On using the hypervolume indicator to compare Pareto fronts: Applications to multi-criteria optimal experimental design

Summary The current paper presents a multi‐objective approach for the optimal placement of phasor measurement units (PMUs) for small‐signal stability assessment of a power system. The proposed methodology is based on a multi‐signal Prony analysis of the voltage amplitude, voltage angle, and frequency signals measured by the PMUs. A Pareto Archive Differential Evolution (PADE) algorithm is used to determine the best location of PMUs minimizing the PMUs number and maximizing the signal‐to‐noise ratio (SNR) subject to full system constraints. The capability of the proposed approach has been demonstrated through several cases studies, where it gives an accurate estimation of electromechanical modes when confronted with modal analysis under various scenarios, disturbances, and measurement noise. Additionally, the PADE algorithm is compared with nondominated sorting approach (NSGA)‐III, multi‐objective differential evolution (MODE), and multi‐objective particle swarm optimization (MOPSO) algorithms, and the superiority of PADE algorithm for solving the optimal PMUs placement (OPP) problem is demonstrated.

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“…To compare the performance of PADE with that of other MOEAs, the hyper‐volume indicator used by another study are used.…”

Section: Case Studymentioning

confidence: 99%

Multi‐objective optimal PMUs placement for online assessment of small‐signal stability

Tarif

Amrane

Chabane

2019

Int Trans Electr Energ Syst

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“…Hybrid measures which overlap the above three categories have been also introduced in the literature. An example is the hypervolume measure, a well-established indicator of a front's quality [3][4].…”

Section: Pareto Optimality-dominance Relationmentioning

confidence: 99%

Responses’ Prediction Standard Error Analysis in Pareto Solutions

Costa

Lourenço

2017

MATEC Web Conf.

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A Pareto front provides to the decision-maker a set of optimal solutions from where a unique solution should be selected to solve a multiresponse problem. However, the responses' prediction standard error for each one of the optimal solutions is different, which impacts on the reproducibility of Pareto solutions. This means that the decision-maker has to take into account the responses' prediction standard error in the solution selection process. For this purpose, a metric is presented. A bi-objective problem is used as example and results displayed graphically.

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“…the solutions scaled to be between 0 and 1) obtained by the algorithm and the hypervolume enclosed by the standardized P F 351 ; (5) the CPU time (minutes) required for an algorithm to reach the stopping criterion; (6) N E; and (7) N C. Note that the hypervolume measure requires a user-defined reference point, which we choose to be r = (−0.0031, −0.0031, −0.0031) T , leading to a hypervolume of 0.6157 for the standardized P F 351 ; for justification and details see Cao et al (2015).…”

Section: Three-criteria Benchmark Examplementioning

confidence: 99%

A hybrid elitist pareto-based coordinate exchange algorithm for constructing multi-criteria optimal experimental designs

2016

Self Cite

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This paper presents a new Pareto-based coordinate exchange algorithm for populating or approximating the true Pareto front for multi-criteria optimal experimental design problems that arise naturally in a range of industrial applications. This heuristic combines an elitist-like operator inspired by evolutionary multi-objective optimization algorithms with a coordinate exchange operator that is commonly used to construct optimal designs. Benchmarking results from both a two-dimensional and three-dimensional example demonstrate that the proposed hybrid algorithm can generate highly reliable Pareto fronts with less computational effort than existing procedures in the statistics literature. The proposed algorithm also utilizes a multi-start operator, which makes it readily parallelizable for high performance computing infrastructures.

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On using the hypervolume indicator to compare Pareto fronts: Applications to multi-criteria optimal experimental design

Cited by 90 publications

References 12 publications

Multi‐objective optimal PMUs placement for online assessment of small‐signal stability

Multi‐objective optimal PMUs placement for online assessment of small‐signal stability

Responses’ Prediction Standard Error Analysis in Pareto Solutions

A hybrid elitist pareto-based coordinate exchange algorithm for constructing multi-criteria optimal experimental designs

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