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Necessary and sufficient conditions for unified optimality of interval linear program in the general form

linear ALGEBRA AND ITS APPLICATIONS 2015年 484卷 154-174页

作者： Li, Haohao Zhejiang Univ Finance & Econ Sch Math & Stat Hangzhou 310018 Zhejiang Peoples R China

This paper considers optimal solutions of general interval linear programming problems. The most general concepts of optimal solutions are introduced in a unified framework. The existing optimal solution concepts of interval linear program such as weak and strong optimal solutions are all the special cases in this framework. Necessary and sufficient conditions for checking a class of optimality are developed according to the KKT conditions. Also, the comparison among several conclusions using KKT conditions and tangent core technique in various forms of interval linear programming is proposed. (C) 2015 Elsevier Inc. All rights reserved.

关键词： interval linear programming Unified optimal solutions Unified feasible solutions KKT conditions

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Long-term emissions of hexabromocyclododecane as a chemical of concern in products in China

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ENVIRONMENT INTERNATIONAL 2016年第May期91卷 291-300页

作者： Li, Li Weber, Roland Liu, Jianguo Hu, Jianxin Peking Univ Coll Environm Sci & Engn Beijing 100871 Peoples R China POPs Environm Consulting Lindenfirststr 23 D-73527 Schwabisch Gmund Germany

There has been ever-increasing international interest in investigating the long-term emissions of chemicals in products (CiPs) throughout their entire life cycle in the anthroposphere. Hexabromocyclododecane (HBCDD) is a contemporary example of special interest due to the recent listing of this hazardous flame retardant in the Stockholm Convention and the consequent need for parties to take appropriate measures to eliminate this compound. Here, we conducted a scenario-based dynamic substance flow analysis, coupled with interval linear programming, to forecast the future HBCDD emissions in China in order to assist with the implementation of the Stockholm Convention in this current world's predominant HBCDD manufacturing and consuming country. Our results indicate that, under a business-as-usual scenario, the cumulative HBCDD production will amount to 238,000 tonnes before its phase-out, 79% of which will be consumed in domestic market, accumulate as stocks in flame-retarded polystyrene insulation boards, and ultimately end up in demolition waste. While the production is scheduled to end in ca. 2021, emissions of HBCDD would continue until after 2100. For the entire simulation period 2000-2100, 44% of total cumulative emissions will arise from the industrial manufacture of HBCDD-associated end-products, whereas 49% will come from the end-of-life disposals of HBCDD-containing waste. The most effective end-of-life disposal option for minimizing emissions we found was, a pre-demolition screening combined with complete incineration. Our study warns of the huge challenges that China would face in its eliminating HBCDD contamination in the following decades, and provides an effective methodology for a wider range of countries to recognize and tackle their long-term emission problems of hazardous CiPs. (C) 2016 Elsevier Ltd. All rights reserved.

关键词： Hexabromocyclododecane Emissions Chemicals in products Dynamic substance flow analysis interval linear programming End-of-life

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Resources and environmental systems management under synchronic interval uncertainties

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STOCHASTIC ENVIRONMENTAL RESEARCH AND RISK ASSESSMENT 2018年第2期32卷 435-456页

作者： Cheng, Guanhui Huang, Guohe Dong, Cong Lv, Ying Zhang, Junlong Yao, Yao Chen, Xiujuan Univ Regina Inst Energy Environm & Sustainable Communities 3737 Wascana Pkwy Regina SK S4S 0A2 Canada UR BNU Inst Energy Environm & Sustainabil Res 3737 Wascana Pkwy Regina SK S4S 0A2 Canada Beijing Jiaotong Univ Sch Traff & Transportat Beijing 100044 Peoples R China North China Elect Power Univ Resources & Environm Res Acad Beijing 102206 Peoples R China

Resources and environmental systems management (RESM) is challenged by the synchronic effects of interval uncertainties in the related practices. The synchronic interval uncertainties are misrepresented as random variables, fuzzy sets, or interval numbers in conventional RESM programming techniques including stochastic programming. This may lead to ineffectiveness of resources allocation, high costs of recourse measures, increased risks of unreasonable decisions, and decreased optimality of system profits. To fill the gap of few corresponding studies, a synchronic interval linear programming (SILP) method is proposed in this study. The proposition of interval sets and interval functions and coupling them with linear programming models lead to development of an SILP model for RESM. This enables incorporation of interval uncertainties in resource constraints and synchronic interval uncertainties in the programming objective into the optimization process. An analysis of the distribution-independent geometric properties of the feasible regions of SILP models results in proposition of constraint violation likelihoods. The tradeoff between system optimality and constraint violation is analyzed. The overall optimality of SILP systems under synchronic intervalness is quantified through proposition of integrally optimal solutions. Integration of these efforts leads to a violation-constrained interval integral method for optimization of RESM systems under synchronic interval uncertainties. Comparisons with selected existing methods reveal the effectiveness of SILP at eliminating negativity of synchronic intervalness, enabling risk management of and achieving overall optimality of RESM systems, and enhancing the reliability of optimization techniques for RESM problems. The exploited framework for analyzing synchronic interval uncertainties in RESM systems is helpful for addressing synchronisms of other uncertainties such as randomness or fuzziness and avoiding the resultant de

关键词： Resources and environmental systems management Synchronic interval uncertainty interval linear programming Interaction Risk analysis

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An inexact two-stage stochastic robust programming for residential micro-grid management-based on random demand

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ENERGY 2014年 67卷 186-199页

作者： Ji, L. Niu, D. X. Huang, G. H. North China Elect Power Univ Sch Econ & Management Res Inst Technol Econ Forecasting & Assessment Beijing 102206 Peoples R China Univ Regina Fac Engn Environm Syst Engn Program Regina SK S4S 0A2 Canada

In this paper a stochastic robust optimization problem of residential micro-grid energy management is presented. Combined cooling, heating and electricity technology (CCHP) is introduced to satisfy various energy demands. Two-stage programming is utilized to find the optimal installed capacity investment and operation control of CCHP (combined cooling heating and power). Moreover, interval programming and robust stochastic optimization methods are exploited to gain interval robust solutions under different robustness levels which are feasible for uncertain data. The obtained results can help micro-grid managers minimizing the investment and operation cost with lower system failure risk when facing fluctuant energy market and uncertain technology parameters. The different robustness levels reflect the risk preference of micro-grid manager. The proposed approach is applied to residential area energy management in North China. Detailed computational results under different robustness level are presented and analyzed for providing investment decision and operation strategies. (C) 2014 Elsevier Ltd. All rights reserved.

关键词： Stochastic robust optimization interval linear programming Two-stage stochastic programming Micro-grid Uncertainty

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Generalized solutions to interval linear programmes and related necessary and sufficient optimality conditions

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OPTIMIZATION METHODS & SOFTWARE 2015年第3期30卷 516-530页

作者： Li, Wei Liu, Xiao Li, Haohao Hangzhou Dianzi Univ Inst Operat Res & Cybernet Hangzhou 310018 Peoples R China Zhejiang Univ Finance & Econ Sch Math & Stat Hangzhou 310018 Peoples R China

Recently, some new concepts of optimal solution to interval linear program are introduced which include some existing concepts of optimal solution as special cases. This paper considers generalized optimal solution to interval linear programming problems. The new concepts of optimal solution are introduced in a more general and unified framework. Most existing optimal solution concepts of interval linear program in the literature are special cases in this framework. Necessary and sufficient conditions for checking three kinds of these newly defined optimal solutions are developed.

关键词： interval linear system interval linear programming optimal solution tangent cone

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A Conditional Value-at-Risk Based Inexact Water Allocation Model

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WATER RESOURCES MANAGEMENT 2011年第9期25卷 2125-2145页

作者： Shao, L. G. Qin, X. S. Xu, Y. Nanyang Technol Univ Sch Civil & Environm Engn Singapore 639798 Singapore Peking Univ Coll Environm Sci & Engn Beijing 100871 Peoples R China N China Elect Power Univ SC Energy & Environm Res Acad Beijing 102206 Peoples R China

A conditional value-at-risk (CVaR) based inexact two-stage stochastic programming (CITSP) model was developed in this study for supporting water resources allocation problems under uncertainty. A CITSP model was formulated through incorporating a CVaR constraint into an inexact two-stage stochastic programming (ITSP) framework, and could be used to deal with uncertainties expressed as not only probability distributions but also discrete intervals. The measure of risks about the second-stage penalty cost was incorporated into the model, such that the trade-off between system economy and extreme expected loss could be analyzed. The developed model was applied to a water resources allocation problem involving a reservoir and three competing water users. The results indicated that the CITSP model performed better than the ITSP model in its capability of reflecting the economic loss from extreme events. Also, it could generate interval solutions within which the decision alternatives could be selected from a flexible decision space. Overall, the CITSP model was useful for reflecting the decision maker's attitude toward risk aversion and could help seek cost-effective water resources management strategies under complex uncertainties.

关键词： Conditional value-at-risk interval linear programming Two-stage stochastic programming Water resources management Uncertainty

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Checking weak optimality of the solution to interval linear program in the general form

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OPTIMIZATION LETTERS 2016年第1期10卷 77-88页

作者： Li, Wei Liu, Pengzhen Li, Haohao Hangzhou Dianzi Univ Inst Operat Res & Cybernet Hangzhou 310018 Zhejiang Peoples R China Zhejiang Univ Finance & Econ Sch Math & Stat Hangzhou 310018 Zhejiang Peoples R China

One of the basic and difficult tasks in interval linear programming (IvLP) problems is to check whether a given point is weak optimal. In this paper, we investigate IvLP problem in the general form, in which the constraints contain mixed interval linear equations and inequalities with both non-negative and free variables. Necessary and sufficient conditions for checking weak optimality of a given vector are established, based on the KKT conditions of linear programming and the newly established weak solvability characterizations of mixed interval linear systems by Hladik. The result solves one of the open problems proposed by Hladik (linear programming New Frontiers. Nova Science Publishers, Inc 2012).

关键词： interval linear programming Weak feasible solution Weak optimal solution KKT conditions

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Parameter uncertainty in the optimal coordination of overcurrent relays

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INTERNATIONAL TRANSACTIONS ON ELECTRICAL ENERGY SYSTEMS 2018年第7期28卷 1-1页

作者： Noghabi, Abbas Saberi Sadeh, Javad Mashhadi, Habib Rajabi Univ Birjand Fac Elect & Comp Engn Dept Elect Engn Birjand Iran Ferdowsi Univ Mashhad Dept Elect Engn Fac Engn Mashhad Iran

Generally, the relay coordination problem is solved without considering parameter uncertainties, while uncertainties in the line parameters and current transformer ratios make the fault current passing through the overcurrent relay inaccurate and could cause the miscoordination. To overcome this drawback, in this paper, a novel method based on interval analysis is introduced to model parameter uncertainties in the coordination problem. Considering parameter uncertainties, the coordination constraints are formulated as a set of inequalities with interval coefficients. Monte Carlo simulation technique is used to determine the boundary values of these interval coefficients. In this case, the optimal coordination problem is formulated as an interval linear programming problem. Using mathematical theorems, the optimal value of interval linear programming problem can be obtained by solving a standard linear programming problem. The proposed method is applied to the 8-bus and Institute of Electrical and Electronics Engineers 30-bus test systems, and the results show the ability of interval method to model the parametric uncertainties.

关键词： interval linear programming Monte Carlo simulation overcurrent relay coordination parameter uncertainty

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New pruning tests for the branch-and-prune framework for interval parametric linear systems

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SOFT COMPUTING 2023年第18期27卷 12897-12912页

作者： Rada, Miroslav Garajova, Elif Horacek, Jaroslav Hladik, Milan Prague Univ Econ & Business Dept Econometr W Churchilla 4 Prague 13067 Czech Republic Prague Univ Econ & Business Dept Financial Accounting & Auditing W Churchilla 4 Prague 13067 Czech Republic Charles Univ Prague Fac Math & Phys Dept Appl Math Malostranske 25 Prague 11800 Czech Republic

Parametric linear systems with interval coefficients arise in many practical applications in engineering and other related areas. In this paper, we derive a connection between parametric systems and interval linear programming, where interval parametric linear systems can be used to describe the weak optimal solution set. Then, we discuss the branch-and-prune framework for generating an approximation of the weak feasible set of such systems via a union of interval boxes. We propose two new pruning conditions that can be used to test infeasibility of interval boxes within the framework, based on interval linear algebra and on the geometry of zonotopes. Furthermore, we also design a condition for pruning the interval boxes by feasibility, which allows us to generate an inner approximation of the weak feasible set. Computational experiments illustrate competitiveness of the proposed pruning tests in comparison with other available pruning conditions. The experiments indicate that the test based on interval linear algebra usually produces the least number of boxes, while the zonotope-based test is right behind and runs several times faster.

关键词： interval parametric linear systems interval linear programming Branch-and-prune Zonotope

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Energy crop supply in France:: a min-max regret approach

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JOURNAL OF THE OPERATIONAL RESEARCH SOCIETY 2007年第11期58卷 1470-1479页

作者： Kazakci, A. O. Rozakis, S. Vanderpooten, D. Agr Univ Athens Dept Agr Econ & Rural Dev Athens 11855 Greece Univ Paris 09 F-75775 Paris 16 France

This paper attempts to estimate energy crop supply using a linear programming ( LP) model comprising hundreds of representative farms of the arable cropping sector in France. In order to enhance the predictive ability of such a model and to provide an analytical tool useful to policy makers, interval linear programming is used to formalize bounded rationality conditions. In the presence of uncertainty related to yields and prices, it is assumed that the farmer may adopt a min- max regret ( MMR) criterion as an alternative to the classic profit maximization criterion. Recent advances in operational research are exploited, permitting an efficient implementation of the min- max criterion within an LP model. Model validation based on observed activity levels suggests that about 40% of the farms adopt the MMR criterion. Energy crop supply curves generated by the MMR model prove to be upward- sloped, like classic LP supply curves.

关键词： interval linear programming min-max regret energy crops France

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