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200777:100026788(2007)07201372071,1,2(11,710048;21,710048):.(),,.,,,;,;,.,.:;;;;:TU991102:ATheSynthesisOptimalDesignMethodofLoopedWaterSupplyNetworksBAIDan1,YANGPei2jun1,SONGLi2xun2(11NorthWestKeyLaboratoryofWaterResourceandEnvironmentEcology,MinistyofEducation,XianUniversityofTechnology,Xian710048,China;21XianPolytechnicUniversity&Technology,Xian710048,China)Abstract:Thesynthesisprocedure,inwhichtheminimumannualcost(orinvestment)isusedastheobjectivefunction,ispresentedtooptimizeloopedwatersupplynetworks,combiningthequadricorthogonalcircumrotationregressiondesign,thequadraticprogrammingandthelinearprogrammingtogether.Firstly,theflowdistributionschemesaresetdownbymeansofquadricorthogonalcircumrotationregressiondesign,theannualcostofeachflowdistributionschemeisdeterminedbylinearprogramming,thequadricmultipleregressionequationbetweentheannualcostandthepipesegmentdischargesisestablishedflowdistributionscheme.Secondly,theoptimalflowdistributionschemeinwhichthequadricmultipleregressionequationisusedastheobjectivefunctionisdeterminedbythequadraticprogramming.Finally,theoptimaldesignofloopednetworkisdeterminedbythelinearprogrammingbasedontheoptimalflowdistributionscheme.Theprocedurecanbeusedtooptimizethesingleresourceloopednetworkwithpumpstationandgravity.Keywords:loopedwatersupplynetwork;optimaldesign;quadricorthogonalcircumrotationregressiondesign;quadraticprogramming;linearprogramming:2005202224::(1960-),,,,,.1,,,.,;,,,,,,.,(LPG)[14][57][811],,,LPG;LPG,;,,.,,.221121111,.21112(),.,.,,,.,3mPs;,016mPs.i,,M(i),M(i)i[13].21113(1),.minP=Ni=1M(i)j=1Cijxij,(1):P();N;M(i)i;Cij(Pm);xij(m).211141).M(i)j=1xij=Li,i=1,2,,N,(2)Li(m).2).R(s)i=1M(i)j=1gJijxij=0,s=1,2,,S,(3):s;S;R(s)s;g.g=1-1.(4)3).I(k)i=1M(i)j=1JijxijE0-Ek,k=1,2,,K,(5):k;K;I(k)k;Eo(m);Ek(m);Jij[2].4)xij0,(6)21221211(1),().83120077minW=e(1+e)t(1+e)t-1+p100Ni=1M(i)j=1Cijxij+86103bQpH,(7):W(P);t();e;p;Qp(m3Ps);H(m);b;(Pkwh);.21212(2)(3)(4).1)I(k)i=1M(i)j=1Jijxij-HE0-Ek,k=1,2,,K.(8)2)xij0;H0.(9)3[14,15],,,,,,,,.,s,s,.1311,s,s,s,,.s,.14,q1q2q3q4,q5q6q7q8q9q10q11q12.312zj(j=1,2,,s),yt.Nt=m0+2s+1,(10):m02s;s.z0j=z1j+z2j2,(11)j=z2j-z0j,(12)xj=zj-z0jj,(13):z2jz1jj;z0jj;j;,.,yzjyxj,y=a0+pj=1ajxj+pi;jaijxixj+pj=1ajjx2j,(14):y;a0ajaijajj.9317tyt,,,.4411(13)(14),,minZ=pj=1bjzj+pi;jbijzizj+pj=1bjjz2j,(15):Z;bjbijbjj.4121)z1jzjz2j,j=1,2,,s.(16)2)(016mPs),qmin=0147D2min,(17):qmin(m3Ps);Dmin(m).qkqmin,k=1,2,,P-s,(18):qk(m3Ps),;k;P.2,,.5[12]179,2,W=01228Pi=1(12+372D117i)Li+4910QpH.(19),C=100.,,20.(19)(1).1(m)0.600.500.450.400.350.300.250.200.150.10(P)38.3328.8424.5620.6017.0013.7010.778.236.114.432z1z2x1x2+0.18000.1400+10.16680.129800.13500.1050-10.10320.0802-0.09000.0700:=11414.5112,q1(z1)q2(z2),(2).(11)(12)(13),(2).2,,,3,,.512,04120077(4).3x1x2q1(z1)q2(z2)q3q4q51110.16680.12980.00340.02980.036821-10.16680.08020.0530-0.01980.03683-110.10320.12980.06700.0298-0.02684-1-10.10320.08020.1166-0.0198-0.0268500.18000.10500.01500.00500.05006-00.09000.10500.10500.0050-0.0400700.13500.14000.02500.04000.005080-0.13500.07000.0950-0.03000.00509000.13500.10500.06000.00500.00504x1x2x1x2x21x22yt(P)11.0001.0001.0001.0001.00094228.8921.000-1.000-1.0001.0001.00097103.093-1.0001.000-1.0001.0001.00095497.964-1.000-1.0001.0001.0001.00097215.9551.4140.0000.0001.9990.00094944.596-1.4140.0000.0001.9990.00096324.3370.0001.4140.0000.0001.99995794.2580.000-1.4140.0000.0001.99998123.4890.0000.0000.0000.0000.00095231.134,,(20),019832,.y=9523113-41617x1-98519x2-28911x1x2+13012x21+79216x22.(20)513(15)(20)2,().minZ=-9285z1-262019z2-367030z1z2+128625z21+1293982z22,(21)0109z101180107z20114(22)(17)01005m3Ps,z1+z201295z201105z101135(23)(22)(23)z1+z20129501135z10110501105z101140(24)MATLAB[16],,:z1=011729m3Ps,z2=011221m3Ps,5.51414175q1(z1)q2(z2)q3q4q50.17290.12210.00500.22100.0429,6,,21(201)10(532),6,281564m,9138.6(m)(m)(m)10.6,0.5,0.45,0.4,0.35,0.30.4P0.351190P1020.5,0.45,0.4,0.35,0.3,0.250.35P0.3440P36030.10.1100040.2,0.15,0.10.1120050.3,0.25,0.2,0.150.15800,10116,717%.6,,.,,,,,.,.,,,;,,.:[1]ApprovesE,ShamirU.Designofoptimalwaterdistributionsystem[J].WaterResourceResearch,1977,13(6):885-900.[2]QuindryG,etal.CommentonDesignofoptimalwaterdistributionSystemsbyE,ApprovesandU,Shamir[J].WaterResourceResearch,1979,15(6):1651-1654.[3]FujiwaraO,etal.Amodifiedlinearprogramminggradientmethodforoptimaldesignofloopedwaterdistributionnetworks[J].WaterResourceResearch,1987,23(6):977-982.[4]KesslerA,ShamirU.Analysisofthelinearprogramminggradientmethodforoptimaldesignofwatersupplynetworks[J].WaterResourceResearch,1989,25(7):977-982.[5]EigerG,ShamirU,BenalA.Optimaldesignofwaterdistributionofwaternetworks[J].WaterResourceResearch,1994,30(9):2637-2646.[6]SheraliH,SmithE.Aglobaloptimizationapproachtoawaterdistributionnetworkdesignproblem[J].JournalofGlobalOptimization,1997,2(2):107-132.[7]HanifD,RajivT.Enhancedlowerboundsfortheglobaloptimizationofwaterdistributionnetworks[J].WaterResourceResearch,1998,36(7):1831-1841.[8]MurphyLJ,SimpsonAR.Pipeoptimizationusinggeneticalgorithms[J].ResRepDepofCivEng,UnivofAdelaide,SAust,June,1992:93-95.[9