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

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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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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A multiobjective optimization framework for optimal selection of supplier portfolio

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OPTIMIZATION 2014年第10期63卷 1491-1512页

作者： Guu, Sy-Ming Mehlawat, Mukesh Kumar, Santosh Chang Gung Univ Coll Management Grad Inst Business & Management Taoyuan Hsein Taiwan Univ Delhi Dept Operat Res Delhi 110007 India

Supplier selection problem has been a typical concern of optimization where good supplier selection is essential for firms in the context of supply chain management. If a firm networks with different suppliers, each one having its own advantages over the others, then there is great opportunity to reduce a firm's risk arising from supply concentration and also to provide it with the opportunity to leverage its comparative strength. In this paper, we propose a new approach referred to as Supplier Portfolio Optimization (SPO) that improves the state of the art of supplier selection by incorporating the benefits of supplier diversification using the trade-offs between the criteria of expected unit price, expected score of quality and expected score of delivery. We present three different optimization models with interval coefficients to model the uncertain SPO problem corresponding to optimistic, pessimistic and combination strategies. Further, using lower and upper bonds for fractions of order quantity, we ensure supplier portfolio diversification and also avoidance of the situation of impractical fraction of quantity ordered. Numerical experiments conducted on a dataset of a multinational firm are provided to demonstrate the applicability and efficiency of the SPO models to real-world applications of supplier selection.

关键词： multiobjective optimization interval programming supplier selection portfolio optimization supply chain management diversification

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IFTSQP: An inexact optimization model for water resources management under uncertainty

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WATER INTERNATIONAL 2007年第3期32卷 439-456页

作者： Li, Y. P. Huang, G. H. Nie, S. L. Univ Regina Environm Syst Engn Program Fac Engn 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

An interval-fuzzy two-stage quadratic programming (IFTSQP) method is developed for water resources management under uncertainty. The method incorporates techniques of interval-parameter programming, two-stage stochastic programming, and fuzzy quadratic programming within a general optimization framework to tackle multiple uncertainties presented as intervals, fuzzy sets and probability distributions. In the model formulation, multiple control variables are adopted to handle independent uncertainties in the model's right-hand sides;fuzzy quadratic terms are used in the objective function to minimize the variation in satisfaction degrees among the constraints. Moreover, the method 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 study of water resources management planning. The results indicate that reasonable solutions have been obtained. They can help provide bases for identifying desired water-allocation plans with a maximized system benefit and a minimized constraint-violation risk.

关键词： fuzzy sets interval programming management optimization quadratic two-stage uncertainty water resources

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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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An interval Two-Stage Classified-Allocation Model for Regional Water Management under Nonstationary Condition

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JOURNAL OF THE AMERICAN WATER RESOURCES ASSOCIATION 2021年第4期57卷 610-627页

作者： Chen, Shu Li, Qingqing Xu, Jijun Wang, Dong Wang, Yongqiang Yuan, Zhe Changjiang River Sci Res Inst Wuhan Water Resources Dept Wuhan Peoples R China Hubei Key Lab River Basin Water Resources & Ecol Wuhan Peoples R China

Due to climate change and human activities, the assumption of the stationarity of hydrologic features will no longer hold. Moreover, uncertainties, such as the apparent randomness of hydrologic elements, and complexities, such as the existence of various water users with different characteristics, also introduce huge challenges for water managers. To address nonstationarity, uncertainty, and complexity, a new approach is proposed for the optimal allocation of regional water resources. This objective was achieved via two steps: First, the generalized additive model was chosen to analyze the nonstationary probability distribution of the hydrologic dataset;then, an interval two-stage classified-allocation model is formulated by incorporating two-stage stochastic programming, interval parameter programming and classification thought. The model can not only address uncertainties, which were expressed as interval parameters and probability distributions, but can also handle complexities by classifying the water users into agricultural and nonagricultural users. The approach was applied to the Zhanghe Irrigation District to optimize available water allocation for municipality, industry, hydropower, and agriculture in two planning years (namely 2010 and 2015). The annual inflow of the Zhanghe Reservoir is found to be nonstationary and can be well fitted by Gamma distribution with one location parameter based on a nonlinear function of time. Moreover, the difference in output between the two years with different inflow probability distributions indicates the need for nonstationary analysis. Comparison to the inexact two-stage water management model that did not consider the variation of agricultural water requirement shows the meaning of classification. From the results, municipality and industry are more competitive than agriculture and then hydropower. For agriculture, winter rape and cotton have higher priority than rice. These solutions of the optimal targets and optimal

关键词： classification thought interval programming nonstationary analysis two‐ stage stochastic programming uncertainty water management

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Minimum Resistance Ship Hull Uncertainty Optimization Design Based on Simulation-Based Design Method

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Journal of Shanghai Jiaotong university(Science) 2017年第6期22卷 657-663页

作者：侯远杭游园梁霄 Transportation Equipment and Ocean Engineering College Dalian Maritime University Dalian 116026LiaoningChina

In the ship hull optimization design based on simulation-based design(SBD) technology, low precision of the approximate model leads to an uncertainty form of optimization model. In order to enable the approximate model with finite precision to maximize the effectiveness, uncertainty optimization method is introduced *** resistance coefficient approximation model, built by back propagation(BP) neural network, is represented as a form of interval. Afterwards, a minimum resistance optimization model is established with the design space constituted by principal dimensions and ship form coefficients. Double-level nested optimization architecture is proposed: for outer layer, improved particle swarm optimization(IPSO) algorithm with learning factor improvement strategy is used to generate design variables, and for inner layer, modified very fast simulated annealing(MVFSA) algorithm is used to solve the objective function interval with uncertainty region. Cases calculation proves the effectiveness and superiority of uncertainty optimization method for ship hull SBD optimization design,thus providing a good way for finding optimal designs.

关键词： ship hull optimization approximation model uncertainty optimization interval programming

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COMPLEXITY AND COMPUTABILITY OF SOLUTIONS TO LINEAR-programming SYSTEMS

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INTERNATIONAL JOURNAL OF COMPUTER & INFORMATION SCIENCES 1980年第6期9卷 483-506页

作者： CHARNES, A COOPER, WW DUFFUAA, S KRESS, M HARVARD UNIV GRAD SCH BUSINESS ADMCAMBRIDGEMA 02138

Through key examples and constructs, exact and approximate, complexity, computability, and solution of linear programming systems are reexamined in the light of Khachian's new notion of (approximate) solution. Algorithms, basic theorems, and alternate representations are reviewed. It is shown that the Klee-Minty example hasnever been exponential for (exact) adjacent extreme point algorithms and that the Balinski-Gomory (exact) algorithm continues to be polynomial in cases where (approximate) ellipsoidal “centered-cutoff” algorithms (Levin, Shor, Khachian, Gacs-Lovasz) are exponential. By “model approximation,” both the Klee-Minty and the new J. Clausen examples are shown to be trivial (explicitly solvable) interval programming problems. A new notion of computable (approximate) solution is proposed together with ana priori regularization for linear programming systems. New polyhedral “constraint contraction” algorithms are proposed for approximate solution and the relevance of interval programming for good starts or exact solution is brought forth. It is concluded from all this that the “imposed problem ignorance” of past complexity research is deleterious to research progress on “computability” or “efficiency of computation.”

关键词： Complexity computability linear programming systems constraint contraction algorithms ellipsoidal algorithms nondifferentiable convex programming interval programming

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Optimal selection of different CCS technologies under CO₂ reduction targets

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NATURAL HAZARDS 2017年第2期88卷 1197-1209页

作者： Li, Huanan Qin, Quande Shenzhen Univ Dept Management Sci Coll Management Shenzhen 518060 Peoples R China Beijing Inst Technol Ctr Energy & Environm Policy Res Beijing 100081 Peoples R China Beijing Inst Technol Sch Management & Econ Beijing 100081 Peoples R China Collaborat Innovat Ctr Elect Vehicles Beijing Beijing 100081 Peoples R China Sustainable Dev Res Inst Econ & Soc Beijing Beijing 100081 Peoples R China

In China, carbon capture and storage (CCS) is recognized as one of the most promising technologies through which to achieve a large reduction in CO2 emissions in future. The choice among different CCS technologies is critical for large-scale applications. With the aim of developing instructive policy suggestions for CCS development, this study proposed an interval programming model to select the optimal CCS technology among the different CCS technologies available in China. The analysis results indicate that the selection of CO2 capture technologies should be based on the actual situation of the project and industry being targeted. If the government implements mandatory CO2 emission reductions, storage in deep saline aquifers is the optimal choice for CO2 sequestration when oil prices are low and the number of available CO2 emission permits is large. In contrast, enhanced oil recovery is the optimal choice when oil prices increase and the availability of CO2 emission permits decreases. It is critical that the government reduce the operating cost and the cost of CO2 capture in particular.

关键词： Carbon capture and storage (CCS) interval programming CO2 reduction China

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