Regular coronavirus disease 2019(COVID-19)epidemic prevention and control have raised new require-ments that necessitate operation-strategy innovation in urban rail transit.To alleviate increasingly seri-ous congestio...Regular coronavirus disease 2019(COVID-19)epidemic prevention and control have raised new require-ments that necessitate operation-strategy innovation in urban rail transit.To alleviate increasingly seri-ous congestion and further reduce the risk of cross-infection,a novel two-stage distributionally robust optimization(DRO)model is explicitly constructed,in which the probability distribution of stochastic scenarios is only partially known in advance.In the proposed model,the mean-conditional value-at-risk(CVaR)criterion is employed to obtain a tradeoff between the expected number of waiting passen-gers and the risk of congestion on an urban rail transit line.The relationship between the proposed DRO model and the traditional two-stage stochastic programming(SP)model is also depicted.Furthermore,to overcome the obstacle of model solvability resulting from imprecise probability distributions,a discrepancy-based ambiguity set is used to transform the robust counterpart into its computationally tractable form.A hybrid algorithm that combines a local search algorithm with a mixed-integer linear programming(MILP)solver is developed to improve the computational efficiency of large-scale instances.Finally,a series of numerical examples with real-world operation data are executed to validate the pro-posed approaches.展开更多
A mathematical programming approach rooted in distributionally robust optimization(DRO)provides an effective data-driven strategy for battery energy storage system(BESS)planning.Nevertheless,the DRO paradigm often lac...A mathematical programming approach rooted in distributionally robust optimization(DRO)provides an effective data-driven strategy for battery energy storage system(BESS)planning.Nevertheless,the DRO paradigm often lacks interpretability in its results,obscuring the causal relationships between data distribution characteristics and the outcomes.Furthermore,the current approach to battery type selection is not included in traditional BESS planning,hindering comprehensive optimization.To tackle these BESS planning problems,this paper presents a universal method for BESS planning,which is designed to enhance the interpretability of DRO.First,mathematical definitions of interpretable DRO(IDRO)are introduced.Next,the uncertainties in wind power,photovoltaic power,and loads are modeled by using second-order cone ambiguity sets(SOCASs).In addition,the proposed method integrates selection,sizing,and siting.Moreover,a second-order cone bidirectional-orthogonal strategy is proposed to solve the BESS planning problems.Finally,the effectiveness of the proposed method is demonstrated through case studies,offering planners richer decision-making insights.展开更多
Distributionally robust optimization is a dominant paradigm for decision-making problems where the distribution of random variables is unknown.We investigate a distributionally robust optimization problem with ambigui...Distributionally robust optimization is a dominant paradigm for decision-making problems where the distribution of random variables is unknown.We investigate a distributionally robust optimization problem with ambiguities in the objective function and countably infinite constraints.The ambiguity set is defined as a Wasserstein ball centered at the empirical distribution.Based on the concentration inequality of Wasserstein distance,we establish the asymptotic convergence property of the datadriven distributionally robust optimization problem when the sample size goes to infinity.We show that with probability 1,the optimal value and the optimal solution set of the data-driven distributionally robust problem converge to those of the stochastic optimization problem with true distribution.Finally,we provide numerical evidences for the established theoretical results.展开更多
In this paper,we study the distributionally robust joint chance-constrained Markov decision process.Utilizing the logarithmic transformation technique,we derive its deterministic reformulation with bi-convex terms und...In this paper,we study the distributionally robust joint chance-constrained Markov decision process.Utilizing the logarithmic transformation technique,we derive its deterministic reformulation with bi-convex terms under the moment-based uncertainty set.To cope with the non-convexity and improve the robustness of the solution,we propose a dynamical neural network approach to solve the reformulated optimization problem.Numerical results on a machine replacement problem demonstrate the efficiency of the proposed dynamical neural network approach when compared with the sequential convex approximation approach.展开更多
基金supported the National Natural Science Foundation of China (71621001, 71825004, and 72001019)the Fundamental Research Funds for Central Universities (2020JBM031 and 2021YJS203)the Research Foundation of State Key Laboratory of Rail Traffic Control and Safety (RCS2020ZT001)
文摘Regular coronavirus disease 2019(COVID-19)epidemic prevention and control have raised new require-ments that necessitate operation-strategy innovation in urban rail transit.To alleviate increasingly seri-ous congestion and further reduce the risk of cross-infection,a novel two-stage distributionally robust optimization(DRO)model is explicitly constructed,in which the probability distribution of stochastic scenarios is only partially known in advance.In the proposed model,the mean-conditional value-at-risk(CVaR)criterion is employed to obtain a tradeoff between the expected number of waiting passen-gers and the risk of congestion on an urban rail transit line.The relationship between the proposed DRO model and the traditional two-stage stochastic programming(SP)model is also depicted.Furthermore,to overcome the obstacle of model solvability resulting from imprecise probability distributions,a discrepancy-based ambiguity set is used to transform the robust counterpart into its computationally tractable form.A hybrid algorithm that combines a local search algorithm with a mixed-integer linear programming(MILP)solver is developed to improve the computational efficiency of large-scale instances.Finally,a series of numerical examples with real-world operation data are executed to validate the pro-posed approaches.
基金supported by the National Natural Science Foundation of China(No.51977046)。
文摘A mathematical programming approach rooted in distributionally robust optimization(DRO)provides an effective data-driven strategy for battery energy storage system(BESS)planning.Nevertheless,the DRO paradigm often lacks interpretability in its results,obscuring the causal relationships between data distribution characteristics and the outcomes.Furthermore,the current approach to battery type selection is not included in traditional BESS planning,hindering comprehensive optimization.To tackle these BESS planning problems,this paper presents a universal method for BESS planning,which is designed to enhance the interpretability of DRO.First,mathematical definitions of interpretable DRO(IDRO)are introduced.Next,the uncertainties in wind power,photovoltaic power,and loads are modeled by using second-order cone ambiguity sets(SOCASs).In addition,the proposed method integrates selection,sizing,and siting.Moreover,a second-order cone bidirectional-orthogonal strategy is proposed to solve the BESS planning problems.Finally,the effectiveness of the proposed method is demonstrated through case studies,offering planners richer decision-making insights.
基金the National Natural Science Foundation of China(Nos.11991023,11901449,11735011).
文摘Distributionally robust optimization is a dominant paradigm for decision-making problems where the distribution of random variables is unknown.We investigate a distributionally robust optimization problem with ambiguities in the objective function and countably infinite constraints.The ambiguity set is defined as a Wasserstein ball centered at the empirical distribution.Based on the concentration inequality of Wasserstein distance,we establish the asymptotic convergence property of the datadriven distributionally robust optimization problem when the sample size goes to infinity.We show that with probability 1,the optimal value and the optimal solution set of the data-driven distributionally robust problem converge to those of the stochastic optimization problem with true distribution.Finally,we provide numerical evidences for the established theoretical results.
基金supported by National Natural Science Foundation of China(Grant Nos.11991023 and 12371324)National Key R&D Program of China(Grant No.2022YFA1004000)。
文摘In this paper,we study the distributionally robust joint chance-constrained Markov decision process.Utilizing the logarithmic transformation technique,we derive its deterministic reformulation with bi-convex terms under the moment-based uncertainty set.To cope with the non-convexity and improve the robustness of the solution,we propose a dynamical neural network approach to solve the reformulated optimization problem.Numerical results on a machine replacement problem demonstrate the efficiency of the proposed dynamical neural network approach when compared with the sequential convex approximation approach.
