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Bo Zeng

Publications and source records attributed to Bo Zeng.

At least 55 records · Page 3Linked to original sources
arXiv2022

Two-Stage Robust Optimization with Decision Dependent Uncertainty

The type of decision dependent uncertainties (DDUs) imposes a great challenge in decision making, while existing methodologies are not sufficient to support many real practices. In this paper, we present a systematic study to handle this challenge in two-stage robust optimization~(RO). Our main contributions include three sophisticated variants of column-and-constraint generation method to exactly compute DDU-based two-stage RO. By a novel application of core concepts of linear programming, we provide rigorous analyses on their computational behaviors. Interestingly, in terms of the iteration complexity of those algorithms, DDU-based two-stage RO is not more demanding than its decision independent uncertainty (DIU) based counterpart. It is worth highlighting a counterintuitive discovery that converting a DIU set into a DDU set by making use of "deep knowledge" and then computing the resulting DDU-based formulation may lead to a significant improvement. Indeed, as shown in this paper, in addition to capturing the actual dependence existing in the real world, DDU is a powerful and flexible tool to represent and leverage analytical properties or simply domain expertise to achieve a strong solution capacity. So, we believe it will open a new direction to solve large-scale DIU- or DDU-based RO. Other important results include basic structural properties for two-stage RO, an approximation scheme to deal with mixed integer recourse, and a couple of enhancement techniques for the developed algorithms, as well as an organized numerical study to help us appreciate all algorithms and enhancement techniques' computational performances.

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arXiv2020

Wasserstein Distributionally Robust Inverse Multiobjective Optimization

Inverse multiobjective optimization provides a general framework for the unsupervised learning task of inferring parameters of a multiobjective decision making problem (DMP), based on a set of observed decisions from the human expert. However, the performance of this framework relies critically on the availability of an accurate DMP, sufficient decisions of high quality, and a parameter space that contains enough information about the DMP. To hedge against the uncertainties in the hypothetical DMP, the data, and the parameter space, we investigate in this paper the distributionally robust approach for inverse multiobjective optimization. Specifically, we leverage the Wasserstein metric to construct a ball centered at the empirical distribution of these decisions. We then formulate a Wasserstein distributionally robust inverse multiobjective optimization problem (WRO-IMOP) that minimizes a worst-case expected loss function, where the worst case is taken over all distributions in the Wasserstein ball. We show that the excess risk of the WRO-IMOP estimator has a sub-linear convergence rate. Furthermore, we propose the semi-infinite reformulations of the WRO-IMOP and develop a cutting-plane algorithm that converges to an approximate solution in finite iterations. Finally, we demonstrate the effectiveness of our method on both a synthetic multiobjective quadratic program and a real world portfolio optimization problem.

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arXiv2020

Adversarial Attack on Hierarchical Graph Pooling Neural Networks

Recent years have witnessed the emergence and development of graph neural networks (GNNs), which have been shown as a powerful approach for graph representation learning in many tasks, such as node classification and graph classification. The research on the robustness of these models has also started to attract attentions in the machine learning field. However, most of the existing work in this area focus on the GNNs for node-level tasks, while little work has been done to study the robustness of the GNNs for the graph classification task. In this paper, we aim to explore the vulnerability of the Hierarchical Graph Pooling (HGP) Neural Networks, which are advanced GNNs that perform very well in the graph classification in terms of prediction accuracy. We propose an adversarial attack framework for this task. Specifically, we design a surrogate model that consists of convolutional and pooling operators to generate adversarial samples to fool the hierarchical GNN-based graph classification models. We set the preserved nodes by the pooling operator as our attack targets, and then we perturb the attack targets slightly to fool the pooling operator in hierarchical GNNs so that they will select the wrong nodes to preserve. We show the adversarial samples generated from multiple datasets by our surrogate model have enough transferability to attack current state-of-art graph classification models. Furthermore, we conduct the robust train on the target models and demonstrate that the retrained graph classification models are able to better defend against the attack from the adversarial samples. To the best of our knowledge, this is the first work on the adversarial attack against hierarchical GNN-based graph classification models.

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arXiv2019

A Study on the Block Relocation Problem: Lower Bound Derivations and Strong Formulations

The block relocation problem (BRP) is a fundamental operational issue in modern warehouse and yard management, which, however, is very challenging to solve. In this paper, to advance our understanding on this problem and to provide a substantial assistance to practice, we (i) introduce a classification scheme and present a rather comprehensive review on all 16 BRP variants; (ii) develop a general framework to derive lower bounds on the number of necessary relocations and demonstrate its connection to existing lower bounds of the unrestricted BRP variants; (iii) propose and employ a couple of new critical substructures concepts to analyze the BRP and obtain a lower bound that dominates all existing ones; (iv) build a new and strong mixed integer programming (MIP) formulation that is adaptable to compute 8 BRP variants, and design a novel MIP-formulation-based iterative procedure to compute exact BRP solutions; (v) extend the MIP formulation to address four typical industrial considerations. Computational results on standard test instances show that the new lower bound is significantly stronger, and our new MIP computational methods have superior performances over a state-of-the-art formulation.

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arXiv2019

The conformable fractional grey system model

The fractional order grey models (FGM) have appealed considerable interest of research in recent years due to its higher effectiveness and flexibility than the conventional grey models and other prediction models. However, the definitions of the fractional order accumulation (FOA) and difference (FOD) is computationally complex, which leads to difficulties for the theoretical analysis and applications. In this paper, the new definition of the FOA are proposed based on the definitions of Conformable Fractional Derivative, which is called the Conformable Fractional Accumulation (CFA), along with its inverse operation, the Conformable Fractional Difference (CFD). Then the new Conformable Fractional Grey Model (CFGM) based on CFA and CFD is introduced with detailed modelling procedures. The feasibility and simplicity and the CFGM are shown in the numerical example. And the at last the comprehensive real-world case studies of natural gas production forecasting in 11 countries are presented, and results show that the CFGM is much more effective than the existing FGM model in the 165 subcases.

stat.ME↗
arXiv2019

Multi-component Maintenance Optimization: A Stochastic Programming Approach

Maintenance optimization has been extensively studied in the past decades. However, most of the existing maintenance models focus on single-component systems and are not applicable for complex systems consisting of multiple components, due to various interactions between the components. Multi-component maintenance optimization problem, which joins the stochastic processes regarding the failures of the components with the combinatorial problems regarding the grouping of maintenance activities, is challenging in both modeling and solution techniques, and has remained as an open issue in the literature. In this paper, we study the multi-component maintenance problem over a finite planning horizon and formulate the problem as a multi-stage stochastic integer program with decision-dependent uncertainty. There is a lack of general efficient methods to solve this type of problem. To address this challenge, we use an alternative approach to model the underlying failure process and develop a novel two-stage model without decision-dependent uncertainty. Structural properties of the two-stage problem are investigated, and a progressive-hedging-based heuristic is developed based on the structural properties. Our heuristic algorithm demonstrates a significantly improved capacity in handling practically large-size two-stage problems comparing to three conventional methods for stochastic integer programming, and solving the two-stage model by our heuristic in a rolling horizon provides a good approximation of the multi-stage problem. The heuristic is further benchmarked with a dynamic programming approach commonly adopted in the literature. Numerical results show that our heuristic can lead to significant cost savings compared with the benchmark approach.

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arXiv2018

Generalized Inverse Optimization through Online Learning

Inverse optimization is a powerful paradigm for learning preferences and restrictions that explain the behavior of a decision maker, based on a set of external signal and the corresponding decision pairs. However, most inverse optimization algorithms are designed specifically in batch setting, where all the data is available in advance. As a consequence, there has been rare use of these methods in an online setting suitable for real-time applications. In this paper, we propose a general framework for inverse optimization through online learning. Specifically, we develop an online learning algorithm that uses an implicit update rule which can handle noisy data. Moreover, under additional regularity assumptions in terms of the data and the model, we prove that our algorithm converges at a rate of $\mathcal{O}(1/\sqrt{T})$ and is statistically consistent. In our experiments, we show the online learning approach can learn the parameters with great accuracy and is very robust to noises, and achieves a dramatic improvement in computational efficacy over the batch learning approach.

cs.LG↗
arXiv2018

Achieving SDP Tightness Through SOCP Relaxation with Cycle-Based SDP Feasibility Constraints for AC OPF

In this paper, we show that the standard semidefinite programming (SDP) relaxation of altering current optimal power flow (AC OPF) can be equivalently reformulated as second-order cone programming (SOCP) relaxation with maximal clique- and cycle-based SDP feasibility constraints. The formulation is based on the positive semi-definite (PSD) matrix completion theorem, which states that if all sub-matrices corresponding to maximal cliques in a chordal graph are PSD, then the partial matrix related to the chordal graph can be completed as a full PSD matrix. Existing methods in [1] first construct a chordal graph through Cholesky factorization. In this paper, we identify maximal cliques and minimal chordless cycles first. Enforcing the submatrices related to the maximal cliques and cycles PSD will guarantee a PSD full matrix. Further, we conduct chordal relaxation for the minimal chordless cycles by adding virtual lines and decompose each chordless cycle to 3-node cycles. Thus, the entire graph consists of trees, maximal cliques, and 3-node cycles. The submatrices related to the maximal cliques and 3-node cycles are enforced to be PSD to achieve a full PSD matrix. As majority power grids having the size of maximal cliques limited to 4-node, this graph decomposition method results in a low-rank full PSD matrix. The proposed method significantly reduces computing time for SDP relaxation of AC OPF and can handle power systems with thousands of buses.

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arXiv2018

Application of the novel fractional grey model FAGMO(1,1,k) to predict China's nuclear energy consumption

At present, the energy structure of China is shifting towards cleaner and lower amounts of carbon fuel, driven by environmental needs and technological advances. Nuclear energy, which is one of the major low-carbon resources, plays a key role in China's clean energy development. To formulate appropriate energy policies, it is necessary to conduct reliable forecasts. This paper discusses the nuclear energy consumption of China by means of a novel fractional grey model FAGMO(1,1,k). The fractional accumulated generating matrix is introduced to analyse the fractional grey model properties. Thereafter, the modelling procedures of the FAGMO(1,1,k) are presented in detail, along with the transforms of its optimal parameters. A stochastic testing scheme is provided to validate the accuracy and properties of the optimal parameters of the FAGMO(1,1,k). Finally, this model is used to forecast China's nuclear energy consumption and the results demonstrate that the FAGMO(1,1,k) model provides accurate prediction, outperforming other grey models.

stat.AP↗
arXiv2018

Inferring Parameters Through Inverse Multiobjective Optimization

Given a set of human's decisions that are observed, inverse optimization has been developed and utilized to infer the underlying decision making problem. The majority of existing studies assumes that the decision making problem is with a single objective function, and attributes data divergence to noises, errors or bounded rationality, which, however, could lead to a corrupted inference when decisions are tradeoffs among multiple criteria. In this paper, we take a data-driven approach and design a more sophisticated inverse optimization formulation to explicitly infer parameters of a multiobjective decision making problem from noisy observations. This framework, together with our mathematical analyses and advanced algorithm developments, demonstrates a strong capacity in estimating critical parameters, decoupling "interpretable" components from noises or errors, deriving the denoised \emph{optimal} decisions, and ensuring statistical significance. In particular, for the whole decision maker population, if suitable conditions hold, we will be able to understand the overall diversity and the distribution of their preferences over multiple criteria, which is important when a precise inference on every single decision maker is practically unnecessary or infeasible. Numerical results on a large number of experiments are reported to confirm the effectiveness of our unique inverse optimization model and the computational efficacy of the developed algorithms.

stat.ML↗
arXiv2018

A Projection-Based Reformulation and Decomposition Algorithm for Global Optimization of a Class of Mixed Integer Bilevel Linear Programs

We propose an extended variant of the reformulation and decomposition algorithm for solving a special class of mixed-integer bilevel linear programs (MIBLPs) where continuous and integer variables are involved in both upper- and lower-level problems. In particular, we consider MIBLPs with upper-level constraints that involve lower-level variables. We assume that the inducible region is nonempty and all variables are bounded. By using the reformulation and decomposition scheme, an MIBLP is first converted into its equivalent single-level formulation, then computed by a column-and-constraint generation based decomposition algorithm. The solution procedure is enhanced by a projection strategy that does not require the relatively complete response property. To ensure its performance, we prove that our new method converges to the global optimal solution in a finite number of iterations. A large-scale computational study on random instances and instances of hierarchical supply chain planning are presented to demonstrate the effectiveness of the algorithm.

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arXiv2018

Optimal Allocation of Series FACTS Devices Under High Penetration of Wind Power Within a Market Environment

Series FACTS devices are one of the key enablers for very high penetration of renewables due to their capabilities in continuously controlling power flows on transmission lines. This paper proposes a bilevel optimization model to optimally locate variable series reactor (VSR) and phase shifting transformer (PST) in the transmission network considering high penetration of wind power. The upper level problem seeks to minimize the \textcolor{black}{investment cost} on series FACTS, the cost of wind power curtailment and possible load shedding. The lower level problems capture the market clearing under different operating scenarios. Due to the poor scalability of $Bθ$ formulation, the \textsl{shift factor} structure of FACTS allocation is derived. A customized reformulation and decomposition algorithm is designed and implemented to solve the proposed bilevel model with binary variables in both upper and lower levels. Detailed numerical results based on 118-bus system demonstrate the efficient performance of the proposed planning model and the important role of series FACTS for facilitating the integration of wind power.

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arXiv2017

A Chance Constrained Information-Gap Decision Model for Multi-Period Microgrid Planning

This paper presents a chance constrained information gap decision model for multi-period microgrid expansion planning (MMEP) considering two categories of uncertainties, namely random and non-random uncertainties. The main task of MMEP is to determine the optimal sizing, type selection, and installation time of distributed energy resources (DER) in microgrid. In the proposed formulation, information gap decision theory (IGDT) is applied to hedge against non-random uncertainties of long-term demand growth. Then, chance constraints are imposed in the operational stage to address the random uncertainties of hourly renewable energy generation and load variation. The objective of chance constrained information gap decision model is to maximize the robustness level of DER investment meanwhile satisfying a set of operational constraints with a high probability. The integration of IGDT and chance constrained program, however, makes it very challenging to compute. To address this challenge, we propose and implement a strengthened bilinear Benders decomposition method. Finally, the effectiveness of proposed planning model is verified through the numerical studies on both the simple and practical complex microgrid. Also, our new computational method demonstrates a superior solution capacity and scalability. Compared to directly using a professional mixed integer programming solver, it could reduce the computational time by orders of magnitude.

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arXiv2017

Stochastic and Chance-Constrained Conic Distribution System Expansion Planning Using Bilinear Benders Decomposition

Second order conic programming (SOCP) has been used to model various applications in power systems, such as operation and expansion planning. In this paper, we present a two-stage stochastic mixed integer SOCP (MISOCP) model for the distribution system expansion planning problem that considers uncertainty and also captures the nonlinear AC power flow. To avoid costly investment plans due to some extreme scenarios, we further present a chance-constrained variant that could lead to cost-effective solutions. To address the computational challenge, we extend the basic Benders decomposition method and develop a bilinear variant to compute stochastic and chance-constrained MISOCP formulations. A set of numerical experiments is performed to illustrate the performance of our models and computational methods. In particular, results show that our Benders decomposition algorithms drastically outperform a professional MISOCP solver in handling stochastic scenarios by orders of magnitude.

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arXiv2017

Energy-Aware Disk Storage Management: Online Approach with Application in DBMS

Energy consumption has become a first-class optimization goal in design and implementation of data-intensive computing systems. This is particularly true in the design of database management systems (DBMS), which was found to be the major consumer of energy in the software stack of modern data centers. Among all database components, the storage system is one of the most power-hungry elements. In previous work, dynamic power management (DPM) techniques that make real-time decisions to transition the disks to low-power modes are normally used to save energy in storage systems. In this paper, we tackle the limitations of DPM proposals in previous contributions. We introduced a DPM optimization model integrated with model predictive control (MPC) strategy to minimize power consumption of the disk-based storage system while satisfying given performance requirements. It dynamically determines the state of disks and plans for inter-disk data fragment migration to achieve desirable balance between power consumption and query response time. Via analyzing our optimization model to identify structural properties of optimal solutions, we propose a fast-solution heuristic DPM algorithm that can be integrated in large-scale disk storage systems for efficient state configuration and data migration. We evaluate our proposed ideas by running simulations using extensive set of synthetic workloads based on popular TPC benchmarks. Our results show that our solution significantly outperforms the best existing algorithm in both energy savings and response time.

cs.DB↗
arXiv2017

Capacity Expansion Planning of Wind Power Generation in A Market Environment with Topology Control

Wind power integration is an essential problem for modern power industry. In this paper, we develop a novel bilevel mixed integer optimization model to investigate wind power generation planning problem in an electricity market environment with topology control operations. Different from existing formulations, the lower level market clearing problem introduces binary variables to model line switching decisions, which have been proven very effective to improve transmission capability under different load profiles. To solve this challenging bilevel mixed integer program, a recent decomposition method is customized and a couple of enhancement techniques based on grid structure are designed. Through computing instances from typical IEEE test beds, our solution methods demonstrate a strong solution capacity. Also, we observe that applying topology control on a small number of lines could be very helpful to reduce wind power curtailment and improve the wind penetration level.

math.OC↗
arXiv2016

Chance-Constrained Two-Stage Unit Commitment under Uncertain Load and Wind Power Output Using Bilinear Benders Decomposition

In this paper, we study unit commitment (UC) problems considering the uncertainty of load and wind power generation. UC problem is formulated as a chance-constrained two-stage stochastic programming problem where the chance constraint is used to restrict the probability of load imbalance. In addition to the conventional mixed integer linear programming formulation using Big-M, we present the bilinear mixed integer formulation of chance constraint, and then derive its linear counterpart using McCormick linearization method. Then, we develop a bilinear variant of Benders decomposition method, which is an easy-to-implement algorithm, to solve the resulting large-scale linear counterpart. Our results on typical IEEE systems demonstrate that (i) the bilinear mixed integer programming formula-tion is stronger than the conventional one; (ii) the proposed Benders decomposition algorithm is generally an order of magnitude faster than using a professional solver to directly compute both linear and bilinear chance-constrained UC models.

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