Prescriptive PCA: Dimensionality Reduction for Two-stage Stochastic Optimization

In this paper, we consider the alignment between an upstream dimensionality reduction task of learning a low-dimensional representation of a set of high-dimensional data and a downstream optimization task of solving a stochastic program parameterized by said representation. In this case, standard dimensionality reduction methods (e.g., principal component analysis) may not perform well, as they aim to maximize the amount of information retained in the representation and do not generally reflect the importance of such information in the downstream optimization problem. To address this problem, we develop a prescriptive dimensionality reduction framework that aims to minimize the degree of suboptimality in the optimization phase. For the case where the downstream stochastic optimization problem has an expected value objective, we show that prescriptive dimensionality reduction can be performed via solving a distributionally-robust optimization problem, which admits a semidefinite programming relaxation. Computational experiments based on a warehouse transshipment problem and a vehicle repositioning problem show that our approach significantly outperforms principal component analysis with real and synthetic data sets

Impact of Flexible and Bidirectional Charging in Medium- and Heavy-Duty Trucks on California's Decarbonization Pathway

California has committed to ambitious decarbonization targets across multiple sectors, including decarbonizing the electrical grid by 2045. In addition, the medium- and heavy-duty truck fleets are expected to see rapid electrification over the next two decades. Considering these two pathways in tandem is critical for ensuring cost optimality and reliable power system operation. In particular, we examine the potential cost savings of electrical generation infrastructure by enabling flexible charging and bidirectional charging for these trucks. We also examine costs adjacent to enabling these services, such as charger upgrades and battery degradation. We deploy a large mixed-integer decarbonization planning model to quantify the costs associated with the electric generation decarbonization pathway. Example scenarios governing truck driving and charging behaviors are implemented to reveal the sensitivity of temporal driving patterns. Our experiments show that cost savings on the order of multiple billions of dollars are possible by enabling flexible and bidirectional charging in medium- and heavy-duty trucks in California

A distributionally robust index tracking model with the CVaR penalty: tractable reformulation

We propose a distributionally robust index tracking model with the conditional value-at-risk (CVaR) penalty. The model combines the idea of distributionally robust optimization for data uncertainty and the CVaR penalty to avoid large tracking errors. The probability ambiguity is described through a confidence region based on the first-order and second-order moments of the random vector involved. We reformulate the model in the form of a min-max-min optimization into an equivalent nonsmooth minimization problem. We further give an approximate discretization scheme of the possible continuous random vector of the nonsmooth minimization problem, whose objective function involves the maximum of numerous but finite nonsmooth functions. The convergence of the discretization scheme to the equivalent nonsmooth reformulation is shown under mild conditions. A smoothing projected gradient (SPG) method is employed to solve the discretization scheme. Any accumulation point is shown to be a global minimizer of the discretization scheme. Numerical results on the NASDAQ index dataset from January 2008 to July 2023 demonstrate the effectiveness of our proposed model and the efficiency of the SPG method, compared with several state-of-the-art models and corresponding methods for solving them

Blockchain-Based Water-Energy Transactive Management with Spatial-Temporal Uncertainties

Water resources are vital to the energy conversion process but few efforts have been devoted to the joint optimization problem which is fundamentally critical to the water-energy nexus for small-scale or remote energy systems (e.g., energy hubs). Traditional water and energy trading mechanisms depend on centralized authorities and cannot preserve security and privacy effectively. Also, their transaction process cannot be verified and is subject to easy tampering and frequent exposures to cyberattacks, forgery, and network failures. Toward that end, water-energy hubs (WEHs) offers a promising way to analyse water-energy nexus for greater resource utilization efficiency. We propose a two-stage blockchain-based transactive management method for multiple, interconnected WEHs. Our method considers peer-topeer (P2P) trading and demand response, and leverages blockchain to create a secure trading environment. It features auditing and resource transaction record management via system aggregators enabled by a consortium blockchain, and entails spatial-temporal distributionally robust optimization (DRO) for renewable generation and load uncertainties. A spatial-temporal ambiguity set is incorporated in DRO to characterize the spatial-temporal dependencies of the uncertainties in distributed renewable generation and load demand. We conduct a simulation-based evaluation that includes robust optimization and the moment-based DRO as benchmarks. The results reveal that our method is consistently more effective than both benchmarks. Key findings include i) our method reduces conservativeness with lower WEH trading and operation costs, and achieves important performance improvements by up to 6.1%; and ii) our method is efficient and requires 18.7% less computational time than the moment-based DRO. Overall, this study contributes to the extant literature by proposing a novel two-stage blockchain-based WEH transaction method, developing a realistic spatialtemporal ambiguity set to effectively hedge against the uncertainties for distributed renewable generation and load demand, and producing empirical evidence suggesting its greater effectiveness and values than several prevalent methods.</p

Blockchain-Based Water-Energy Transactive Management with Spatial-Temporal Uncertainties

Water resources are vital to the energy conversion process but few efforts have been devoted to the joint optimization problem which is fundamentally critical to the water-energy nexus for small-scale or remote energy systems (e.g., energy hubs). Traditional water and energy trading mechanisms depend on centralized authorities and cannot preserve security and privacy effectively. Also, their transaction process cannot be verified and is subject to easy tampering and frequent exposures to cyberattacks, forgery, and network failures. Toward that end, water-energy hubs (WEHs) offers a promising way to analyse water-energy nexus for greater resource utilization efficiency. We propose a two-stage blockchain-based transactive management method for multiple, interconnected WEHs. Our method considers peer-topeer (P2P) trading and demand response, and leverages blockchain to create a secure trading environment. It features auditing and resource transaction record management via system aggregators enabled by a consortium blockchain, and entails spatial-temporal distributionally robust optimization (DRO) for renewable generation and load uncertainties. A spatial-temporal ambiguity set is incorporated in DRO to characterize the spatial-temporal dependencies of the uncertainties in distributed renewable generation and load demand. We conduct a simulation-based evaluation that includes robust optimization and the moment-based DRO as benchmarks. The results reveal that our method is consistently more effective than both benchmarks. Key findings include i) our method reduces conservativeness with lower WEH trading and operation costs, and achieves important performance improvements by up to 6.1%; and ii) our method is efficient and requires 18.7% less computational time than the moment-based DRO. Overall, this study contributes to the extant literature by proposing a novel two-stage blockchain-based WEH transaction method, developing a realistic spatialtemporal ambiguity set to effectively hedge against the uncertainties for distributed renewable generation and load demand, and producing empirical evidence suggesting its greater effectiveness and values than several prevalent methods.</p