A minimax regret approach for robust multi-objective portfolio selection problems with ellipsoidal uncertainty sets

Li, Jun; Wang, Lishuai

doi:10.1016/j.cie.2020.106646

Cited by 13 publications

(8 citation statements)

References 49 publications

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“…, s x y define the objective function and the decision variables in optimal values of the above problem, respectively. If x is selected as the decision variables, then the relative regret associated with having decided x rather than * x can be defined as follows (3): [23] ( ) ( )…”

Section: Proposed Lsts-mmrr Methodologymentioning

confidence: 99%

Enhancing the Resilience of Hybrid Microgrids by Minimizing the Maximum Relative Regret in Two-Stage Stochastic Scheduling

2022

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Occurrence severe event with high-impact and low-probability (HILP), can cause significant disturbances to power grids. The strength of the system to withstand such HILP events is interpreted as system resilience. This paper proposes a novel approach for hybrid AC/DC microgrids with the aim of resilience enhancement and based on a linear stochastic two-stage scenario-based minimax relative regret (LSTS-MMRR) optimization according to the optimality robustness concept. Photovoltaic array and wind turbines, microturbines, and energy storage systems are scheduled based on the proposed approach in microgrids. Considering the uncertainty of emergency duration due to disruption from the upstream grid, the optimization problem is decomposed into standard and critical stochastic situations. This work also quantifies the importance of uncertainty with the well-known quantities named Value of Stochastic Solution (VSS) and Expected Value of Perfect Information (EVPI). For both normal and emergency circumstances, exclusive objective function and constraints are considered. Meanwhile, time-related variables maintain their continuity between normal and emergency circumstances. Therefore, the proposed approach minimized the maximum regret of objective function through defined scenarios. The proposed technique is compared with two common methods in resilience enhancement issues, and its effectiveness is demonstrated through an analysis of the VSS and EVPL.

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Section: Proposed Lsts-mmrr Methodologymentioning

confidence: 99%

Enhancing the Resilience of Hybrid Microgrids by Minimizing the Maximum Relative Regret in Two-Stage Stochastic Scheduling

2022

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“…. , u p } ; this setup is later extended to ellipsoidal uncertainty in Li and Wang (2020) . Furthermore, our understanding of the authors' framework is that they also focus solely on linear multiobjective optimization problems.…”

Section: Connection Tomentioning

confidence: 99%

Multiobjective optimization under uncertainty: A multiobjective robust (relative) regret approach

Groetzner

Werner

2022

European Journal of Operational Research

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Consider a multiobjective decision problem with uncertainty in the objective functions, given as a set of scenarios. In the single-criterion case, robust optimization methodology helps to identify solutions which remain feasible and of good quality for all possible scenarios. A well-known alternative method in the single-objective case is to compare possible decisions under uncertainty with the optimal decision with the benefit of hindsight, i.e. to minimize the (possibly scaled) regret of not having chosen the optimal decision. In this contribution, we extend the concept of regret from the single-objective case to the multiobjective setting and introduce a proper definition of multivariate (robust) (relative) regret. In contrast to the few existing ideas that mix scalarization and optimization, we clearly separate the modelling of multiobjective (robust) regret from its numerical solution. Moreover, our approach is not limited to a finite uncertainty set or interval uncertainty and furthermore, computations or at least approximations remain tractable in several important special cases. We illustrate all approaches based on a biobjective shortest path problem under uncertainty.

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“…Li and Wang [33] proposed a robust model for the multiobjective stock portfolio selection model. In their model, the goal programming approach is used to solve the multiobjective model.…”

Section: Literature Reviewmentioning

confidence: 99%

A Robust Multiobjective Mathematical Model Optimizing Stock Portfolio

Sadri

Sadeghi

Zaj

et al. 2022

Discrete Dynamics in Nature and Society

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The present paper investigates the problem of capital portfolio selection under uncertain conditions and uses a robust optimization approach for modeling. The model provided in this paper is a three-objective model that aims to maximize returns, maximize liquidity, and minimize risk. The data extracted from the site of the Tehran Stock Exchange are as follows. These data are related to twenty shares from July 2020 to July 2021. The robust approach used in this research has been analyzed by the real data of the Tehran Stock Exchange and then the optimal portfolio for different robust costs has been formed by solving the robust model. In the following section, the relevant model is solved through real stock market data and using the goal programming approach, and the results are investigated and analyzed.

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A minimax regret approach for robust multi-objective portfolio selection problems with ellipsoidal uncertainty sets

Cited by 13 publications

References 49 publications

Enhancing the Resilience of Hybrid Microgrids by Minimizing the Maximum Relative Regret in Two-Stage Stochastic Scheduling

Enhancing the Resilience of Hybrid Microgrids by Minimizing the Maximum Relative Regret in Two-Stage Stochastic Scheduling

Multiobjective optimization under uncertainty: A multiobjective robust (relative) regret approach

A Robust Multiobjective Mathematical Model Optimizing Stock Portfolio

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