

et al. 2021

IJQRM

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“…从 20 世纪 80 年代开始出版了很多向量优化相关的专著和综述性文献 (参见文献 [42][43][44][45][46][47][48][49]). 与此同时, 这一学科在经济、决策、管理、工程设计、环境保护、医疗卫生、交通运输和国家安全等诸多领域得到了广泛的应用 (参见文献 [50][51][52]). 同样, 在向量优化问题理论与方法的研究中, 向量值映射的凸性或广义凸性概念也作为重要基础被诸多学者广泛研究.…”

Section: 此外我们还需要如下序关系unclassified

The linear scalarizations and Lagrange multipliers for vector optimization

Xinmin¹,

Chen²

2020

Sci. Sin.-Math.

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An alternating direction method of multipliers for elliptic equation constrained optimization problem SCIENCE CHINA Mathematics 60, 361 (2017); A new look at the Lagrange method for continuous-time stochastic optimization SCIENCE CHINA Mathematics 55, 2247 (2012); Continuity for vector optimization problems with equilibrium constraints Science in China Series A-Mathematics 47, 65 (2004); On the existence and regularity of vector solutions for quasilinear systems with linear coupling

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“…However, it was not until the early 2000s that a significant number of multi-objective optimisers began to be developed specifically to tackle uncertain optimisation [12], [13], [14], [5], [6], [15], [7], [16], [17], [18], [19], [20], [21], [22], [23]. Typically uncertainty is modelled as noise added to the function evaluations, although recent work has begun looking at the situation where the objective functions themselves are uncertain [24].…”

Section: Introductionmentioning

confidence: 99%

The Rolling Tide Evolutionary Algorithm: A Multiobjective Optimizer for Noisy Optimization Problems

Fieldsend

Everson

2015

IEEE Trans. Evol. Computat.

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Abstract-As methods for evolutionary multi-objective optimisation (EMO) mature and are applied to a greater number of real world problems, there has been gathering interest in the effect of uncertainty and noise on multi-objective optimisation. Specifically, how algorithms are affected by it, how to mitigate its effects, and whether some optimisers are better suited to dealing with it than others. Here we address the problem of uncertain evaluation, where the uncertainty can be modelled as additive noise in objective space. We develop a novel algorithm, the rolling tide evolutionary algorithm (RTEA), which progressively improves the accuracy of its estimated Pareto set, whilst simultaneously driving the front towards the true Pareto front. It can cope with noise whose characteristics change as a function of location (both design and objective), or which alter during the course of an optimisation. Four state-of-the-art noisetolerant EMO algorithms, as well as four widely used standard EMO algorithms, are compared to RTEA on 70 instances of ten continuous space test problems from the CEC'09 multiobjective optimisation test suite. Different instances of these problems are generated by modifying them to exhibit different types and intensities of noise. RTEA is seen to provide competitive performance across both the range of test problems used, and noise types.

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Multi-objective Optimization under Uncertain Objectives: Application to Engineering Design Problem

Cited by 14 publications

References 20 publications

A robust multiobjective solution approach for mean-variance optimisation of correlated multiple quality characteristics

A robust multiobjective solution approach for mean-variance optimisation of correlated multiple quality characteristics

The linear scalarizations and Lagrange multipliers for vector optimization

The Rolling Tide Evolutionary Algorithm: A Multiobjective Optimizer for Noisy Optimization Problems

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