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A chance-constrained programming framework to handle uncertainties in radiation therapy treatment planning

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2018年第2期266卷 736-745页

作者： Zaghian, Maryam Lim, Gino J. Khabazian, Azin Univ Texas MD Anderson Canc Ctr Off Performance Improvement 1515 Holocombe BlvdUnit 0466 Houston TX 77030 USA Univ Houston Dept Ind Engn 4800 Calhoun Rd Houston TX 77204 USA

A stochastic programming framework is proposed for radiation therapy treatment planning. This framework takes into account uncertainty in setting up or positioning patients identically day-to-day during the treatment period. Because uncertainties are unavoidable, constraint violations are tolerated to some degree in practice. Under this assumption, a chance-constrained programming (CCP) framework is developed to handle setup uncertainties in treatment planning. The proposed framework can be employed under different distributional assumptions. The goal of the proposed approach is to maximize both the statistical confidence level of a treatment plan and the homogeneity of the dose distributions. This novel perspective provides a user-centric and personalized optimization model that allows a trade-off between sufficient tumor coverage and sparing healthy tissues under uncertainty. We describe testing of the performance of the proposed CCP models in terms of plan quality, robustness, and homogeneity and confidence level of the constraints using clinical data for a prostate cancer patient. Optimized CCP plans are also compared to plans developed using a deterministic approach that does not take uncertainties into account. Numerical experiments confirmed that the CCP is able to control setup uncertainties in target coverage and sparing of organs-at-risk. (C) 2017 Elsevier B.V. All rights reserved.

关键词： chance-constrained programming Radiation treatment planning Setup uncertainty

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A long-term intelligent operation and management model of cascade hydropower stations based on chance constrained programming under multi-market coupling

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ENVIRONMENTAL RESEARCH LETTERS 2021年第5期16卷

作者： Lu, Jia Li, Gang Cheng, Chuntian Liu, Benxi Dalian Univ Technol DUT Inst Hydropower Syst & Hydroinformat Dalian 2 Linggong Rd Dalian 116024 Liaoning Peoples R China

Under the medium- and long-term electric markets, cascaded hydropower stations face a series of practical challenges due to the uncertainty of inflow and market price. For long-term dispatch scheduling, the allocation of power generation in multimarkets is critical, including clean energy priority consumption market, inter provincial market and intra provincial market in order to maximize the operator's expected revenue and reduce the market operation risks. Based on the hydro-dominant electricity market structure and settlement rules, we propose a long-term optimal operation method for cascade hydropower stations considering the uncertainty of multiple variables. First, a seasonal autoregressive integrated moving average model is used to handle the time-varying and seasonal characteristics of inflow series by using a copula connect function to fit the joint distribution of the monthly inflow, the clearing price of the intra provincial market and the delivery volume of the inter provincial market. Then, uncertain chance-constrained programming is established. Finally, a developed particle swarm optimization algorithm embedded in a Monte Carlo simulation is solved for hydropower operation policies, and the maximum revenue, resource allocation and scheduling strategy are obtained under the corresponding risk tolerance. Taking the actual data of cascaded hydropower stations in Yunnan Province, China, as an example, a simulation analysis is carried out. The results show that the proposed method can reasonably describe the uncertainty and correlation between the variables, realizing the optimal allocation of resources among multimarkets, and provide references for the long-term optimal operation of cascade hydropower stations in a multimarket environment. The results also show that the decision strategies should be determined considering the decision-maker's risk preference.

关键词： cascade hydropower stations multimarket Copula-SARIMA chance-constrained programming

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Simulation-based interval chance-constrained quadratic programming model for water quality management: A case study of the central Grand River in Ontario, Canada

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ENVIRONMENTAL RESEARCH 2021年 192卷 110206-110206页

作者： Zhang, Qianqian Li, Zhong Huang, Wendy Chengdu Univ Informat Technol Sch Management Chengdu 610225 Peoples R China McMaster Univ Dept Civil Engn Hamilton ON L8S 4L8 Canada

Effective river water quality management and planning is a complex issue challenged by various complexities and uncertainties. A simulation-based interval chance-constrained quadratic programming (ICCQP) model is developed for the seasonal planning of water quality management (WQM) under various uncertainties. The proposed model incorporates interval quadratic programming, chance-constrained programming, and a seasonal water quality simulation model within a general framework for WQM. Uncertainties associated with the objective and the coefficients in the left-hand sides of the constraints are tackled as intervals. Meanwhile, parameter uncertainties on the right-hand sides are characterized using probability distributions. Nonlinearities in the cost function are reflected by quadratic programming. A multi-segment water quality model is used to simulate the dynamic interactions between wastewater discharges and river water quality. The proposed ICCQPWQM model is applied in a real case study for the control of total phosphorus (TP) in the central Grand River in Ontario, Canada. The results demonstrate that the proposed model is able to incorporate uncertainties expressed as intervals and probability information into an optimization framework and provide interval solutions. Thus, different cost-effective schemes for seasonal WQM could be generated. The results show the Kitchener wastewater treatment plant (WWTP) affects the value of the objective function more than the other WWTPs in the study area. It is also found that the Kitchener WWTP's cost accounts for the highest proportion (approximately 35.1-37.9%) of the total annual cost, which implies the control of TP at the Kitchener plant is the most important to the system. Moreover, river water TP standards in spring and autumn are usually difficult to meet, indicating different TP control strategies are needed in these two seasons. The generated results are valuable for local decision makers to generate TP control st

关键词： Interval quadratic programming chance-constrained programming Water quality management Uncertainty The grand river

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Inexact fuzzy chance-constrained programming for community-scale urban stormwater management

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JOURNAL OF CLEANER PRODUCTION 2018年 182卷 937-945页

作者： Cai, Yanpeng Lin, Xuan Yue, Wencong Zhang, Pingping Beijing Normal Univ Sch Environm State Key Lab Water Environm Simulat Beijing 100875 Peoples R China Univ Regina Inst Energy Environm & Sustainable Communities 1202 Res Dr Regina SK S4S 7H9 Canada Beijing Normal Univ Sch Environm Beijing Engn Res Ctr Watershed Environm Restorat Beijing 100875 Peoples R China McGill Univ Dept Civil Engn & Appl Mech 817 Sherbrooke St West Montreal PQ H3A 0C3 Canada Dongguan Univ Technol Sch Ecol Environm & Civil Engn Dongguan 523808 Peoples R China

Due to frequent and serious waterlog and environmental pollution in cities in recent years, urban stormwater management (USM) has become an essential issue of urban sustainable development in China. Low Impact Development (LID) technologies are effective and popular measures of USM, and can be used to reduce urban waterlog and the associated environmental pollution. In this paper, in order to identify an optimal strategy of LID technologies based on economic efficiencies and environmental performances, the construction costs and environmental benefits of the four LID technologies (including grass swales, bioretention cells, green roofs, and permeable pavement) were analyzed. Then, due to the uncertain feature of rainfall, concentration of pollutants and many social-economic factors, an inexact fuzzy chance-constrained programming (IFCCP) model was developed. Multiple uncertainties that can be expressed as interval parameters, fuzzy sets, and stochastic distribution can be addressed effectively and incorporated directly into the modeling process. Based on the analysis of the precipitation probability distribution and land use data, the developed model was applied to a university campus with relatively high building density and plot ratio in Beijing. Then, optimal solutions of multiple precipitation probabilities (p(m)) under varying USM goals were obtained. The four LID technologies were chosen to meet multiple USM goals based on multiple p(m) values. When p(m) = 0.1, 0.05, 0.02 and 0.015, the total construction investments would be 1.46 to 4.66, 1.46 to 5.25, 2.31 to 8.54 and 3.95 to 12.7 million yuan, respectively. The relationship between construction costs and pm represented the relationship between economic benefit and system risk. The results indicated that USM was influenced by the rainfall capacity, construction costs would increase with the increase of precipitation, and the risks of constraint violation would decrease as the construction costs increase. Whe

关键词： Urban stormwater management Low impact development chance-constrained programming Fuzzy sets theory Optimal strategies

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A joint chance-constrained programming approach for the single-item capacitated lot-sizing problem with stochastic demand

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ANNALS OF OPERATIONS RESEARCH 2018年第1-2期264卷 123-155页

作者： Gicquel, Celine Cheng, Jianqiang Univ Paris Sud Lab Rech Informat Paris France Univ Arizona Dept Syst & Ind Engn Tucson AZ 85721 USA

We study the single-item single-resource capacitated lot-sizing problem with stochastic demand. We propose to formulate this stochastic optimization problem as a joint chance-constrained program in which the probability that an inventory shortage occurs during the planning horizon is limited to a maximum acceptable risk level. We investigate the development of a new approximate solution method which can be seen as an extension of the previously published sample approximation approach. The proposed method relies on a Monte Carlo sampling of the random variables representing the demand in all planning periods except the first one. Provided there is no dependence between the demand in the first period and the demand in the later periods, this partial sampling results in the formulation of a chance-constrained program featuring a series of joint chance constraints. Each of these constraints involves a single random variable and defines a feasible set for which a conservative convex approximation can be quite easily built. Contrary to the sample approximation approach, the partial sample approximation leads to the formulation of a deterministic mixed-integer linear problem having the same number of binary variables as the original stochastic problem. Our computational results show that the proposed method is more efficient at finding feasible solutions of the original stochastic problem than the sample approximation method and that these solutions are less costly than the ones provided by the Bonferroni conservative approximation. Moreover, the computation time is significantly shorter than the one needed for the sample approximation method.

关键词： Stochastic lot-sizing chance-constrained programming Joint probabilistic constraint Sample approximation approach Mixed-integer linear programming

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A chance-constrained programming Approach to the Design of Robust Broadband Beamformers With Microphone Mismatches

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IEEE-ACM TRANSACTIONS ON AUDIO SPEECH AND LANGUAGE PROCESSING 2018年第12期26卷 2475-2488页

作者： Bao, Yu Chen, Huawei Nanjing Univ Aeronaut & Astronaut Coll Elect & Informat Engn Nanjing 210016 Jiangsu Peoples R China

This paper addresses the design of robust broadband beamformers by taking into account the prior knowledge of uncertain means and variances of microphone mismatches. A chance-constrained programming (CCP) based design approach is proposed, which is a generic extension of the existing worst case mean performance optimization (WMPO) based counterpart by using a chance-constrained stopband level constraint instead of a hard one. The original CCP-based design problem, however, is NP-hard to solve. To deal with the problem, a relaxed convex optimization formulation is developed by exploiting the distribution property of array response distortion due to microphone mismatches. The relation between the proposed CCP- and WMPO-based design approaches is analyzed theoretically. It shows that there always exists a chance constraint probability under which the CCP-based design is comparable to the WMPO-based one, which provides an insight into the overconservatism problem in the WMPO-based design from the perspective of the CCP-based framework. Moreover, a criterion on the setting of the chance constraint probability is also derived for the proposed design approach in order to remedy the overconservatism problem. Simulation and real experimental results are presented to show the superior performance of the proposed design approach compared with its state-of-the-art counterparts.

关键词： Broadband beamformers microphone arrays microphone mismatches robustness chance-constrained programming worst-case mean performance optimization

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chance-constrained programming for day-ahead scheduling of variable wind power amongst conventional generation mix and energy storage

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IET RENEWABLE POWER GENERATION 2017年第14期11卷 1785-1793页

作者： Tan, Wen-Shan Shaaban, Mohamed Abdullah, Md Pauzi Univ Teknol Malaysia Inst Future Energy CEES Fac Elect Engn Johor Baharu 81310 Johor Malaysia Univ Malaysia Sarawak Dept Elect & Elect Engn Fac Engn Kota Samarahan 94300 Sarawak Malaysia Port Said Univ Dept Elect Engn Fac Engn Port Fouad 42523 Port Said Egypt

This study presents a day-ahead scheduling of a generation portfolio incorporating large shares of intermittent wind generation. The scheduling utilises the cycling of conventional generation as well as the dispatch of energy storage (ES) to mitigate the impact of net load ramps. Inherent system flexibility, expressed as a chance constraint, is quantified in terms of ramping capability and operating reserves of conventional generation and ES. The flexibility chance constraint is then factorised into a set of linear deterministic inequalities, to preserve the mixed-integer linear programming structure of the resulting problem. Numerical simulations are performed and results are analysed for IEEE 24-bus and 118-bus systems. Test results show that implementation of ES improves the flexibility of the system, in terms of alleviation of the cycling of thermal generation as well as wind generation curtailment.

关键词： power generation scheduling power generation dispatch wind power integer programming linear programming power generation economics investment chance-constrained programming day-ahead scheduling variable wind power conventional generation mix and energy storage dispatch generation portfolio intermittent wind generation net load ramp impact mitigation flexibility chance constraint linear deterministic inequalities mixed-integer linear programming structure IEEE 24-bus system IEEE 118-bus system thermal generation cycling wind generation curtailment

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Optimal Dispatch Based on chance-constrained programming 10

Optimal Dispatch Based on Chance-constrained Programming

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IEEE PES Asia-Pacific Power and Energy Engineering Conference (APPEEC)

作者： Zeng, Kaiwen Pan, Mengqi Li, Bo Liu, Jianing Wang, Qi Guo, Yufeng Guangdong Power Grid Power Dispatch Control Ctr Guangzhou Guangdong Peoples R China Univ Hong Kong Dept Elect & Elect Engn Hong Kong Peoples R China Harbin Inst Technol Sch Elect Engn & Automat Harbin Peoples R China

ISBN: (纸本)9781538656860

Because of wind turbulent fluctuation, it is difficult to predict wind power fluctuation, which brings problems of randomness and uncertainty to power system stability. This study introduces a method to analyze wind power fluctuation characteristics. An optimal dispatch model-based on chance-constrained programming is established. The function formula of the wind power fluctuation is included in the power balance constraint. Finally, a genetic algorithm is proposed for the model solution, and the economic costs are calculated from this model. The algorithm is consistent with traditional ones and the models proposed in this study are shown to be reasonable and effective.

关键词： power system wind turbulent fluctuation wind power fluctuation chance-constrained programming optimal dispatch

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A type-2 fuzzy chance-constrained programming method for planning Shanghai's energy system

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INTERNATIONAL JOURNAL OF ELECTRICAL POWER & ENERGY SYSTEMS 2017年 90卷 37-53页

作者： Suo, C. Li, Y. P. Wang, C. X. Yu, L. North China Elect Power Univ Sino Canada Energy & Environm Res Ctr Beijing 102206 Peoples R China Beijing Normal Univ Sch Environm Environm & Energy Syst Engn Res Ctr Beijing 100875 Peoples R China

In this, study, a type-2 fuzzy chance-constrained programming (TFCP) method is developed for supporting energy systems planning (ESP) under uncertainty. TFCP incorporates chance-constrained programming within a type-2 fuzzy programming framework to handle uncertainties (i.e. type-2 fuzzy sets and probabilistic distributions) in the objective and constraints, as well as to examine the reliability of satisfying (or risk of violating) system constraints. A TFCP-based energy system (TFCP-ES) model is then formulated for energy systems planning of Shanghai, where multi-energy resources, multi-processing technologies, multi-conversion technologies and multi-end users are considered. Solutions of energy supply, electricity generation, capacity expansion, and air-pollutant emission associated with different constraint-violation risks are obtained. Results reveal that (i) natural gas is one of the major energy-supply sources for the city in the future (increasing by 13.0%);(ii) the city's electricity-generation structure tends to the transition from coal-dominated into clean energy-dominated (e.g., natural gas, onshore wind, offshore wind, and photovoltaic power);(iii) the city's energy-supply security is enhanced by provoking the utilization of renewable energies (increasing by 1.0%). The results are helpful for managers to adjust the city's current energy structure, enhance the energy supply security, as well as make tradeoff between system cost and constraint-violation risk. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： chance-constrained programming Energy systems Planning Risk analysis Type-2 fuzzy Uncertainty

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A fuzzy chance-constrained programming model with type 1 and type 2 fuzzy sets for solid waste management under uncertainty

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ENGINEERING OPTIMIZATION 2017年第6期49卷 1040-1056页

作者： Ma, Xiaolin Ma, Chi Wan, Zhifang Wang, Kewei Univ Sci & Technol Liaoning Sch Business Adm Anshan Peoples R China Univ Sci & Technol Liaoning Coll Software Anshan Peoples R China Northeast Forestry Univ Coll Econ & Management Harbin Peoples R China

Effective management of municipal solid waste (MSW) is critical for urban planning and development. This study aims to develop an integrated type 1 and type 2 fuzzy sets chance-constrained programming (ITFCCP) model for tackling regional MSW management problem under a fuzzy environment, where waste generation amounts are supposed to be type 2 fuzzy variables and treated capacities of facilities are assumed to be type 1 fuzzy variables. The evaluation and expression of uncertainty overcome the drawbacks in describing fuzzy possibility distributions as oversimplified forms. The fuzzy constraints are converted to their crisp equivalents through chance-constrained programming under the same or different confidence levels. Regional waste management of the City of Dalian, China, was used as a case study for demonstration. The solutions under various confidence levels reflect the trade-off between system economy and reliability. It is concluded that the ITFCCP model is capable of helping decision makers to generate reasonable waste-allocation alternatives under uncertainties.

关键词： Type 2 fuzzy variable chance-constrained programming solid waste management Dalian

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