Jianqiang Cheng

Interests

Research

Stochastic programming; Robust optimization;Distributionally robust optimization; Semidefinite and copositive optimization; Energy management

Courses

Scholarly Contributions

Chapters

• Fathabad, A. M., Cheng, J., & Pan, K. (2021). Integrated power transmission and distribution systems. In Renewable-Energy-Driven Future(pp 169--199). Academic Press.
• Fathabad, A. M., Cheng, J., & Pan, K. (2020). Integrated power transmission and distribution systems. In Renewable-Energy-Driven Future: Technologies, Applications, Sustainability, and Policies. doi:10.1016/b978-0-12-820539-6.00005-4
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  Abstract The penetration of on-site electricity generations through devices referred to as distributed energy resources (DERs) is reaching levels that cannot be neglected anymore. The negligence of detailed operations of DERs in the power distribution systems (DSs) can lead to extreme operational problems of the whole power grid. Such problems include high pressure on the power transmission system (TS) and reverse power flow from the DSs towards the TS, while the potential benefits from the DSs are also overlooked. In this chapter, through a careful and systematic analysis of the power system planning problems, we underline the necessity of developing methods that can tackle such problems and realize the potential profits by considering both the TS and DS in an coordinated mode. Furthermore, we introduce an integrated transmission and distribution system problem which minimizes the unit commitment costs of the TS and the distributed energy resource management costs of the DSs, respectively, while respecting the technical constraints of both systems. In our model, we consider both the combinatorial nature of unit commitment decisions and the AC power flow characteristics of the DS. We show that our integrated model achieves significant lower costs as compared to solving these problems separately. Finally we tighten the proposed mixed-integer linear programming formulation by adding valid inequalities for the problem. The computational results verified the efficiency of our proposed integrated model combined with the valid inequalities.
• Cheng, J., Lisser, A., & Xu, C. (2015). Stochastic Semidefinite Optimization Using Sampling Methods. In International Conference on Operations Research and Enterprise Systems (ICORES). doi:10.1007/978-3-319-27680-9_6
• Cheng, J., Lisser, A., & Gicquel, C. (2012). A Second-Order Cone Programming Approximation to Joint Chance-Constrained Linear Programs. In International Symposium on Combinatorial Optimization. doi:10.1007/978-3-642-32147-4_8
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  We study stochastic linear programs with joint chance constraints, where the random matrix is a special triangular matrix and the random data are assumed to be normally distributed. The problem can be approximated by another stochastic program, whose optimal value is an upper bound of the original problem. The latter stochastic program can be approximated by two second-order cone programming (SOCP) problems [5]. Furthermore, in some cases, the optimal values of the two SOCPs problems provide a lower bound and an upper bound of the approximated stochastic program respectively. Finally, numerical examples with probabilistic lot-sizing problems are given to illustrate the effectiveness of the two approximations.

Journals/Publications

• Cheng, J., Jiang, S., Pan, K., Qiu, F., & Yang, B. (2022). Data-Driven Chance-Constrained Planning for Distributed Generation: A Partial Sampling Approach. IEEE Transactions on Power Systems, 1-16. doi:10.1109/tpwrs.2022.3230676
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  The planning of distributed energy resources has been challenged by the significant uncertainties and complexities of distribution systems. To ensure system reliability, one often employs chance-constrained programs to seek a highly likely feasible solution while minimizing certain costs. The traditional sample average approximation (SAA) is commonly used to represent uncertainties and reformulate a chance-constrained program into a deterministic optimization problem. However, the SAA introduces additional binary variables to indicate whether a scenario sample is satisfied and thus brings great computational complexity to the already challenging distributed energy resource planning problems. In this paper, we introduce a new paradigm, i.e., the partial sample average approximation (PSAA) using real data, to improve computational tractability. The innovation is that we sample only a part of the random parameters and introduce only continuous variables corresponding to the samples in the reformulation, which is a mixed-integer convex quadratic program. Our extensive experiments on the IEEE 33-Bus and 123-Bus systems show that the PSAA approach performs better than the SAA because the former provides better solutions in a shorter time in in-sample tests and provides better guaranteed probability for system reliability in out-of-sample tests. All the data used in the experiments are real data acquired from Pecan Street Inc. and ERCOT. More importantly, our proposed chance-constrained model and PSAA approach are general enough and can be applied to solve other valuable problems in power system planning and operations. Thus, this paper fits one of the journal scopes: Distribution System Planning in Power System Planning and Implementation .
• Cheng, J., Kosuch, S., & Lisser, A. (2022). Restricted Shortest Path Problems with Uncertain Delays.
• Cheramin, M., Cheng, J., Pan, K., & Jiang, R. (2022). Computationally Efficient Approximations for Distributionally Robust Optimization Under Moment and Wasserstein Ambiguity. INFORMS journal on computing, 34(3), 1768-1794. doi:10.1287/ijoc.2021.1123
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  Distributionally robust optimization (DRO) is a modeling framework in decision making under uncertainty in which the probability distribution of a random parameter is unknown although its partial information (e.g., statistical properties) is available. In this framework, the unknown probability distribution is assumed to lie in an ambiguity set consisting of all distributions that are compatible with the available partial information. Although DRO bridges the gap between stochastic programming and robust optimization, one of its limitations is that its models for large-scale problems can be significantly difficult to solve, especially when the uncertainty is of high dimension. In this paper, we propose computationally efficient inner and outer approximations for DRO problems under a piecewise linear objective function and with a moment-based ambiguity set and a combined ambiguity set including Wasserstein distance and moment information. In these approximations, we split a random vector into smaller pieces, leading to smaller matrix constraints. In addition, we use principal component analysis to shrink uncertainty space dimensionality. We quantify the quality of the developed approximations by deriving theoretical bounds on their optimality gap. We display the practical applicability of the proposed approximations in a production–transportation problem and a multiproduct newsvendor problem. The results demonstrate that these approximations dramatically reduce the computational time while maintaining high solution quality. The approximations also help construct an interval that is tight for most cases and includes the (unknown) optimal value for a large-scale DRO problem, which usually cannot be solved to optimality (or even feasibility in most cases). Summary of Contribution: This paper studies an important type of optimization problem, that is, distributionally robust optimization problems, by developing computationally efficient inner and outer approximations via operations research tools. Specifically, we consider several variants of such problems that are practically important and that admit tractable yet large-scale reformulation. We accordingly utilize random vector partition and principal component analysis to derive efficient approximations with smaller sizes, which, more importantly, provide a theoretical performance guarantee with respect to low optimality gaps. We verify the significant efficiency (i.e., reducing computational time while maintaining high solution quality) of our proposed approximations in solving both production–transportation and multiproduct newsvendor problems via extensive computing experiments.
• Fathabad, A. M., Cheng, J., Yang, B., & Pan, K. (2022). Asymptotically Tight Conic Approximations for Chance-Constrained AC Optimal Power Flow. European Journal of Operational Research. doi:10.1016/j.ejor.2022.06.020
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  • We study a two-sided chance constrained AC optimal power flow problem (TCC-ACOPF). • We develop an efficient second-order cone programming (SOCP) approximation of TCC-ACOPF under Gaussian Mixture distribution. • We show that our SOCP formulation has adjustable rates of accuracy and its optimal value enjoys asymptotic convergence properties. • We demonstrate the effectiveness of our proposed approaches with both real historical data and synthetic data on two IEEE test systems. The increasing penetration of renewable energy in power systems calls for secure and reliable system operations under significant uncertainty. To that end, the chance-constrained AC optimal power flow (CC-ACOPF) problem has been proposed. Most research in the literature of CC-ACOPF focuses on one-sided chance constraints; however, two-sided chance constraints (TCCs), albeit more complex, provide more accurate formulations as both upper and lower bounds of the chance constraints are enforced simultaneously. In this paper, we introduce a fully two-sided CC-ACOPF problem (TCC-ACOPF), in which the active/reactive generation, voltage, and power flow all remain within their upper/lower bounds simultaneously with a predefined probability. Instead of applying Bonferroni approximation or scenario-based approaches, we present an efficient second-order cone programming (SOCP) approximation of the TCCs under Gaussian Mixture (GM) distribution via a piecewise linear (PWL) approximation. Compared to the conventional normality assumption for forecast errors, the GM distribution adds an extra level of accuracy representing the uncertainties. Moreover, we show that our SOCP formulation has adjustable rates of accuracy and its optimal value enjoys asymptotic convergence properties. Furthermore, an algorithm is proposed to speed up the solution procedure by optimally selecting the PWL segments. Finally, we demonstrate the effectiveness of our proposed approaches with both real historical data and synthetic data on the IEEE 30-bus and 118-bus systems. We show that our formulations provide significantly more robust solutions (about 60% reduction in constraint violation) compared to other state-of-art ACOPF formulations.
• Lisser, A., Cheng, J., & Houda, M. (2022). Elliptically distributed joint probabilistic constraints.
• Cheng, J., Jin, H., Paul, S. K., Saha, A. K., & Cheramin, M. (2021). Resilient NdFeB magnet recycling under the impacts of COVID-19 pandemic: Stochastic programming and Benders decomposition. Transportation Research Part E-logistics and Transportation Review. doi:10.1016/j.tre.2021.102505
• Cheramin, M., Chen, R. L., Cheng, J., & Pinar, A. (2021). Data-Driven Robust Optimization Using Scenario-Induced Uncertainty Sets. arXiv preprint arXiv:2107.04977.
• Cheramin, M., Cheng, J., Jiang, R., & Pan, K. (2021). Computationally Efficient Approximations for Distributionally Robust Optimization under Moment and Wasserstein Ambiguity. INFORMS Journal on Computing.
• Cheramin, M., Saha, A. K., Cheng, J., Paul, S. K., & Jin, H. (2021). Resilient NdFeB magnet recycling under the impacts of COVID-19 pandemic: Stochastic programming and Benders decomposition. Transportation Research Part E: Logistics and Transportation Review, 155, 102505.
• Dashti, H., Cheng, J., & Krokhmal, P. (2021). Chance-constrained optimization-based solar microgrid design and dispatch for radial distribution networks. Energy Systems, 1--23.
• Karimi, R., Cheng, J., & Lejeune, M. A. (2021). A Framework for Solving Chance-Constrained Linear Matrix Inequality Programs. INFORMS Journal on Computing, 33(3), 1015--1036.
• Karimi, R., Cheng, J., & Lejeune, M. A. (2021). A Framework for Solving Chance-Constrained Linear Matrix Inequality Programs. INFORMS journal on computing, 33(3), 1015-1036. doi:10.1287/ijoc.2020.0982
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  We propose a novel partial sample average approximation (PSAA) framework to solve the two main types of chance-constrained linear matrix inequality (CCLMI) problems: CCLMI with random technology matrix and CCLMI with random right-hand side. We propose a series of computationally tractable PSAA-based approximations for CCLMI problems, analyze their properties, and derive sufficient conditions that ensure convexity for the two most popular—normal and uniform—continuous distributions. We derive several semidefinite programming PSAA reformulations efficiently solved by off-the-shelf solvers and design a sequential convex approximation method for the PSAA formulations containing bilinear matrix inequalities. The proposed methods can be generalized to other continuous random variables whose cumulative distribution function can be easily computed. We carry out a comprehensive numerical study on three practical CCLMI problems: robust truss topology design, calibration, and robust control. The tests attest to the superiority of the PSAA reformulation and algorithmic framework over the scenario and sample average approximation methods. Summary of Contribution: In line with the mission and scope of IJOC, we study an important type of optimization problems, chance-constrained linear matrix inequality (CCLMI) problems, which require stochastic linear matrix inequality (LMI) constraints to be satisfied with high probability. To solve CCLMI problems, we propose a novel partial sample average approximation (PSAA) framework: (i) develop a series of computationally tractable PSAA-based approximations for CCLMI problems, (ii) analyze their properties, (iii) derive sufficient conditions ensuring convexity, and (iv) design a sequential convex approximation method. We evaluate our proposed method via a comprehensive numerical study on three practical CCLMI problems. The tests attest the superiority of the PSAA reformulation and algorithmic framework over standard benchmarks.
• Cheramin, M., Cheng, J., Jiang, R., & Pan, K. (2020). Computationally Efficient Approximations for Distributionally Robust Optimization. Optimization online.
• Fathabad, A. M., Cheng, J., Pan, K., & Qiu, F. (2020). Data-driven planning for renewable distributed generation integration. IEEE Transactions on Power Systems, 35(6), 4357--4368.
• Fathabad, A. M., Cheng, J., Qiu, F., & Pan, K. (2020). Data-Driven Planning for Renewable Distributed Generation Integration. IEEE Transactions on Power Systems. doi:10.1109/tpwrs.2020.3001235
• Fathabad, A. M., Yazzie, C. B., Cheng, J., & Arnold, R. G. (2020). Optimization of solar-driven systems for off-grid water nanofiltration and electrification. Reviews on Environmental Health, 35(2), 211--217.
• Fathabad, A. M., Yazzie, C. B., Cheng, J., & Arnold, R. G. (2020). Optimization of solar-driven systems for off-grid water nanofiltration and electrification. Reviews on environmental health, 35(2), 211-217. doi:10.1515/reveh-2019-0079
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  Abstract The work described is motivated by an inability to extend central infrastructure for power and water to low-population-density areas of the Navajo Nation and elsewhere. It is estimated that 35% of the Navajo population haul water for household use, frequently from unregulated sources of poor initial quality. The proposed household-scale, solar-driven nanofiltration (NF) system designs are economically optimized to satisfy point-of-use water purification objectives. The systems also provide electrical energy for a degree of nighttime household illumination. Results support rational design of multiple-component purification systems consisting of solar panels, a high-pressure pump, NF membranes, battery storage and an electrical control unit subject to constraints on daily water treatment and excess energy generation. The results presented are conditional (based on initial water quality, membrane characteristics and geography) but can be adapted to satisfy alternative treatment objectives in alternate geographic, etc. settings. The unit costs of water and energy from an optimized system that provides 100 gpd (1 gallon is 3.78 L) and 2 kWh/day of excess electrical energy are estimated at $0.16 per 100 gallons of water treated and $0.26 per kWh of nighttime electrical energy delivered. Methods can be used to inform dispersed infrastructure design subject to alternate constraint sets in similarly remote areas.
• Karimi, R., Lejeune, M. A., & Cheng, J. (2020). A Framework for Solving Chance-Constrained Linear Matrix Inequality Programs. Informs Journal on Computing, 33(3), 1015-1036. doi:10.1287/ijoc.2020.0982
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  We propose a novel partial sample average approximation (PSAA) framework to solve the two main types of chance-constrained linear matrix inequality (CCLMI) problems: CCLMI with random technology ma...
• Karimi, R., Lejeune, M. A., & Cheng, J. (2020). A Framework for Solving Chance-Constrained Linear Matrix Inequality Programs. Informs Journal on Computing. doi:10.1287/ijoc.2020.0982
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  We propose a novel partial sample average approximation (PSAA) framework to solve the two main types of chance-constrained linear matrix inequality (CCLMI) problems: CCLMI with random technology ma...
• Bomze, I. M., Cheng, J., Dickinson, P. J., Lisser, A., & Liu, J. (2019). Notoriously hard (mixed-) binary QPs: empirical evidence on new completely positive approaches. Computational Management Science, 16(4), 593--619.
• Cheng, J., Gicquel, C., & Lisser, A. (2019). Partial sample average approximation method for chance constrained problems. Optimization Letters, 13(4), 657--672.
• Cheng, J., Lisser, A., & Gicquel, C. (2019). Partial sample average approximation method for chance constrained problems. Optimization Letters. doi:10.1007/s11590-018-1300-8
• Cheng, J., & Gicquel, C. (2018). A joint chance-constrained programming approach for the single-item capacitated lot-sizing problem with stochastic demand. Annals of Operations Research. doi:10.1007/s10479-017-2662-5
• Cheng, J., Chen, R. L., Najm, H. N., Pinar, A., Safta, C., & Watson, J. (2018). Chance-constrained economic dispatch with renewable energy and storage. Computational Optimization and Applications, 70(2), 479--502.
• Cheng, J., Li-Yang, C. R., Najm, H. N., Pinar, A., Safta, C., & Watson, J. (2018). Distributionally Robust Optimization with Principal Component Analysis. SIAM Journal on Optimization, 28(2), 1817--1841.
• Cheng, J., Watson, J., Safta, C., Pinar, A., Najm, H. N., & Chen, R. (2018). Distributionally Robust Optimization with Principal Component Analysis. Siam Journal on Optimization. doi:10.1137/16m1075910
• Cheng, J., Watson, J., Safta, C., Pinar, A., Najm, H. N., & Chen, R. L. (2018). Chance-constrained economic dispatch with renewable energy and storage. Computational Optimization and Applications. doi:10.1007/s10589-018-0006-2
• Gicquel, C., & Cheng, J. (2018). A joint chance-constrained programming approach for the single-item capacitated lot-sizing problem with stochastic demand. Annals of Operations Research, 264(1-2), 123--155.
• Bomze, I. M., Cheng, J., Dickinson, P. J., & Lisser, A. (2017). A fresh CP look at mixed-binary QPs: new formulations and relaxations. Mathematical Programming, 166(1-2), 159--184.
• Cheng, J., Leung, J. H., & Lisser, A. (2016). Stochastic nonlinear resource allocation problem. Electronic Notes in Discrete Mathematics. doi:10.1016/j.endm.2016.03.022
• Cheng, J., Leung, J., & Lisser, A. (2016). New reformulations of distributionally robust shortest path problem. Computers & Operations Research, 74, 196--204.
• Cheng, J., Leung, J., & Lisser, A. (2016). Random-payoff two-person zero-sum game with joint chance constraints. European Journal of Operational Research, 252(1), 213--219.
• Cheng, J., Lisser, A., & Leung, J. (2016). Stochastic nonlinear resource allocation problem. Electronic Notes in Discrete Mathematics, 52, 165--172.
• Cheng, J., Lisser, A., & Leung, J. H. (2016). New reformulations of distributionally robust shortest path problem. Computers & Operations Research. doi:10.1016/j.cor.2016.05.002
• Cheng, J., Lisser, A., & Leung, J. M. (2016). Random-payoff two-person zero-sum game with joint chance constraints. European Journal of Operational Research. doi:10.1016/j.ejor.2015.12.024
• Cheng, J., & Lisser, A. (2015). Maximum probability shortest path problem. Discrete Applied Mathematics, 192, 40--48.
• Cheng, J., & Lisser, A. (2015). Maximum probability shortest path problem. Discrete Applied Mathematics. doi:10.1016/j.dam.2014.05.009
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  The maximum probability shortest path problem involves the constrained shortest path problem in a given graph where the arcs resources are independent normally distributed random variables. We maximize the probability that all resource constraints are jointly satisfied while the path cost does not exceed a given threshold. We use a second-order cone programming approximation for solving the continuous relaxation problem. In order to solve this stochastic combinatorial problem, a branch-and-bound algorithm is proposed, and numerical examples on randomly generated instances are given.
• Cheng, J., Houda, M., & Lisser, A. (2015). Chance constrained 0--1 quadratic programs using copulas. Optimization Letters, 9(7), 1283--1295.
• Cheng, J., Lisser, A., & Houda, M. (2015). Chance constrained 0–1 quadratic programs using copulas. Optimization Letters. doi:10.1007/s11590-015-0854-y
• Cheng, J., Delage, E., & Lisser, A. (2014). Distributionally robust stochastic knapsack problem. SIAM Journal on Optimization, 24(3), 1485--1506.
• Cheng, J., Houda, M., & Lisser, A. (2014). Second-order cone programming approach for elliptically distributed joint probabilistic constraints with dependent rows. Optimization.
• Cheng, J., Lisser, A., & Delage, E. (2014). Distributionally Robust Stochastic Knapsack Problem. Siam Journal on Optimization. doi:10.1137/130915315
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  This paper considers a distributionally robust version of a quadratic knapsack problem. In this model, a subsets of items is selected to maximizes the total profit while requiring that a set of knapsack constraints be satisfied with high probability. In contrast to the stochastic programming version of this problem, we assume that only part of the information on random data is known, i.e., the first and second moment of the random variables, their joint support, and possibly an independence assumption. As for the binary constraints, special interest is given to the corresponding semidefinite programming (SDP) relaxation. While in the case that the model only has a single knapsack constraint we present an SDP reformulation for this relaxation, the case of multiple knapsack constraints is more challenging. Instead, two tractable methods are presented for providing upper and lower bounds (with its associated conservative solution) on the SDP relaxation. An extensive computational study is given to illustrate...
• Gicquel, C., Cheng, J., & Lisser, A. (2014). A joint chance-constraint programming approach for a stochastic lot-sizing problem. Program Schedule, 21.
• LISSER, A., Cheng, J., Delage, E., & Lisser, A. (2014). Distributionally Robust Stochastic Knapsack Problem. HAL, 2014.
• LISSER, A., N\'u\~nez, B., ADASME, P., Soto, I., Cheng, J., Letournel, M., & Lisser, A. (2014). A chance constrained approach for uplink wireless OFDMA networks. HAL, 2014.
• Cheng, J., & Lisser, A. (2013). A completely positive representation of 0–1 linear programs with joint probabilistic constraints. Operations Research Letters. doi:10.1016/j.orl.2013.08.008
• Cheng, J., & Lisser, A. (2013). A completely positive representation of 0--1 linear programs with joint probabilistic constraints. Operations Research Letters, 41(6), 597--601.
• Cheng, J., Letournel, M., & Lisser, A. (2013). Distributionally robust stochastic shortest path problem. Electronic Notes in Discrete Mathematics. doi:10.1016/j.endm.2013.05.132
• Cheng, J., Lisser, A., & Letournel, M. (2013). Distributionally robust stochastic shortest path problem. Electronic Notes in Discrete Mathematics, 41, 511--518.
• Cheng, J., & Lisser, A. (2012). A second-order cone programming approach for linear programs with joint probabilistic constraints. Operations Research Letters, 40(5), 325--328.
• Cheng, J., & Lisser, A. (2012). A second-order cone programming approach for linear programs with joint probabilistic constraints. Operations Research Letters. doi:10.1016/j.orl.2012.06.008
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  Abstract This paper deals with a special case of Linear Programs with joint Probabilistic Constraints (LPPC) with normally distributed coefficients and independent matrix vector rows. Through the piecewise linear approximation and the piecewise tangent approximation, we approximate the stochastic linear programs with two second-order cone programming (SOCP for short) problems. Furthermore, the optimal values of the two SOCP problems are a lower and upper bound of the original problem respectively. Finally, numerical experiments are given on randomly generated data.
• Cheng, J., He, Y., & Shen, H. (2010). Improved estimator of the continuous-time kernel estimator. Journal of Shanghai University. doi:10.1007/s11741-010-0675-1
• Cheng, J., Shen, H., & He, Y. (2010). Improved estimator of the continuous-time kernel estimator. Journal of Shanghai University (English Edition), 14(6), 442-451.

Proceedings Publications

• Cheng, J., Cheng, J., Wang, H., Wang, H., Wang, F., Wang, F., Gao, F., & Gao, F. (2022). Submodule Capacitor Sizing for Cascaded H-Bridge STATCOM with Sum of Squares Formulation. In International Power Electronics Conference.
• Cheng, J., & Gicquel, C. (2018). Partial Sample Average Approximation Approach for Stochastic Lot-Sizing Problems. In 2018 IISE Annual Conference.
• Dabiri, A., Cheng, J., Butcher, E. A., & Karimi, R. (2018). Probabilistic-Robust Optimal Control for Uncertain Linear Time-delay Systems by State Feedback Controllers with Memory. In Annual American Control Conference (ACC).
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  In this paper, a new method is developed for robust control of uncertain linear time-delay systems with feedback control whose gain matrix is time-varying. In contrast to the available linear matrix inequality (LMI)-based techniques for stabilizing linear time-invariant (LTI) uncertain time-delay systems where the feedback controller is chosen memoryless with a constant gain matrix, the feedback control has memory over time in the new proposed LMI-based technique. In addition, two new constraint removal approaches are proposed to solve this problem as a chance-constrained optimization problem. The proposed approaches are developed such that the closed-loop systems are robustly asymptotically stable in the presence of uncertainties. In an illustrative example, it is shown that the proposed techniques can successfully stabilize a linear second-order time-delay system with a time-varying feedback control. It is also shown that the proposed constraint removal approaches are more efficient in comparison to the current approaches for approximating chance-constrained problems.
• Karimi, R., Dabiri, A., Cheng, J., & Butcher, E. A. (2018). Probabilistic-Robust Optimal Control for Uncertain Linear Time-delay Systems by State Feedback Controllers with Memory. In 2018 Annual American Control Conference (ACC).
• Cheng, J., Lisser, A., & Xu, C. (2015). A Sampling Method to Chance-constrained Semidefinite Optimization. In International Conference on Operations Research and Enterprise Systems (ICORES).
• Xu, C., Cheng, J., & Lisser, A. (2015). A Sampling Method to Chance-constrained Semidefinite Optimization. In Proceedings of the International Conference on Operations Research and Enterprise Systems, 75-81.
• Xu, C., Cheng, J., & Lisser, A. (2015). A Sampling Method to Chance-constrained Semidefinite Optimization. In Proceedings of the International Conference on Operations Research and Enterprise Systems.
• Xu, C., Cheng, J., & Lisser, A. (2015). Stochastic Semidefinite Optimization Using Sampling Methods. In International Conference on Operations Research and Enterprise Systems, 93-103.
• Xu, C., Cheng, J., & Lisser, A. (2015). Stochastic Semidefinite Optimization Using Sampling Methods. In International Conference on Operations Research and Enterprise Systems.
• Cheng, J., Gicquel, C., & Lisser, A. (2014). A modified sample approximation method for chance constrained problems. In SIAM Conference on optimization 2014.
• Cheng, J., Lisser, A., & Gicquel, C. (2014). A modified sample approximation approach for chance-constrained problems. In PGMO-COPI'14; Conference on Optimization and Practices in Industry.
• Cheng, J., Lisser, A., & Gicquel, C. (2014). A modified sample approximation method for chance constrained problems. In International Conference on Operations Research and Enterprise Systems (ICORES).
• Cheng, J., Lisser, A., Letournel, M., Soto, I., Adasme, P., & Nuñez, B. (2014). A chance constrained approach for uplink wireless OFDMA networks. In 9th International Symposium on Communication Systems, Networks & Digital Sign (CSNDSP).
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  In this paper, we compare individual and joint probabilistic constraints for a resource allocation problem in an uplink (UL) wireless OFDMA network. For this purpose, we formulate the problem as a stochastic linear programming (SLP) problem. Then, we transform this model into equivalent deterministic Second-Order Cone Programming (SOCP) problems. All models are intended to maximize the bit rates throughput of the network subject to subcarrier and power user constraints. Our preliminary numerical results show that the joint chance constraint formulation is slightly conservative than the individual probabilistic one. Finally, we show that our approximation of the deterministic joint probabilistic model is very tight.
• Gicquel, C., Cheng, J., & Lisser, A. (2014). A joint chance-constraint programming approach for a stochastic lot-sizing problem. In Proceedings International Workshop on Lot-sizing, IWLS, Porto, Portuga.
• Gicquel, C., Cheng, J., Cheng, J., & Gicquel, C. (2014). Solving a stochastic lot-sizing problem with a modified sample approximation approach.. In 44th International Conference on Computers and Industrial Engineering.
• Nu~nez, B., Adasme, P., Soto, I., Cheng, J., Letournel, M., & Lisser, A. (2014). A chance constrained approach for uplink wireless OFDMA networks. In Communication Systems, Networks & Digital Signal Processing (CSNDSP), 2014 9th International Symposium on.
• Nuñez, B., Adasme, P., Soto, I., Cheng, J., Letournel, M., & Lisser, A. (2014). A chance constrained approach for uplink wireless OFDMA networks. In Communication Systems, Networks & Digital Signal Processing (CSNDSP), 2014 9th International Symposium on, 754-757.
• Cheng, J., Gicquel, C., & Lisser, A. (2012). A second-order cone programming approximation to joint chance-constrained linear programs. In International Symposium on Combinatorial Optimization, 71-80.
• Cheng, J., Gicquel, C., & Lisser, A. (2012). A second-order cone programming approximation to joint chance-constrained linear programs. In International Symposium on Combinatorial Optimization.
• Cheng, J., Kosuch, S., & Lisser, A. (2012). Stochastic Shortest Path Problem with Uncertain Delays.. In ICORES, 256-264.
• Cheng, J., Kosuch, S., & Lisser, A. (2012). Stochastic Shortest Path Problem with Uncertain Delays.. In ICORES.
• Cheng, J., Lisser, A., & Kosuch, S. (2012). STOCHASTIC SHORTEST PATH PROBLEM WITH UNCERTAIN DELAYS. In International Conference on Operations Research and Enterprise Systems (ICORES).
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  This paper considers a stochastic version of the shortest path problem, the Stochastic Shortest Path Problem with Delay Excess Penalty on directed, acyclic graphs. In this model, the arc costs are deterministic, while each arc has a random delay, assumed normally distributed. A penalty occurs when the given delay constraint is not satisfied. The objective is to minimize the sum of the path cost and the expected path delay penalty. In order to solve the model, a Stochastic Projected Gradient method within a branch-and-bound framework is proposed and numerical examples are given to illustrate its effectiveness. We also show that, within given assumptions, the Stochastic Shortest Path Problem with Delay Excess Penalty can be reduced to the classic shortest path problem.

Others

• Safta, C., Cheng, J., Chen, R. L., Pinar, A., Najm, H. N., & Watson, J. (2022). Surrogate-based model for optimization under uncertainty..
• Fathabad, A. M., Cheng, J., Pan, K., & Yang, B. (2021). Tight Conic Approximations for Chance-Constrained AC Optimal Power Flow.
• Cheng, J. (2013). Stochastic Combinatorial Optimization.