arXiv subjects

Ruiwei Jiang

Publications and source records attributed to Ruiwei Jiang.

27 records · Page 2Linked to original sources

arXiv2022

Chance-Constrained Optimization under Limited Distributional Information: A Review of Reformulations Based on Sampling and Distributional Robustness

Chance-constrained programming (CCP) is one of the most difficult classes of optimization problems that has attracted the attention of researchers since the 1950s. In this survey, we focus on cases when only a limited information on the distribution is available, such as a sample from the distribution, or the moments of the distribution. We first review recent developments in mixed-integer linear formulations of chance-constrained programs that arise from finite discrete distributions (or sample average approximation). We highlight successful reformulations and decomposition techniques that enable the solution of large-scale instances. We then review active research in distributionally robust CCP, which is a framework to address the ambiguity in the distribution of the random data. The focal point of our review is on scalable formulations that can be readily implemented with state-of-the-art optimization software. Furthermore, we highlight the prevalence of CCPs with a review of applications across multiple domains.

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arXiv2020

Distributionally Robust Partially Observable Markov Decision Process with Moment-based Ambiguity

We consider a distributionally robust Partially Observable Markov Decision Process (DR-POMDP), where the distribution of the transition-observation probabilities is unknown at the beginning of each decision period, but their realizations can be inferred using side information at the end of each period after an action being taken. We build an ambiguity set of the joint distribution using bounded moments via conic constraints and seek an optimal policy to maximize the worst-case (minimum) reward for any distribution in the set. We show that the value function of DR-POMDP is piecewise linear convex with respect to the belief state and propose a heuristic search value iteration method for obtaining lower and upper bounds of the value function. We conduct numerical studies and demonstrate the computational performance of our approach via testing instances of a dynamic epidemic control problem. Our results show that DR-POMDP can produce more robust policies under misspecified distributions of transition-observation probabilities as compared to POMDP, but has less costly solutions than robust POMDP. The DR-POMDP policies are also insensitive to varying parameter in the ambiguity set and to noise added to the true transition-observation probability values obtained at the end of each decision period.

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arXiv2019

The Value of Including Unimodality Information in Distributionally Robust Optimal Power Flow

To manage renewable generation and load consumption uncertainty, chance-constrained optimal power flow (OPF) formulations and various solution methodologies have been proposed. However, conventional solution approaches often rely on accurate estimates of uncertainty distributions, which may not exist. When the distributions are not known but can be limited to a set of plausible distributions, termed an ambiguity set, distributionally robust (DR) optimization can be used to ensure that chance constraints hold for all distributions in that set. However, DR OPF yields conservative solutions if the ambiguity set is too large. In this paper, we assess the value of using both moment and unimodality information, which shrinks the ambiguity set and reduces conservatism, in DR OPF problems. Most practical uncertainty distributions in power systems are unimodal. Exact reformulations, approximations, and efficient solving techniques were developed in a previous paper. This paper develops an optimal parameter selection approach that searches for an optimal approximation, significantly improving the computational efficiency and solution quality. We evaluate the performance of the approach against existing chance-constrained OPF approaches using modified IEEE 118-bus and 300-bus systems with high penetrations of renewable generation. Results show that including unimodality information reduces solution conservatism and cost without significantly degrading reliability.

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arXiv2019

Data-Driven Distributionally Robust Appointment Scheduling over Wasserstein Balls

We study a single-server appointment scheduling problem with a fixed sequence of appointments, for which we must determine the arrival time for each appointment. We specifically examine two stochastic models. In the first model, we assume that all appointees show up at the scheduled arrival times yet their service durations are random. In the second model, we assume that appointees have random no-show behaviors and their service durations are random given that they show up at the appointments. In both models, we assume that the probability distribution of the uncertain parameters is unknown but can be partially observed via a set of historical data, which we view as independent samples drawn from the unknown distribution. In view of the distributional ambiguity, we propose a data-driven distributionally robust optimization (DRO) approach to determine an appointment schedule such that the worst-case (i.e., maximum) expectation of the system total cost is minimized. A key feature of this approach is that the optimal value and the set of optimal schedules thus obtained provably converge to those of the true model, i.e., the stochastic appointment scheduling model with regard to the true probability distribution of the uncertain parameters. While our DRO models are computationally intractable in general, we reformulate them to copositive programs, which are amenable to tractable semidefinite programming problems with high-quality approximations. Furthermore, under some mild conditions, we recast these models as polynomial-sized linear programs. Through an extensive numerical study, we demonstrate that our approach yields better out-of-sample performance than two state-of-the-art methods.

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arXiv2018

Distributionally Robust Chance Constrained Optimal Power Flow Assuming Unimodal Distributions with Misspecified Modes

Chance constrained optimal power flow (CC-OPF) formulations have been proposed to minimize operational costs while controlling the risk arising from uncertainties like renewable generation and load consumption. To solve CC-OPF, we often need access to the (true) joint probability distribution of all uncertainties, which is rarely known in practice. A solution based on a biased estimate of the distribution can result in poor reliability. To overcome this challenge, recent work has explored distributionally robust chance constraints, in which the chance constraints are satisfied over a family of distributions called the ambiguity set. Commonly, ambiguity sets are only based on moment information (e.g., mean and covariance) of the random variables; however, specifying additional characteristics of the random variables reduces conservatism and cost. Here, we consider ambiguity sets that additionally incorporate unimodality information. In practice, it is difficult to estimate the mode location from the data and so we allow it to be potentially misspecified. We formulate the problem and derive a separation-based algorithm to efficiently solve it. Finally, we evaluate the performance of the proposed approach on a modified IEEE-30 bus network with wind uncertainty and compare with other distributionally robust approaches. We find that a misspecified mode significantly affects the reliability of the solution and the proposed model demonstrates a good trade-off between cost and reliability.

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arXiv2018

Ambiguous Chance-Constrained Binary Programs under Mean-Covariance Information

We consider chance-constrained binary programs, where each row of the inequalities that involve uncertainty needs to be satisfied probabilistically. Only the information of the mean and covariance matrix is available, and we solve distributionally robust chance-constrained binary programs (DCBP). Using two different ambiguity sets, we equivalently reformulate the DCBPs as 0-1 second-order cone (SOC) programs. We further exploit the submodularity of 0-1 SOC constraints under special and general covariance matrices, and utilize the submodularity as well as lifting to derive extended polymatroid inequalities to strengthen the 0-1 SOC formulations. We incorporate the valid inequalities in a branch-and-cut algorithm for efficiently solving DCBPs. We demonstrate the computational efficacy and solution performance using diverse instances of a chance-constrained bin packing problem.

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arXiv2018

Distributionally Robust Distribution Network Configuration Under Random Contingency

Topology design is a critical task for the reliability, economic operation, and resilience of distribution systems. This paper proposes a distributionally robust optimization (DRO) model for designing the topology of a new distribution system facing random contingencies (e.g., imposed by natural disasters). The proposed DRO model optimally configures the network topology and integrates distributed generation to effectively meet the loads. Moreover, we take into account the uncertainty of contingency. Using the moment information of distribution line failures, we construct an ambiguity set of the contingency probability distribution, and minimize the expected amount of load shedding with regard to the worst-case distribution within the ambiguity set. As compared with a classical robust optimization model, the DRO model explicitly considers the contingency uncertainty and so provides a less conservative configuration, yielding a better out-of-sample performance. We recast the proposed model to facilitate the column-and-constraint generation algorithm. We demonstrate the out-of-sample performance of the proposed approach in numerical case studies.

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arXiv2018

Distributionally Robust Co-Optimization of Power Dispatch and Do-Not-Exceed Limits

To address the challenge of the renewable energy uncertainty, the ISO New England (ISO-NE) has proposed to apply do-not-exceed (DNE) limits, which represent the maximum nodal injection of renewable energy the grid can accommodate. Unfortunately, it appears challenging to compute DNE limits that simultaneously maintain the system flexibility and incorporate a large portion of the available renewable energy at the minimum cost. In addition, it is often challenging to accurately estimate the joint probability distribution of the renewable energy. In this paper, we propose a two-stage distributionally robust optimization model that co-optimizes the power dispatch and the DNE limits, by adopting an affinely adjustable power re-dispatch and an adjustable joint chance constraint that measures the renewable utilization. Notably, this model admits a second-order conic reformulation that can be efficiently solved by the commercial solvers (e.g., MOSEK). We conduct case studies based on modified IEEE test instances to demonstrate the effectiveness of the proposed approach and analyze the trade-off among the system flexibility, the renewable utilization, and the dispatch cost.

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arXiv2016

Multi-Period Portfolio Optimization: Translation of Autocorrelation Risk to Excess Variance

Growth-optimal portfolios are guaranteed to accumulate higher wealth than any other investment strategy in the long run. However, they tend to be risky in the short term. For serially uncorrelated markets, similar portfolios with more robust guarantees have been recently proposed. This paper extends these robust portfolios by accommodating non-zero autocorrelations that may reflect investors' beliefs about market movements. Moreover, we prove that the risk incurred by such autocorrelations can be absorbed by modifying the covariance matrix of asset returns.

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