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An interval-parameter fuzzy nonlinear optimization model for stream water quality management under uncertainty

EUROPEAN JOURNAL OF OPERATIONAL RESEARCH 2007年第3期180卷 1331-1357页

作者： Qin, X. S. Huang, G. H. Zeng, G. M. Chakma, A. Huang, Y. F. Univ Regina Fac Engn Regina SK S4S 0A2 Canada N China Elect Power Univ SinoCanada Ctr Energy & Environm Res Beijing 102206 Peoples R China Hunan Univ Dept Environm Sci & Engn Changsha 410082 Peoples R China Univ Waterloo Dept Chem Engn Waterloo ON N2L 3G1 Canada Tsing Hua Univ Inst River & Coastal Engn Beijing 100084 Peoples R China

Planning for water quality management systems is complicated by a variety of uncertainties and nonlinearities, where difficulties in formulating and solving the resulting inexact nonlinear optimization problems exist. With the purpose of tackling such difficulties, this paper presents the development of an interval-fuzzy nonlinear programming (IFNP) model for water quality management under uncertainty. Methods of interval and fuzzy programming were integrated within a general framework to address uncertainties in the left- and right-hand sides of the nonlinear constraints. Uncertainties in water quality, pollutant loading, and the system objective were reflected through the developed IFNP model. The method of piecewise linearization was developed for dealing with the nonlinearity of the objective function. A case study for water quality management planning in the Changsha section of the Xiangjiang River was then conducted for demonstrating applicability of the developed IFNP model. The results demonstrated that the accuracy of solutions through linearized method normally rises positively with the increase of linearization levels. It was also indicated that the proposed linearization method was effective in dealing with IFNP problems;uncertainties can be communicated into optimization process and generate reliable solutions for decision variables and objectives;the decision alternatives can be obtained by adjusting different combinations of the decision variables within their solution intervals. It also suggested that the linearized method should be used under detailed error analysis in tackling IFNP problems. (c) 2006 Elsevier B.V. All rights reserved.

关键词： environment interval programming fuzzy programming nonlinear optimization uncertainty linear programming

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An interval multistage water allocation model for crop different growth stages under inputs uncertainty

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AGRICULTURAL WATER MANAGEMENT 2017年 186卷 86-97页

作者： Chen, Shu Shao, Dongguo Gu, Wenquan Xu, Baoli Li, Haoxin Fang, Longzhang Wuhan Univ State Key Lab Water Resources & Hydropower Engn S Wuhan 430072 Peoples R China

Due to different responses of crop growth stages to the water deficit, it is necessary to optimize water allocation between different growth stages to obtain the maximum food production in reservoir irrigation systems which are widely distributed throughout Southern China and India. In order to address the inputs uncertainties and dynamics existing in the above agricultural water management, an interval multistage water allocation model is developed. By incorporating multistage stochastic programming and interval parameter programming, the developed model can deal with uncertain inputs both expressed as interval parameters and probability distributions, and realize a dynamic irrigation among different growth stages from a reservoir. In the model, water requirement targets are first treated as first-stage decision variables to tackle the unique problem of agricultural water management. Additionally, given that net benefit and penalty of each growth stage are key parameters due to their determinative roles for allocation between different growth stages, a crop water production function is introduced into the calculation to make them factually reflect the competition among different growth stages. The model is then applied to the Yangshudang Irrigation District to plan rice irrigation and demonstrate its applicability. Rainfall has been divided into five levels with probability distributions in each growth stage and parameters have been characterized as interval numbers to show system uncertainty. Five scenarios that represent different initial active storage levels of the reservoir are set to acquire more detailed results. Through the parameter estimation, net benefits are [1.08,1.29], [5.04, 6.01], [11.79,14.08] and [1.61,1.92] RMB/m(3), and penalties are [2.39, 2.48], [11.13, 11.54], [26.05, 27.01] and [3.55, 3.68] RMB/m(3) for tillering stage, booting stage, heading stage and milky stage respectively. Through the model simulation, water requirement targets in booti

关键词： Crop growth stage interval programming Irrigation water allocation Multistage stochastic programming Water production function Inputs uncertainty

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Decarbonization pathways for bulk vessels: Integrating power systems, fuels, and control measures

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OCEAN ENGINEERING 2024年 300卷

作者： Zhao, Yuzhe Ge, Rui Zhou, Jingmiao Notteboom, Theo Dalian Maritime Univ Collaborat Innovat Ctr Transport Studies Dalian 116026 Peoples R China Dalian Univ Foreign Languages Business Sch Dalian 116044 Peoples R China Univ Ghent Maritime Inst B-9000 Ghent Belgium Univ Antwerp Fac Business & Econ B-2000 Antwerp Belgium Antwerp Maritime Acad Fac Sci B-2030 Antwerp Belgium

The shipping industry must delineate feasible switching pathways of emission reduction technologies for vessels if it wants to meet the emission reduction targets set forth by the International Maritime Organization (IMO). This paper introduces a programming model integrating power systems, alternative fuels, and air emission control measures to decarbonize bulk vessel operations. The model captures the uncertainty in fuel prices and carbon emission prices. Reliable decision-making schemes are generated using interval quadratic programming. The results reveal that power systems will switch from mono-fuel internal combustion engines (MF ICE) to dualfuel internal combustion engines (DF ICE). Traditional fossil fuels will progressively give way to carbon-neutral alternatives. The combination of air emission control measures will markedly reduce emissions.

关键词： Bulk vessels Decarbonization pathway Power systems and alternative fuels Air emission control measures interval programming

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A two-stage inexact-stochastic programming model for planning carbon dioxide emission trading under uncertainty

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APPLIED ENERGY 2010年第3期87卷 1033-1047页

作者： Chen, W. T. Li, Y. P. Huang, G. H. Chen, X. Li, Y. F. Peking Univ Lab Earth Surface Proc Coll Urban & Environm Sci Beijing 100871 Peoples R China N China Elect Power Univ Energy & Environm Res Ctr Beijing 102206 Peoples R China Univ Regina Environm Syst Engn Program Fac Engn Regina SK S4S 0A2 Canada Chinese Acad Sci Key Lab Oasis Ecol & Desert Environm Xinjiang Inst Ecol & Geog Urumqi 830011 Xinjiang Peoples R China

In this study, a two-stage inexact-stochastic programming (TISP) method is developed for planning carbon dioxide (CO2) emission trading under uncertainty. The developed TISP incorporates techniques of interval-parameter programming (IPP) and two-stage stochastic programming (TSP) within a general optimization framework. The TISP can not only tackle uncertainties expressed as probabilistic distributions and discrete intervals, but also provide an effective linkage between the pre-regulated greenhouse gas (GHG) management policies and the associated economic implications. The developed method is applied to a case study of energy systems and CO2 emission trading planning under uncertainty. The results indicate that reasonable solutions have been generated. They can be used for generating decision alternatives and thus help decision makers identify desired GHG abatement policies under various economic and system-reliability constraints. (C) 2009 Elsevier Ltd. All rights reserved.

关键词： Carbon dioxide Energy interval programming Stochastic Two-stage Trading Uncertainty

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Long-term panning of waste diversion under interval and probabilistic uncertainties

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RESOURCES CONSERVATION AND RECYCLING 2010年第7期54卷 449-461页

作者： Sue, J. Huang, G. H. Xi, B. D. Qin, X. S. Huo, S. L. Jiang, Y. H. Chen, X. R. Univ Regina Fac Engn Regina SK S4S 0A2 Canada Beijing Normal Univ Sch Environm Beijing 100875 Peoples R China Chinese Res Inst Environm Sci Beijing 100012 Peoples R China Nanyang Technol Univ Sch Civil & Environm Engn Singapore 639798 Singapore

An inexact chance-constraint mixed integer linear programming (ICMILP) model was proposed for supporting long-term planning of waste management in the City of Foshan, China. The presented model took waste generation, collection, transportation and treatment processes into consideration, and was specifically designed to reflect the practical situations of waste management in Chinese cities. Three special characteristics of the developed method made it unique compared with the other optimization techniques that deal with uncertainties. Firstly, it provided a linkage to pre-regulated policies that had to be respected when a modeling effort was undertaken;secondly, it was useful for tackling uncertainties presented as intervals probabilities;thirdly, it could facilitate dynamic analysis for decisions of facility expansions within a multi-facility, multi-period, multi-level, and multi-option context. Three scenarios were considered based on various combinations of financial capability and environmental demand. The results indicate that the city would attain a relatively low diversion rate if its waste management practices continue to be based on the existing policy over 15 years. However, higher diversion rates associated with lower system cost would be achieved if the City's policy is to be based on an aggressive capacity-expansion plan for composting and incinerating facilities. The model solutions would be valuable for supporting the long-term capacity planning for waste-management facilities as well as the formulation of policies regarding waste generation, diversion and management. (C) 2009 Elsevier B.V. All rights reserved.

关键词： interval programming Decision making Chance-constraint Waste management Uncertainty Environment

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Inexact credibility constrained programming for environmental system management

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RESOURCES CONSERVATION AND RECYCLING 2011年第4期55卷 441-447页

作者： Zhang, Yi Mei Huang, Guo He Univ Regina Fac Engn Environm Syst Engn Program Regina SK S4S 0A2 Canada Univ Regina Fac Engn & Appl Sci Environm Syst Engn Program Regina SK S4S 0A2 Canada

This study proposed an inexact credibility constrained programming (ICCP) to deal with multi-formats of uncertainties in parameters and variables for an agricultural water planning system. The study system includes three subareas with different crop distributions. The redundant water in the wet season can be stored in the reservoir and utilized in the dry season. The ICCP method can reflect not only inexact uncertainties in the objective function, variables and parameters, but also fuzzy uncertainties in the right-hand side. interval credibility levels which represent satisfaction degrees of the constraints can be analyzed. Scenario analysis is conducted to analyze possible events in wet and dry years. The resulting solutions can provide stable intervals for the objective function and decision variables with different levels of risk when violating the constraints. (C) 2011 Elsevier B.V. All rights reserved.

关键词： Credibility Water resource Reservoir Water conversation interval programming Agricultural Fuzzy

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Development of a fuel management model for a multi-source district heating system under multi-uncertainty and multi-dimensional constraints

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ENERGY CONVERSION AND MANAGEMENT 2017年 153卷 243-256页

作者： Fu, D. Z. Zheng, Z. Y. Gui, J. Xiao, R. Huang, G. H. Li, Y. P. Chinese Acad Sci Shenyang Inst Automat Key Lab Network Control Syst Shenyang 110016 Liaoning Peoples R China Shenyang Univ Technol Sch Informat Sci & Engn Shenyang 110870 Liaoning Peoples R China Univ Penn Perelman Sch Med Dept Biostat & Epidemiol Philadelphia PA 19104 USA Univ Regina Fac Engn & Appl Sci Environm Syst Engn Program Regina SK S4S 0A2 Canada North China Elect Power Univ SC Resources & Environm Res Acad MOE Key Lab Reg Energy & Environm Syst Optimizat Beijing 102206 Peoples R China

In this paper, an interval single-sided fuzzy chance-constrained mixed-integer programming model is developed for the fossil fuel management of a multi-source district heating system under multiple uncertainties, where the heat-supply-capacity expansion planning can also be reflected. The non-dimensional comprehensive equations method is simultaneously improved to quantify the ambiguous heat provisions, utilized as a type of boundary condition inputs to the proposed model. A real-world case study of a heating system located in northeastern China is undertaken to show the feasibility and applicability of the proposed methods. To obtain the reasonable fossil-fuel management schemes, multi-dimensional constraints are incorporated into the model based on a comprehensive consideration in terms of fuel supply and demand, quality and quantity, economic cost and environment protection, as well as their interactions. Results obtained from the case study indicate that the solutions for both continuous and binary variables have been generated, which are useful for identifying suitable fuel-supply patterns and heat-source operational modes for a heating system under different system reliabilities and heating-load distribution states. In addition, the results also reveal that the fossil-fuel management and heating-capacity-expansion pattern, as well as the economic cost and pollutant emission performances are sensitive to the thermal coefficient and system reliability level, which may provide in-depth analyses of tradeoffs for further supporting robust fossil-fuel management under uncertainty.

关键词： Decision making Uncertainty interval programming Fossil fuel management Heating system Fuzzy programming

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IFTCP: An integrated method for petroleum waste management under uncertainty

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PETROLEUM SCIENCE AND TECHNOLOGY 2008年第7-8期26卷 912-936页

作者： Li, Y. P. Huang, G. H. Qin, X. S. Nie, S. L. Univ Waterloo Dept Civil & Environm Engn Waterloo ON N2L 3G1 Canada Univ Regina Environm Syst Engn Program Regina SK S4S 0A2 Canada N China Elect Power Univ Chinese Res Acad Environm Sci Beijing Peoples R China Huazhong Univ Sci & Technol Sch Mech Sci & Engn Wuhan 430074 Hubei Peoples R China

Petroleum waste management has been of much concern in recent years since pollution from petroleum industries may lead to various impacts and risks to environmental systems. In this study, an interval fuzzy two-stage chance-constrained linear programming (IFTCP) method is developed for planning petroleum waste management systems. The IFTCP improves upon the existing optimization methods by allowing uncertainties presented in terms of intervals, fuzzy sets, and probability distributions to be effectively incorporated within the optimization framework. Moreover, it can support the analysis of policy scenarios that are associated with economic penalties when the promised targets are violated. The developed method is then applied to a case of long-term petroleum waste management planning. interval solutions, which are associated with different levels of constraint-violation risk and system satisfaction degree, have been obtained by solving two submodels based on an interactive algorithm. They can be used to generate decision alternatives and support an in-depth analysis of the tradeoff between system cost and system-failure risk.

关键词： chance constrained fuzzy interval programming optimization petroleum waste management two-stage uncertainty

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Neutrosophic goal programming strategy for multi-level multi-objective linear programming problem

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JOURNAL OF AMBIENT INTELLIGENCE AND HUMANIZED COMPUTING 2020年第8期11卷 3175-3186页

作者： Maiti, Indrani Mandal, Tarni Pramanik, Surapati Natl Inst Technol Dept Math Jamshedpur 831014 Bihar India Nandalal Ghosh BT Coll Dept Math PO NarayanpurNorth 24 Paraganas Kolkata 743126 India

Neutrosophic set theory plays an important role in dealing with the impreciseness and inconsistency in data encountered in solving real life problems. This article aims to present a novel goal programming based strategy which will be helpful to solve Multi-Level Multi-Objective Linear programming Problem (MLMOLPP) with parameters as neutrosophic numbers (NNs). Difficulty in decision making arises due to the presence of multiple decision makers (DMs) and impreciseness in information. Here each level DM has multiple linear objective functions with parameters considered as NNs which are represented in the formc+dI wherecanddare considered real numbers and the symbolIdenotes indeterminacy. The constraints are also linear with the parameters as NNs. Firstly the NNs are changed into intervals and the problem turns into a multi-level multi-objective linear programming problem considering interval parameters. Then interval programming technique is employed to obtain the target interval of each objective function. In order to avoid decision deadlock which may arise in hierarchical (multi-level) problem, a possible relaxation is imposed by each level DM on the decision variables under his/her control. Finally a goal programming strategy is presented to solve the MLMOLPP with interval parameters. The method presented in this paper facilitates to solve MLMOLPP with multiple conflicting objectives in an uncertain environment represented through NNs of the formc+dI where indeterminacyIplays a pivotal role. Lastly, a mathematical example is solved to show the novelty and applicability of the developed strategy.

关键词： Multi-level multi-objective programming Neutrosophic number interval programming Goal programming

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An interval multistage classified model for regional inter- and intra-seasonal water management under uncertain and nonstationary condition

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AGRICULTURAL WATER MANAGEMENT 2017年 191卷 98-112页

作者： Chen, Shu Shao, Dongguo Tan, Xuezhi Gu, Wenquan Lei, Caixiu Wuhan Univ State Key Lab Water Resources & Hydropower Engn S Wuhan Hubei Peoples R China Univ Alberta Dept Civil & Environm Engn Edmonton AB Canada Hubei Prov Water Resources & Hydropower Planning Wuhan Hubei Peoples R China

In regional water management, various uncertainties such as randomness, non-stationarities, dynamics and complexities, lead to difficulties for water managers. To deal with the above problems, a new methodology is proposed by introducing two methods nonstationary analysis, where the generalized additive model is selected to analyze and fit the distribution of water inflow;and model optimization, where an interval multistage water classified-allocation model (IMWCA) is formulated to optimally allocate the available water. By incorporating multistage stochastic programming, interval parameter programming and classification thought, the IMWCA model can tackle both stochastic and imprecise uncertainties, realize inter-seasonal dynamic allocation, and address the complexity of various water users. The methodology is applied to the Zhanghe Irrigation District to optimize water allocation for municipality, industry, hydropower and agriculture among winter, spring, summer and autumn. The Zhanghe Reservoir seasonal inflow is found to be nonstationary for all the seasons and can be well fitted by the corresponding distributions, showing the sense of nonstationary analysis. Additionally, the comparison with the other model demonstrates the need for classification. From the results, municipality and industry are more competitive than hydropower. The Dongbao, Dangyang and Zhanghe districts have a higher priority than the Jingzhou and Shayang districts for irrigation water. Water requirements are more likely to be satisfied in autumn. These solutions of optimal targets and optimal water allocation are valuable for optimizing inter- and intra-seasonal water resource allocation under uncertainty. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Classification interval programming Nonstationary analysis Multistage stochastic programming Uncertainty Inter-seasonal water management

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