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Fuzzy distributional chance-constrained programming for handling stochastic and epistemic uncertainties during flotation processes

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CHEMICAL ENGINEERING RESEARCH & DESIGN 2020年 164卷 248-260页

作者： Liang, Yu He, Dakuo Wang, Qingkai Lu, Xianlun Northeastern Univ Coll Informat Sci & Engn Shenyang 110004 Liaoning Peoples R China Northeastern Univ State Key Lab Synthet Automat Proc Ind Shenyang 110004 Peoples R China State Key Lab Proc Automat Min & Met Beijing 100160 Peoples R China

During the flotation process, a fuzzy distributional chance-constrained programming approach is proposed to design the circuit structure, equipment size and operating conditions considering stochastic and epistemic uncertainties. Stochastic uncertainties are irreducible, such as fluctuations in copper price and circuit feed mass flowrate, and epistemic uncertainties are due to the complicated flotation mechanism. To achieve the probability measure in the chance constraints, a finite number of scenarios are defined for the stochastic uncertainties by using discrete probability distribution sets. Moreover, the epistemic uncertainties are handled by fuzzy sets. In this context, a fuzzy probability-box of profits combining probability theory with fuzzy theory can be obtained to assess the distribution profile. The integral whole optimization of the flotation process is solved by using rule-oriented genetic algorithm, adapted from the non-dominated sorting genetic algorithm (NSGA-II), and the design rules are embedded in initialization, crossover and mutation. Finally, the sensitivity analysis of epistemic uncertainties on the optimal designs is carried out to get the critical uncertain variable. The method proposed here can fully reflect the flexibility of the process design under mixed uncertainties, and the optimal designs are compromise solutions that take into account the economic indicator and uncertainty quantification. (c) 2020 Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.

关键词： Fuzzy distributional chance-constrained programming Flotation process Uncertainty Scenario generation Fuzzy simulation NSGA-II

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Interval joint-probabilistic chance-constrained programming with two-side multi-randomness: an application to energy-environment systems management

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STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT 2018年第7期32卷 2093-2110页

作者： Li, Gongchen Sun, Wei Lv, Ying Cheng, Guanhui Chen, Yumin Huang, Guo H. Inst Energy Environm & Sustainable Communities Regina SK S4S 0A2 Canada Beijing Jiaotong Univ Sch Traff & Transportat Inst Transportat Syst Sci & Engn MOE Minist EducKey Lab Transportat Complex Syst Beijing 100044 Peoples R China Univ Regina Fac Engn & Appl Sci Regina SK S4S 0A2 Canada Alberta Environm & Pk Edmonton AB T5K 2J6 Canada North China Elect Power Univ S&C Resources & Environm Res Acad MOE Key Lab Reg Energy Syst Optimizat Beijing 102206 Peoples R China

Regional energy-environment systems management become more and more focused on greenhouse gas emission control through improving energy efficiency and efficiently managing energy activities. Inexact linear programming models are developed for supporting the management. Due to the weather/climatic variations in the future, electricity demands and renewable power generations (in the right/left hand sides of constraints) have random characteristics. Moreover, an overall satisfactory level needs to be quantified based on multiple chance constraints. Therefore, this study improved upon traditional chance-constrained programming and interval linear programming, and developed an interval joint-probabilistic two-side chance-constrained programming (IJTCP) approach. A sufficient but non-equivalent linearization form of the model was proposed so that the inexact model could be solved through the two-step solution algorithm. The IJTCP was then applied to an integrated energy-environment systems management under dual uncertainties. The application demonstrated that the IJTCP can effectively address the uncertainties presented as not only interval numbers and two-side multi-randomness but also the reliability of satisfying the entire system constraints. The application implicated that the IJTCP approach can be applied to other energy-environment management problems under dual uncertainties.

关键词： Uncertainty chance-constrained programming Greenhouse gas Mitigation Energy-environment systems

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A hybrid fuzzy-stochastic multi-criteria ABC inventory classification using possibilistic chance-constrained programming

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SOFT COMPUTING 2021年第2期25卷 1065-1083页

作者： Razavi Hajiagha, Seyed Hossein Daneshvar, Maryam Antucheviciene, Jurgita Khatam Univ Fac Management & Finance Dept Management Tehran Iran Vilnius Gediminas Tech Univ Dept Construct Management & Real Estate Sauletekio Ave 11 LT-10223 Vilnius Lithuania

Inventory classification is a fundamental issue in the development of inventory policy that assigns each inventory item to several classes with different levels of importance. This classification is the main determinant of a suitable inventory control policy of inventory classes. Therefore, a great deal of research is done on solving this problem. Usually, the problem of inventory classification is considered in a multi-criteria and uncertain environment. The proposed method in this paper inspired by the notion of heterogeneous decision-making problems in which decision-makers deal with different types of data. To this aim, a mathematical modeling-based approach is proposed considering different types of uncertainty in classification information. Demand information is considered to be stochastic due to its time-varying nature and cost information is considered to be fuzzy due to its cognitive ambiguity. A hybrid algorithm based on chance-constrained and possibilistic programming is proposed to solve the problems. Considering the stochastic nature of demand information, solving the proposed model using the hybrid algorithm, the classification of items to three classes of extremely important, class A, moderately important, class B, and relatively unimportant, class C, items are determined along with a minimum inventory level required to deal with the stochasticity of demands information. The proposed approach is applied to a case study of classifying 51 inventory items. The obtained results assigned 22%, 39%, and 39% of the items to A, B, and C classes, respectively.

关键词： Multi-criteria inventory classification chance-constrained programming Possibilistic programming

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A LINEAR-APPROXIMATION FOR chance-constrained programming

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 1987年第3期38卷 261-267页

作者： OLSON, DL SWENSETH, SR TEXAS A&M UNIV DEPT BUSINESS ANALCOLLEGE STNTX 77843 USA

Decision environments involve the need to solve problems with varying degrees of uncertainty as well as multiple, potentially conflicting objectives. chance constraints consider the uncertainty encountered. Codes incorporating chance constraints into a mathematical programming model are not available on a widespread basis owing to the non-linear form of the chance constraints. Therefore, accurate linear approximations would be useful to analyse this class of problems with efficient linear codes. This paper presents an approximation formula for chance constraints which can be used in either the single- or multiple-objective case. The approximation presented will place a bound on the chance constraint at least as tight as the true non-linear form, thus overachieving the chance constraint at the expense of other constraints or objectives.

关键词： chance-constrained programming goal programming multiple-objective programming

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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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SRCCP: A stochastic robust chance-constrained programming model for municipal solid waste management under uncertainty

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RESOURCES CONSERVATION AND RECYCLING 2009年第6期53卷 352-363页

作者： Xu, Y. Huang, G. H. Qin, X. S. Cao, M. F. Univ Regina Fac Engn Environm Syst Engn Program Regina SK S4S 0A2 Canada N China Elect Power Univ Sino Canada Ctr Energy & Environm Res Beijing 102206 Peoples R China Nanyang Technol Univ Sch Civil & Environm Engn Singapore 639798 Singapore

A hybrid stochastic robust chance-constraint programming (SRCCP) model was developed in this study for supporting municipal solid waste management under uncertainty. The method improves upon the existing robust-optimization (RO) and chance-constraint programming (CCP) approaches by allowing analysis on trade-offs among expected value of the objective function, variation in the value of the objective function and the risk of violating constraints that contain uncertain parameters. SRCCP could be used to examine the balance between solution robustness and model robustness. and was especially useful for analyzing the reliability of satisfying (or risk of violating) system constraints under complex uncertainties. A long-term municipal solid waste management problem was used to demonstrate the applicability of SRCCP, with violations for capacity constraints being assumed under various significance levels. The study results demonstrated that a higher system cost may guarantee that waste-management requirements and environmental criteria be met, and a lower cost may lead to a higher risk of violating the related regulations. The proposed SRCCP model could be used by waste managers for identifying desired waste-management policies under various environmental, economic, and system-reliability constraints and complex uncertainties. (C) 2009 Elsevier B.V. All rights reserved.

关键词： Robust optimization chance-constrained programming Environment Compromise programming Solid waste management Uncertainty

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

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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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Proportional Fair Resource Allocation Based on chance-constrained programming for Cognitive OFDM Network

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WIRELESS PERSONAL COMMUNICATIONS 2014年第2期79卷 1591-1607页

作者： Xu, Lei Lv, Tong-ming Li, Qian-mu Yang, Yu-wang Li, Ya-ping Zhang, Xiao-fei Nanjing Univ Sci & Technol Sch Comp Sci & Engn Nanjing Jiangsu Peoples R China Nanjing Univ Aeronaut & Astronaut Coll Econ & Management Nanjing Jiangsu Peoples R China Nanjing Univ Aeronaut & Astronaut Coll Elect & Engn Nanjing Jiangsu Peoples R China

Proportional fair resource allocation plays a critical role to balance the spectrum efficiency and fairness for cognitive orthogonal frequency division multiplexing (OFDM) network. However, due to the lack of cooperation between cognitive radio (CR) network and primary network, channel state information between CR base station (CRBS) and primary user (PU) could not be estimated precisely. Therefore, the interference of CRBS-PU couldn't be computed precisely and chance-constrained programming is adopted to formulate the resource allocation problem. In this work, we study the proportional fair resource allocation problem based on chance-constrained programming for cognitive OFDM network. The objective function maximizes the spectral efficiency of cognitive OFDM network over subcarrier and power allocation. The constraint conditions include the interference constraint of PU with the target probability requirement and the proportional fair rate requirement of CR users. In order to solve the above optimization problem, two steps are taken to develop hybrid immune optimization algorithm (HIOA). In the first step, the probabilistic interference constraint condition is transformed as an uncertain function which is computed by a generalized regression neural network (GRNN). In the second step, we combine immune optimization algorithm and GRNN to develop HIOA. Simulation results demonstrate that HIOA yields higher spectral efficiency while the probabilistic interference constraint condition and the proportional fair rate constraint condition could be satisfied very well.

关键词： Cognitive OFDM network Proportional fair resource allocation chance-constrained programming Hybrid immune optimization algorithm

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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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Interval-parameter chance-constrained programming model for uncertainty-based decision making in tire retreading industry

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JOURNAL OF CLEANER PRODUCTION 2017年第Nov.20期167卷 1490-1498页

作者： Simic, Vladimir Dabic-Ostojic, Svetlana Univ Belgrade Fac Transport & Traff Engn Vojvode Stepe 305 Belgrade 11000 Serbia

Tire retreading is an economically attractive and environmentally beneficial process for extending the lifetime of used tires. It reduces the negative influence of used tires on the environment as well as natural resources exploitation. According to the latest data, 4.7 million units of used truck tires were retreaded in 2014 in Europe. This paper proposes an interval-parameter chance-constrained programming model for uncertainty-based decision making in tire retreading industry. A case study is conducted in order to demonstrate its potentials and applicability. When constraints violation level increases (0.01, 0.05 and 0.10), the system profit obtained in the analyzed nine-year planning horizon correspondingly raises ((sic)[35.08, 82.03] x 10(6), (sic)[38.94, 90.78] x 10(6) and (sic)[40.87, 95.16] x 10(6) respectively). The uncertainty degree of the objective function under three considered system violation levels is around 80%, which demonstrates that used tires retreading management systems are highly uncertain. Profit per tonne of processed used tires is in (sic)[1594.64, 3730.84] interval. The developed model can efficiently handle uncertainties expressed as interval values and probability distributions. It can address multiple interrelationships among numerous components of used tires retreading management systems. The proposed model can examine various admissible risk levels of violating retreading capacities. It can provide a trade-off between economic efficiency of tires retreading management systems and capacity constraints violations. Compared with the conventional chance-constrained programming approach, the formulated model can incorporate much more uncertain information. The presented model can provide valuable support for tire retreading managers in avoiding inferior or simply wrong decisions. In fact, it can help tire retreading managers optimize long-term purchasing, retreading and inventory planning schemes, and allocation patterns of retreaded, re

关键词： Used tires Retreading Management chance-constrained programming Interval-parameter programming Uncertainty

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