On the diversity and robustness of parameterised multi-objective test suites

Yap, Estefania; Muñoz, Mario A.; Smith‐Miles, Kate

doi:10.1016/j.asoc.2021.107613

Cited by 3 publications

(3 citation statements)

References 36 publications

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“…To validate the developed APCE‐NSGA‐III algorithm, a classic multi‐objective optimization problem, ZDT1, is utilized in this section to illustrate the algorithm's accuracy. The ZDT1 problem and the corresponding theoretical Pareto frontier are expressed as follows (Yap et al., 2021):

\begin{equation}\left\{ { \def\eqcellsep{&}\begin{array}{@{}*{1}{l}@{}} {{g}_1\left( \bf{X} \right) = {x}_1}\\ {{g}_2\left( \bf{X} \right) = h\left( \bf{X} \right)\left[ {1 - \sqrt {{x}_1/h\left( {\bm{X}} \right)} } \right],\;h\left( \bf{X} \right) = 1 + \frac{9}{{n - 1}}\mathop \sum \limits_{i = 2}^n {x}_i}\\ {{x}_i \in \left[ {0,\;1} \right],\;i = 1,2,\; \ldots ,n}\\ {{\mathrm{with}}\;{\mathrm{Pareto}}\;{\mathrm{solutions}}\text{:}\;{x}_1 \in \left[ {0,\;1} \right]\;and\;{x}_i = 0,\;i = 2,3, \ldots ,n\;} \end{array} } \right.\end{equation}

…”

Section: Discussionmentioning

confidence: 99%

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Inverse analysis of deformation moduli for high arch dams using the displacement reconstruction technique and multi‐objective optimization

Li,

Wu,

Chen

et al. 2023

Computer aided Civil Eng

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The inverse analysis of the deformation moduli of high arch dams based on displacement monitoring data is essential for structural safety assessment. In traditional inverse analysis methods, the deformation moduli are identified based on the single‐objective optimization and the hydrostatic component derived from the statistical model. This type of method has two main shortcomings: First, it treats the essential multi‐objective optimization problem as a single‐objective problem; second, the extracted hydrostatic component may be biased due to the multicollinearity of variables in the statistical model. This paper presents a methodology for the inverse analysis of the deformation moduli of high arch dams under a multi‐objective optimization strategy. The methodology employs empirical mode decomposition to extract the aging component from displacement monitoring data. Then, thermomechanical analysis is used to reconstruct the remaining hydrostatic and temperature components, thereby avoiding the biases encountered in solving the statistical model. The adaptive polynomial chaos expansion method is embedded in the NSGA‐III algorithm to establish and solve multi‐objective functions in the inverse analysis. Additionally, a composite decision index considering errors and test information is proposed to determine acceptable deformation moduli from the Pareto solution set. A high arch dam is selected to illustrate this methodology with static and dynamic monitoring data. The results show that the identified deformation moduli have errors of 3.8% and 7.2% in displacement and acceleration, respectively. The proposed methodology can yield deformation modulus values that are more consistent with the physical implications than those of the single‐objective optimization method.

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\begin{equation}\left\{ { \def\eqcellsep{&}\begin{array}{@{}*{1}{l}@{}} {{g}_1\left( \bf{X} \right) = {x}_1}\\ {{g}_2\left( \bf{X} \right) = h\left( \bf{X} \right)\left[ {1 - \sqrt {{x}_1/h\left( {\bm{X}} \right)} } \right],\;h\left( \bf{X} \right) = 1 + \frac{9}{{n - 1}}\mathop \sum \limits_{i = 2}^n {x}_i}\\ {{x}_i \in \left[ {0,\;1} \right],\;i = 1,2,\; \ldots ,n}\\ {{\mathrm{with}}\;{\mathrm{Pareto}}\;{\mathrm{solutions}}\text{:}\;{x}_1 \in \left[ {0,\;1} \right]\;and\;{x}_i = 0,\;i = 2,3, \ldots ,n\;} \end{array} } \right.\end{equation}

…”

Section: Discussionmentioning

confidence: 99%

“…To validate the developed APCE-NSGA-III algorithm, a classic multi-objective optimization problem, ZDT1, is utilized in this section to illustrate the algorithm's accuracy. The ZDT1 problem and the corresponding theoretical Pareto frontier are expressed as follows (Yap et al, 2021):…”

Section: Performance Of Apce-nsga-iii Algorithmmentioning

confidence: 99%

Inverse analysis of deformation moduli for high arch dams using the displacement reconstruction technique and multi‐objective optimization

Li,

Wu,

Chen

et al. 2023

Computer aided Civil Eng

View full text Add to dashboard Cite

show abstract

“…In this paper, the ZDT,UF and DTLZ series of test functions [28] are selected instead of the real functions for expensive multi-objective optimization problems. The number of objectives for the ZDT and UF series test function is 2, the number of decision variables is 10, and the population size is 100.…”

Section: ) Test Problem and Algorithm Parameter Settingmentioning

confidence: 99%

Expensive Multiobjective Optimization Algorithm Based on Equivariate Component Analysis

Zi'an

Liu

2022

IEEE Access

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In order to reduce the cost of candidate solution evaluation in the process of solving expensive optimization problems, an expensive multi-objective optimization algorithm based on equivalence component analysis was proposed to study the influence of decision space equivalence components on the prediction accuracy of agent models. Based on the analysis of the equivalence of decision space attributes, a limit learning network based on the equivalence components was constructed for Pareto dominance prediction among candidate solutions. A multi-objective test problem with equivalent components was selected in Pareto dominance prediction experiments, the results of which showed that the algorithm can effectively improve the accuracy of Pareto dominance prediction among candidate solutions. Successively the candidate solutions were scored with multiple ELM (Extreme Learning Machine) models, selected for evaluation and updated, and integrated into the Pareto-based multi-objective evolutionary algorithm. Through comparative experiments on the test problem, the method could achieve a better Pareto approximation solution under the limitation of a limited number of evaluations, and the goal of reducing the cost of expensive multi-objective optimization calculations.INDEX TERMS expensive multi-objective optimization, equivalent components, Pareto dominance, Surrogate model.

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Informing Multiobjective Optimization Benchmark Construction Through Instance Space Analysis

Yap

Muñoz

Smith‐Miles

2022

IEEE Trans. Evol. Computat.

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On the diversity and robustness of parameterised multi-objective test suites

Cited by 3 publications

References 36 publications

Inverse analysis of deformation moduli for high arch dams using the displacement reconstruction technique and multi‐objective optimization

Inverse analysis of deformation moduli for high arch dams using the displacement reconstruction technique and multi‐objective optimization

Expensive Multiobjective Optimization Algorithm Based on Equivariate Component Analysis

Informing Multiobjective Optimization Benchmark Construction Through Instance Space Analysis

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