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作者： Chen, Zhihao University of Michigan

学位级别：Ph.D.

This thesis proposes three risk-averse models applied under demand uncertainty: a chance-constrained approach to network design problems (NDPs), a distributionally robust approach to NDPs, and a carsharing model to maximize profitability. The first stage makes strategic network design decisions, and the second stage utilizes risk-averse approaches to ensure high levels of demand satisfaction while minimizing network design, commodity flow, and potential quality of service (QoS) penalty costs. The first model optimizes the probabilistic network design problem (PNDP), where we maintain QoS through chance constraints. The chance-constrained models are reformulated as a mixed-integer linear programs (MILPs), and we develop polynomial-time algorithms for special cases. The PNDP is benchmarked against a stochastic programming model that penalizes unmet demand via a linear penalty function. The numerical results suggest cost savings for customized QoS parameters and decreased computational time when using the polynomial-time algorithm over the MILP formulation. The second model proposes a distributionally robust NDP (DR-NDP) with a marginal moment-based ambiguity set, to obtain arc capacity solutions that optimize the worst-case total cost over all candidate distributions. We estimate the optimal value of DR-NDP with an MILP, optimized via a cutting-plane algorithm that iteratively generates valid cuts for the approximate problem. We benchmark the DR-NDP against a sample average approximation-based model, testing on grid and real-world network instances. Our results show the robustness of DR-NDP solutions and their response to changes in observed demand levels, highlighting potential niche uses of DR-NDP in data-scarce contexts. The third model maximizes carsharing profits. The first-stage problem determines fleet allocation and the number of parking lots and permits to purchase. The second stage solves a stochastic minimum cost flow problem on a spatial-temporal network t

关键词： Two-stage stochastic optimization chance-constrained programming Distributionally robust optimization Carsharing Mixed-integer programming Thesis

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The Capacitated Vehicle Routing Problem with Evidential Demands: A Belief-constrained programming Approach 1

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4th International Conference on Belief Functions (BELIEF)

作者： Helal, Nathalie Pichon, Frederic Porumbel, Daniel Mercier, David Lefevre, Eric Univ Artois LGI2A EA 3926 F-62400 Bethune France Conservatoire Natl Arts & Metiers EA 4629 F-75003 Paris France

ISBN: (数字)9783319455594

ISBN: (纸本)9783319455587;9783319455594

This paper studies a vehicle routing problem, where vehicles have a limited capacity and customer demands are uncertain and represented by belief functions. More specifically, this problem is formalized using a belief function based extension of the chance-constrained programming approach, which is a classical modeling of stochastic mathematical programs. In addition, it is shown how the optimal solution cost is influenced by some important parameters involved in the model. Finally, some instances of this difficult problem are solved using a simulated annealing metaheuristic, demonstrating the feasibility of the approach.

关键词： Vehicle routing problem Stochastic programming chance-constrained programming Belief functions

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Robust optimization approach for a chance-constrained binary knapsack problem

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MATHEMATICAL programming 2016年第1期157卷 277-296页

作者： Han, Jinil Lee, Kyungsik Lee, Chungmok Choi, Ki-Seok Park, Sungsoo Catholic Univ Louvain CORE B-1348 Louvain Belgium Korea Adv Inst Sci & Technol Dept Ind & Syst Engn 291 Daehak Ro Taejon 305701 South Korea Seoul Natl Univ Dept Ind Engn 1 Gwanak Ro Seoul 151742 South Korea Seoul Natl Univ Inst Ind Syst Innovat 1 Gwanak Ro Seoul 151742 South Korea Hankuk Univ Foreign Studies Dept Ind & Management Engn San 89 Yongin 449791 Gyeonggi Do South Korea

We consider a certain class of chance-constrained binary knapsack problem where each item has a normally distributed random weight that is independent of the other items. For this problem we propose an efficient pseudo-polynomial time algorithm based on the robust optimization approach for finding a solution with a theoretical bound on the probability of satisfying the knapsack constraint. Our algorithm is tested on a wide range of random instances, and the results demonstrate that it provides qualified solutions quickly. In contrast, a state-of-the-art MIP solver is only applicable for instances of the problem with a restricted number of items.

关键词： Knapsack problem Combinatorial optimization chance-constrained programming Robust optimization

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Sample Bound Estimate Based chance-constrained Immune Optimization and Its Applications

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International Journal of Automation and computing 2016年第5期13卷 468-479页

作者： Zhu-Hong Zhang Kai Yang Da-Min Zhang College of Big Data & Information Engineering Guizhou University College of Computer Science & Technology Guizhou University

This work investigates a simple and practical bio-immune optimization approach to solve a kind of chance-constrained programming problem without known noisy attributes, after probing into a lower bound estimate of sample size for any random variable. Such approach mainly consists of sample allocation, evaluation, proliferation and mutation. The former two, depending on a lower bound estimate acquired, not only decide the sample size of random variable and the importance level of each evolving B cell, but also ensure that such B cell is evaluated with low computational cost; the third makes diverse B cells participate in evolution and suppresses the influence of noise; the last, which associates with the information on population diversity and fitness inheritance, creates diverse and high-affinity B cells. Under such approach, three similar immune algorithms are derived after selecting different mutation rules. The experiments, by comparison against two valuable genetic algorithms, have illustrated that these immune algorithms are competitive optimizers capable of effectively executing noisy compensation and searching for the desired optimal reliable solution.

关键词： chance-constrained programming immune optimization sample allocation lower bound estimate noise attenuation

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A purely proactive scheduling procedure for the resource-constrained project scheduling problem with stochastic activity durations

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JOURNAL OF SCHEDULING 2016年第4期19卷 409-428页

作者： Lamas, Patricio Demeulemeester, Erik Katholieke Univ Leuven Dept Decis Sci & Informat Management Fac Business & Econ Res Ctr Operat Management Leuven Belgium

The purpose of this research is to develop a new procedure for generating a proactive baseline schedule for the resource-constrained project scheduling problem. The main advantage of this new procedure is that it is completely independent of the reactive policy applied. This contrasts with the traditional methods that assume a predefined reactive policy. First, we define a new robustness measure, then we introduce a branch-and-cut method for solving a sample average approximation of our original problem. In a computational experiment, we show that our procedure outperforms two other published methods, assuming different robustness measures.

关键词： Proactive RCPSP Robust RCPSP chance-constrained programming SAA

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Fixed charge solid transportation problem in uncertain environment and its algorithm

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COMPUTERS & INDUSTRIAL ENGINEERING 2016年 102卷 186-197页

作者： Zhang, Bo Peng, Jin Li, Shengguo Chen, Lin Zhongnan Univ Econ & Law Sch Math & Stat Wuhan 430073 Peoples R China Huanggang Normal Univ Inst Uncertain Syst Huanggang 438000 Peoples R China Tianjin Univ Inst Syst Engn Tianjin 300072 Peoples R China

In this paper, the fixed charge solid transportation problem under uncertainty is investigated. As a result, three mathematical models are constructed for the problem, i.e., expected value model, chance constrained programming model and measure-chance programming model, where the supplies, demands, conveyance capacities, direct costs and fixed charges are regarded as uncertain variables. After that, the crisp equivalences of the models are discussed. What is more, a hybrid intelligent algorithm is designed based on the uncertainty theory and tabu search algorithm to solve the models. Compared with the existing work, the innovations of the proposed work are briefly illustrated. Finally, some numerical examples are given to show the applications of the models and the algorithm. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Transportation problem chance-constrained programming Measure-chance programming Uncertainty theory Tabu search algorithm

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Dispatching strategies for coordinating environmental awareness and risk perception in wind power integrated system

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ENERGY 2016年 106卷 453-463页

作者： Jin, Jingliang Zhou, Dequn Zhou, Peng Qian, Shuqu Zhang, Mingming Nantong Univ Coll Sci 9 Seyuan Rd Nantong Peoples R China Nanjing Univ Aeronaut & Astronaut Coll Econ & Management 29 Jiangjun Ave Nanjing Jiangsu Peoples R China Anshun Univ Coll Sci 25 Xueyuan Rd Anshun Peoples R China

Wind power plays a significant role in economic and environmental operation of electric power system. Meanwhile, the variability and uncertainty characteristics of wind power generation bring technical and economical challenges for power system operation. In order to harmonize the relationship between environmental protection and risk management in power dispatching, this paper presents a stochastic dynamic economic emission dispatch model combining risk perception with environmental awareness of decision-makers by following the principle of chance-constrained programming. In this power dispatching model, the description of wind power uncertainty is derived from the probability statistic character of wind speed. Constraints-handling techniques as a heuristic strategy are embedded into non dominated sorting genetic algorithm-II. In addition, more information is digested from the Pareto optimum solution set by cluster analysis and fuzzy set theory. The simulation results eventually demonstrate that the increase of the share of wind power output will bring higher risk, though it is beneficial for economic cost and environmental protection. Since different risk perception and environmental awareness can possibly lead to diverse non-dominated solutions, decision-makers may choose an appropriate dispatching strategy according to their specific risk perception and environmental awareness. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Wind power Uncertainty Dynamic economic emission dispatch chance-constrained programming

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Stochastic security-constrained economic dispatch for random responsive price-elastic load and wind power

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IET RENEWABLE POWER GENERATION 2016年第7期10卷 936-943页

作者： Yang, Shengchun Zeng, Dan Ding, Hongfa Yao, Jianguo Wang, Ke Li, Yaping Huazhong Univ Sci & Technol State Key Lab Adv Electromagnet Engn & Technol Wuhan 430074 Peoples R China State Grid Power Automat Dept China Elect Power Res Inst Nanjing 210003 Jiangsu Peoples R China

Price-elastic load (PEL) is a typical demand response resource. PEL provides an effective option to address the challenge of wind power output fluctuation. This study proposes a stochastic scheduling model, considering uncertainties of variable wind power and PEL response. A PEL stochastic security-constrained economic dispatch model using chance-constrained programming is presented for scheduling. The authors propose that the chance-constrained transmission interface flow constraints should be considered to control the probability of transmission interface flow limit violation via the parameter of security probability. An approach is suggested to transform the stochastic model into a deterministic quadratic programming problem via linearising the branch flow constraints and transmission interface flow constraints with sensitivity analysis method. Then, the probabilistic transmission interface flow constraints are equivalently transformed into conventional constraints. Case simulations on a provincial power system with 151 buses demonstrate the effectiveness and feasibility of the proposed mechanism, models, and methods.

关键词： pricing load dispatching wind power power generation scheduling stochastic processes quadratic programming sensitivity analysis stochastic security-constrained economic dispatch random responsive price-elastic load wind power output fluctuation stochastic scheduling model PEL chance-constrained programming stochastic model deterministic quadratic programming problem branch flow constraints sensitivity analysis method transmission interface flow constraints

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chance-constrained problems and rare events: an importance sampling approach

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MATHEMATICAL programming 2016年第1期157卷 153-189页

作者： Barrera, Javiera Homem-de-Mello, Tito Moreno, Eduardo Pagnoncelli, Bernardo K. Canessa, Gianpiero Univ Adolfo Ibanez Fac Sci & Engn Santiago Chile Univ Adolfo Ibanez Sch Business Santiago Chile Univ Adolfo Ibanez IE&OR Program Santiago Chile

We study chance-constrained problems in which the constraints involve the probability of a rare event. We discuss the relevance of such problems and show that the existing sampling-based algorithms cannot be applied directly in this case, since they require an impractical number of samples to yield reasonable solutions. We argue that importance sampling (IS) techniques, combined with a Sample Average Approximation (SAA) approach, can be effectively used in such situations, provided that variance can be reduced uniformly with respect to the decision variables. We give sufficient conditions to obtain such uniform variance reduction, and prove asymptotic convergence of the combined SAA-IS approach. As it often happens with IS techniques, the practical performance of the proposed approach relies on exploiting the structure of the problem under study;in our case, we work with a telecommunications problem with Bernoulli input distributions, and show how variance can be reduced uniformly over a suitable approximation of the feasibility set by choosing proper parameters for the IS distributions. Although some of the results are specific to this problem, we are able to draw general insights that can be useful for other classes of problems. We present numerical results to illustrate our findings.

关键词： chance-constrained programming Sample average approximation Importance sampling Rare-event simulation

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Corrective economic dispatch and operational cycles for probabilistic unit commitment with demand response and high wind power

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APPLIED ENERGY 2016年第0期182卷 634-651页

作者： Azizipanah-Abarghooee, Rasoul Golestaneh, Faranak Gooi, Hoay Beng Lin, Jeremy Bavafa, Farhad Terzija, Vladimir Univ Manchester Sch Elect & Elect Engn Manchester M13 9PL Lancs England Nanyang Technol Univ Sch Elect & Elect Engn Singapore Singapore PJM Interconnect Norristown PA USA Shiraz Univ Technol Sch Elect Elect Engn Shiraz Iran

We propose a probabilistic unit commitment problem with incentive-based demand response and high level of wind power. Our novel formulation provides an optimal allocation of up/down spinning reserve. A more efficient unit commitment algorithm based on operational cycles is developed. A multi-period elastic residual demand economic model based on the self- and cross-price elasticities and customers' benefit function is used. In the proposed scheme, the probability of residual demand falling within the up/down spinning reserve imposed by n - 1 security criterion is considered as a stochastic constraint. A chance-constrained method, with a new iterative economic dispatch correction, wind power curtailment, and commitment of cheaper units, is applied to guarantee that the probability of loss of load is lower than a pre-defined risk level. The developed architecture builds upon an improved Jaya algorithm to generate feasible, robust and optimal solutions corresponding to the operational cost. The proposed framework is applied to a small test system with 10 units and also to the IEEE 118-bus system to illustrate its advantages in efficient scheduling of generation in the power systems. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： chance-constrained programming Cycle based on/off Wind energy Incentive-based demand response program Unit commitment Improved Jaya algorithm

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