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首页 > 过刊浏览>2016年第8卷第1期 >23-33. DOI:10.13878/j.cnki.jnuist.2016.01.002
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区间系统与区间优化模型——理论与应用
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国家自然科学基金(71471051);浙江省自然科学基金(LY14A010028);国家自然科学基金委员会和浙江省人民政府联合基金重点资助项目(U1509217)


Interval systems and interval optimization: Theory and applications
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    摘要:

    区间系统与区间优化模型是一种应用广泛的描述不确定性问题的数学模型.本文综述区间系统与区间优化模型在理论与应用方面的研究进展.特别地,本文将介绍区间线性系统的解和可解性问题、区间线性优化模型的最优解和最优性问题以及区间二次优化模型的最优解和最优性问题,最后简单概述它们的各种应用实例.

    Abstract:

    We give an overview on theorem and applications of interval systems and interval optimization.Among others we discuss solutions and solubility of interval linear systems,optimal solution and optimality of interval linear programming problem and interval quadratic programming problem.We also introduce some applications such as energy systems planning,air quality management,Fault Detection etc.

    参考文献
    [1] Birge J,Louveaux F.Introduction to stochastic programming[M].New York:Physica-Verlag,1997
    [2] Tanaka H,Asal K.Fuzzy linear programming problemwith fuzzy numbers[J].Fuzzy Sets and Systems,1984,13:1-10
    [3] Chanas S,Kuchta D.A concept of the optimal solution of the transportation problem with fuzzy cost coefficients[J].Fuzzy Sets and Systems,1996,82:299-305
    [4] Moore R.Interval analysis[M].Prentice-Hall,Englewood Cliffs,NJ,1966
    [5] Moore R.Interval arithmetic and automatic error analysis in digital computing[M].Thesis:Stanford University,1962
    [6] Moore R,Kearfott R,Cloud M.Introduction to intervalanalysis[M].SIAM,Philadelphia,2009
    [7] Fiedler M,Nedoma J,Ramik J,et al.Linear optimization problems with inexact data[M].New York:Springer-Verlag,2006
    [8] Oettli W,Prager W.Compatibility of approximate solution of linear equations with given error bounds for coeficients and right-hand sides[J].Numerische Mathematik,1964,6:405-409
    [9] Gerlach W.Zur losung hearer ungleichungssysteme bei storung der rechten seite und der koefizientenmatrix,mathematische operationsforschung und statistik[J].Series Optimization,1981,12:41-43
    [10] Rohn J.Solvability of systems of linear interval equations[J].SIAM Journal on Matrix Analysis and Applications,2003,25:237-245
    [11] Poljak S,Rohn J.Checking robust nonsingularity is NP-hard[J].Mathematics of Control,Signals,and Systems,1993,6:1-9
    [12] Shary S.Solving the interval linear tolerance problem[J].Math Comput Simulation,1995,39:53-85
    [13] Shary S.Controllable solution set to interval static systems[J].Math Comput Simulation,1997,86:185-196
    [14] Shary S.A new technique in systems analysis under interval uncertainty and ambiguity[J].Reliab Comput,2002,8(5):321-418
    [15] Li W,Wang H,Wang Q.Localized solutions to interval linear equations[J].Journal of Computational and Applied Mathematics,2013,238(15):29-38
    [16] Worrawate L,Phantipa T.L-and R-localized solvabilities of max-separable interval linear equations and its applications[J].Journal of computational and applied mathematics,2015,279:306-317
    [17] Hladík M.Weak and strong solvability of interval linear systems of equations and inequalities[J].Linear Algebra and its Applications,2013,438:4156-4165
    [18] Li H,Luo J,Wang Q.Solvability and feasibility of interval linear equations andinequalities[J].Linear Algebra Appl,2014,463:78-94
    [19] Li W,Liu X,Li H.Generalized solutions to interval linear programmes and related necessary and sufficient optimality conditions[J].Optimization Methods &Software,2015,30(3):516-530
    [20] Alefeld G,Herzberger J.Introduction to interval computations[M].New York:Academic Press,1983
    [21] Neumaier A.Interval methods for systems of equations[M].Cambridge:Cambridge University Press,1990.
    [22] Popova E.Solvability of parametric interval linear systems of equations and inequalities[J].SIAM Journal on Matrix Analysis and Applications,2015,36(2):615-633
    [23] Farkas J.Theorie der einfachen ungleichungen[J].Journal für die Reine und Angewandte Mathematik,1902,124:1-27
    [24] Rohn J.A farkas-type theorem for linear interval equations[J].Computing,1989,43:93-95
    [25] Karademir S,Prokopyev O.A short note on solvability of systems of interval linear equations[J].Linear Multilinear Algebra,2011,59:707-710
    [26] Rohn J.A farkas-type theorem for interval linear inequalities[J].Optim Lett,2014,8:1591-1598
    [27] Xia M,Li W,Li H.Farkas-type theorems for interval linear systems[J].Linear &Multilinear Algebra,2015,63(7):1390-1400
    [28] Ishibuchi H,Tanaka H.Multiobjective programming in optimization of the interval objective function[J].European Journal of Operational Research,1990,48(2):219-225.
    [29] Ishibuchi H,Tanaka H.Formulation and analysis of linearprogramming problem with interval coefficients[J].Journal ofJapan Industrial Management Association,1989,40(5):320-329 (InJapanese)
    [30] Facchinetti G,Ricci R,Muzzioli S.Note on rankingfuzzy triangular numbers[J].International Journal of Intelligent Systems,1998,13:613-622
    [31] 刘新旺,达庆利.一种区间线性规划的满意解[J].系统工程学报,1999,14(2):123-128 LIU Xinwang,DA Qingli.A satisfactory solution for interval linear programming[J].Journal of Systems Engineering,1999,14(2):123-128[ZK)]
    [32] Liu X.Measuring the satisfaction of constraints in fuzzy linearprogramming[J].Fuzzy Sets and Systems,2001,122:263-275
    [33] Sengupta A,Pal T,Chakraborty D.Interpretation ofinequality constraints involving interval coefficients and asolution to interval linear programming[J].Fuzzy Sets andSystems,2001,119:129-138
    [34] Xu Z,Da Q.Possibility degree method for ranking intervalnumbers and its application[J].Journal of systems engineering,2003,18(1):67-70
    [35] Sengupta A,Pal T.On comparing interval numbers[J].European Journal of Operational Research,2000,127:28-43
    [36] Angiz Z,Emrouznejad L,Mustafa A,et al.Aggregating preference ranking with fuzzy data envelopment analysis[J].Knowledge-Based Systems,2010,23(6):512-519
    [37] Yue Z.An extended TOPSIS for determining weights of decision makerswith interval numbers[J].Knowledge-Based Systems,2011,24:146-153
    [38] Dai J,Wang W,Xu Q,et al.Uncertaintymeasurement for interval-valued decision systems based on extendedconditional entropy[J].Knowledge-Based Systems,2012,27:443-450
    [39] Song P,Liang J,Qian Y.A two-gradeapproach to ranking interval data[J].Knowledge-Based Systems,2012,27:234-244
    [40] 李炜,线性优化及其扩展[M].北京:国防工业出版社,2011 LI Wei,Linear optimization and extensions[M].Beijing:National Defence Industry Press,2011
    [41] Tong S.Interval number and fuzzy number linear programming[J].Fuzzy Sets and Systems,1994,66(3):301-306.
    [42] Chinneck J,Ramadan K.Linear programming with interval coefficients[J].J Oper Res Soc,2000,51(2):209-220
    [43] Soleimani D M,Jahanshahloo G.Optimal and strongly optimal solutions for linear programming models with variable parameters[J].Applied Mathematics Letters,2007,20(10):1052-1056.
    [44] Hladik M.Optimal value range in interval linear programming[J].Fuzzy Optim Decis Mak,2009,8(3):283-294
    [45] Li W,Luo J,Wang Q,et al,Checking weak optimality of the solution to linear programming with interval right-hand side[J].Optim Lett,2014,8(4):1287-1299
    [46] Li W,Luo J,Deng C.Necessary and sufficient conditions of some strong optimal solutions to the interval linear programming[J].Linear Algebra and its Applications,2013,439:3241-3255
    [47] Luo J,Li W.Strong optimal solutions of interval linear programming[J].Linear Algebra Appl,2013,439:2479-2493
    [48] Luo J,Li W,WANG Q.Checking strong optimality of interval linear programming with inequality constraints and nonnegative constraints[J].Journal of Computational and Applied Mathematics,2014,260:180-190
    [49] Li H.Necessary and sufficient conditions for unified optimality of interval linear program in the general form[J].Linear Algebra and its Applications,2015,484:154-174
    [50] Li Wei.A note on dependency between interval linear systems[J].Optimization Letters,2015,9(4):795-797
    [51] Rohn J.Strong solvability of interval linear programming problems[J].Comp,1981,26:79-82
    [52] Hladík M.Interval linear programming:A survey[M]//Linear Programming New Frontiers,Nova Science Publishers Inc,2011
    [53] Luo J,Li W.Checking strong optimality of interval linear programming[J].Advances in intelligence systems research,2013,37:152-155
    [54] 史加荣,刘三阳,熊文涛.区间数线性规划的一种新解法[J].,系统工程理论与实践,2005,25(2):101-106 SHI Jiarong,LIU Sanyang,XIONG Wentao.A new solution method for interval linear programming[J].System engineering theory and Practice,2005,25(2):101-106
    [55] 郭均鹏,李汶华.区间线性规划的标准型及其最优值区间[J].管理科学学报,2004,7(3):59-63 GUO Junpeng,LI Wenhua.Standard form of interval linear programming and its optimal objectiveinterval value[J].Journal of Management Sciences in China,2004,7(3):59-63[ZK)]
    [56] Hladík M.How to determine basis stability in interval linear programming[J].Optim Lett,2014,8(1):375-389
    [57] Wang X,Huang G.Violation analysis on two-step method for interval linearprogramming[J].Information Sciences,2014,281:85-96
    [58] Steuer R.Algorithms for linear programming problems with interval objective function coefficients[J].Math Oper Res,1981,6:333-348
    [59] Allahdadi M,Nehi H.The optimal solution set of the interval linear programming problems[J].Optim Lett,2013,7(8):1893-1911
    [60] Liu S,Wang R.A numerical solution method to intervalquadratic programming[J].Applied Mathematics and Computation,2007,189(2):1274-1281
    [61] Li W.Tian X.Numerical solution method for generalinterval quadratic programming[J].Applied Mathematics and Computation,2008,202:589-595
    [62] Li W.Algorithm for interval quadratic programming with equality constraints[C]//Proceedings of FSKD'09,2009,6:78-81
    [63] Li W.An improving procedure of the numerical solution method for interval quadratic programming[C]//Proceedings of ICICTA09,2009,1:165-168
    [64] Hladík M.Optimal value bounds in nonlinear programming with interval data[J].Top,2011,19:93-106
    [65] Li W,Xia M,Li H.New method for computing the upper bound of optimal value in interval quadratic program[J].Journal of Computational and Applied Mathematics,2015,288:70-80
    [66] Li W,Xia M,Li H.Some results on the upper bound of optimal values in interval quadratic programming,(submmited)
    [67] Alefeld G,Mayer G.Interval analysis:Theory and applications[J].Journal of Computational and Applied Mathematics,2000,121:421-464
    [68] Soleimani D M,Jahanshahloo G.Optimal and strongly optimal solutions for linear programming models with variable parameters[J].Applied Mathematics Letters,2007,20(10):1052-1056
    [69] Wu X,Huang G,Liu L,et al.An interval nonlinear program for the planning of waste management systems with economies-of-scale effects:A case study for the region of Hamilton,Ontario,Canada[J].Eur J Oper Res,2006,171(2):349-372
    [70] Agarwal P,Bohner M.Basic calculus on time scales and some of its applications[J].Results Math,1999,35:3-22
    [71] Stefanini L,Bede B.Generalized Hukuhara differentiability of interval valued functions and interval differential equations[J].Nonlinear Anal,2009,71:1311-1328.
    [72] Vasile L.Hukuhara differentiability of interval-valued functionsand interval differential equations on time scales[J].Information Sciences,2013,248:50-67
    [73] Chang N,Chen H,Shaw D,et al.Water pollution controlin river basin by interactive fuzzy interval multiobjectiveprogramming[J].Environ Eng,1997,123(12):1208-1216
    [74] Chang N,Chen Y,Wang S.A fuzzy interval multiobjectivemixed integer programming approach for the optimal planning of solid waste management systems[J].Fuzzy Sets Syst,1997,89(1):35-60
    [75] Cai Y,Huang G,Yang Z,et al.Community scalerenewable energy systems planning under uncertainty-aninterval chance-constrained programming approach[J].Renew Sustain Energy Rev,2009,13(4):721-735
    [76] Matsveichuk N M,Sotskov Yu N,Egorova N G,et al.Scheduleexecution for two-machine flow-shop with interval processingtimes[J].Mathematical and Computer Modelling,2009,49:991-1011
    [77] Pires A,Chang N,Martinho G.An AHP-based fuzzy intervalTOPSIS assessment for sustainable expansion of the solid wastemanagement system in Setubal Peninsula,Portugal[J].Resour Conserv Recycl,2011,56(1):7-21
    [78] Zhang X D,Huang G H,Nie X H.Possibilistic stochastic watermanagement model for agricultural nonpoint source pollution[J].Water Resour Plan Manag,2011,137(1):101-112
    [79] Li W,Tian X.Fault detection in discrete dynamic systems with uncertainty based on interval optimization[J].Mathematical Modelling and Analysis,2011,16(4):549-557
    [80] Nikoo M,Kerachian R,Poorsepahy-Samian H.An intervalparameter model for cooperative inter-basin water resources allocation considering the water quality issues[J].Water Resour Manag,2012,26(11):3329-3343
    [81] Nikoo M,Kerachian R,Karimi A.A nonlinear intervalmodel for water and waste load allocation in river basins[J].WaterResour Manag,2012,26(10):2911-2926
    [82] Dong C,Huang G,Cai Y,et al.An inexact optimizationmodeling approach for supporting energy systems planning andair pollution mitigation in Beijing city[J].Energy,2012,37(1):673-688
    [83] Vidal T,Crainic T,Gendreau M,et al.A hybrid geneticalgorithm with adaptive diversity management for a large class of vehicle routing problems with time-windows[J].Comput Oper Res,2013,40(1):475-489
    [84] Dong C,Huang G,Tan Q,et al.Coupled planning of waterresources and agricultural land-use based on an inexactstochasticprogramming model[J].Front Earth Sci,2014,8(1):70-80
    [85] Cheng G,Huang G,Dong C.Synchronic interval Gaussianmixed-integer programming for air quality management[J].SciTotal Environ,2015,538(15):986-996
    [86] Zhu Y,Li Y,Huang G.An optimization decision supportapproach for risk analysis of carbon emission trading in electricpower systems[J].Environ Model Software,2015,67:43-56
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李炜,黄金花.区间系统与区间优化模型——理论与应用[J].南京信息工程大学学报(自然科学版),2016,8(1):23-33
LI Wei, HUANG Jinhua. Interval systems and interval optimization: Theory and applications[J]. Journal of Nanjing University of Information Science & Technology, 2016,8(1):23-33

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  • 收稿日期:2015-12-20
  • 在线发布日期: 2016-02-24

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