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$uWaterloo LaTeX Thesis Template - UWSpace - University of Waterloo$

LnonAntUQ(hydro,u,peri4,seniO) .. LLevel(hydro-~,peri4,senlO) =1= Llevel(hyàro-u,peri4,senlO++l); LnonAnc4S(hydro-~,peri4,senll) .. Llevel(hydro,u,peri4,sen11) =1= Llevel (hydre-u, peri4, sen11++L) ; Lno~t46(hydro-~,peri4,senl2) .. Llevel(hydro,u,peri4,senl2) =1= Llevel (hydre-u, peri4, senl2++1) ; 1;no~t47 (hyüro-u, peri4, sen13 1 . . 5level(hyàrc-u,pexi4,senl31 =1= Llevel (bydro-u, peri4, senl3++1) LnonAnt48(hydro-~,peri4,senU) .. Llevel(hydro-~,peri4,senl4) =1= Llevel (hydre-u, peri4, senl4++1) ; OPTION 52 =WATPA.R; MODEL MtT /XL/; SOLVE MFT XING LP MAXXMIZE COST; *Colunibir.drt SETS the,?n-u /therA, ther9, . . . . , cherU/ hyàrro-LI :hydrA, hydrB, . . . . , hyck5 / periads / TL8T5 i senarlos /S1°S16/ senIlsenarios) /SiWS8/, sen2(senarios) /S9*516/ sen3(senarios) ;SlWS4/, sen4 (senarios 1 /S5*S8/ sen5 (senarios) /S9'S12/, sen6(senarios) !S13*S16/ ncaes : leIo / areas ! regLwregL6 / ALIAS !hydro,~. t-,ydzrl-aLl ALIAS t areas, areasl) , paramecer initial(hydra,ul , hydrA 500, hye3 700, ,... , hydrZ 690 i ; parameter convers ion l hydro-u) , hydzA 4, hy&S 6, . . . - , hyürZ 5 1; Farameter Vmax (hydro-u) ;
hydrEI 1100, hydrB 1200, ..... hydrZ 1250 /; parameter Vmin (hydre-u 1 / hydrA 530,hydrB SCO. ..... hydrZ 630 /; parameter hydro-e f f ( hydro-u ) / hyàrA 25, hydrB 6 . y 25 /; parameter Fmin ( hydro-u 1 / hydrA S. hydrB 4, hydrZ S 1 ; ..... table links(hydro-u, hydro-ul) hydrA hydr9 hydrC .... IlydrJ hydrK hydrL hydrA 0.5 0.2 0.25 .... parameter prob(senarios) / S1 0.03, S2 0.02, S3 0-016. 54 0.024 cable inflow(hyciro-u. periods, senarios) Tl.Sl'S16 T2,Sl'Sa .... TS.Sl6 hydrA 33 17 .... 29 -*.* .... m... * . S . ..*. hy&Z O5 22 .... 30 table demand(modes, periods) Tl TS T3 T4 TS 1 6.3 6.3 6.2 6.9 7.3 ..............-..... . LO 3.7 4.9 5.7 7.4 7.9 ; table duracion(modes, periodsl T1 T2 T3 T4 TS L 0.3 0.2 0.25 0.3 0.L tabie f racArea (nodes, areaç ) reg1 reg2 .... reg15 reg16 1 0.05 a-U8 .... 0.1 0.1 parameter ixport(areas1 . m . / reg1 25000, table hydro,isA(hydro-u, areasl reg1 reg2 .... reg15 reg16 fiydrll 1 hydr9 . A
Page 1 and 2:
A PARALLEL PRIMAL-DUAL DECOMPOSITIO
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The University of Waterloo requires
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WATPAR, and in each of the tests, t
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To Soyoung and Katherine Eugene Par
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3.5 Sumary and Observations on the
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Table 4 . I Table 5.1 Table 5.2 Tab
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Chapter 1 Introduction 1.1 Brief Hi
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1.2 Motivation and Objectives of th
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2. Pmve and dernonstrate the conver
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Chapter 2 Literature Review This ch
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Benders komposition Method In the B
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in this algorithm, both subproblems
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SIMD vs MIMD Panllel computers cm b
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apan. In mmy LAN's, communication i
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angular linear programs by fixing t
Page 31 and 32:
Chapter 3 Paralle1 Decomposition of
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ound constraints. The two parts are
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constnicted in the sarne way by res
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1T 17 t-IT T nlk*'T )' and &'-' = (
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a proposal is passed back to the fi
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END - solve ; if it is infeasible o
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l, and Theorem 3. lb mles out the p
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nonlinking constraints and upper bo
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(The "only if* part) If P is infeas
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. - Thmm 3.6 Suppose (-ri. )Jik, VI
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the optimal value has ken reached.
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spfl, we have have k .J< k PI -1 -
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zi - $' 5 z+ - &J-[, and by Theorem
Page 57 and 58:
Chapter 4 Paraiiel Decomposition of
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upper bound constraints and nonnega
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type subproblem. The lower bound su
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An algorithm could be defined to ex
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Figure 43 9-stage decomposition pri
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combinations of known solutions of
Page 69 and 70:
lower bound subproblem (parts 1 and
Page 71 and 72:
&.',* and CI::;, are a 1 x (i - 1)
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from the same aggregated subproblem
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problems is discussed. Various prop
Page 77 and 78:
Processor 2 Step O. Set level I cou
Page 79 and 80: - update and solve spi ; record opt
Page 81 and 82: for the optimum by exchanging the p
Page 83 and 84: The next result guarantees that in
Page 85 and 86: fonn a nondecreasing senes of lower
Page 87 and 88: one upper bound subproblem. The alg
Page 89 and 90: su, , for al1 i Note that when k= 1
Page 91 and 92: with proposals or cuts from other s
Page 93 and 94: - if t is an upper bound subproblem
Page 95 and 96: Proof : The Assumption guarantees t
Page 97 and 98: nNk-'. Proof : For i= 1.2. ... . N
Page 99 and 100: Chapter 5 Preliminary Implementatio
Page 101 and 102: 5.1.1 Decomposition Phase In the de
Page 103 and 104: NB,~,PEI 8 # Selectmg the rows ROWS
Page 105 and 106: Figure 53 Example of multi-part str
Page 107 and 108: in each computer as discussed in Ch
Page 109 and 110: followiag 4 parts: scenarios 1 to 1
Page 111 and 112: "WSET' is the time taken on the RSI
Page 113 and 114: esults of the parallel decompositio
Page 115 and 116: Table 5.6 Performance of Parailel D
Page 117 and 118: We dso anaiyzed the speed-ups and e
Page 119 and 120: Chapter 6 Conclusions and Future Re
Page 121 and 122: 8. tested several models for conver
Page 123 and 124: computational speed for some real w
Page 125 and 126: APPENDIX A GAMS codes of the test m
Page 127 and 128: hydrA 25, ...., hydrZ 1s /; paramet
Page 129: NwatBal(hydro,u,pericds,senarios1 .
Page 133 and 134: VARIABLES En 'Expectation of the ut
Page 135 and 136: APPENDIX B The C codes of WSET We p
Page 137 and 138: k denoces an index of SubProblern t
Page 139 and 140: SPb~[kl-+; 1 else ( if (rowinfoIi]
Page 141 and 142: * Pack initial &ta and send '/ for(
Page 143 and 144: Appendiv C C codes of WATPAR We pre
Page 145 and 146: if (LpSub [k] ->rwnmbs [pl > HISPb-
Page 147 and 148: * Use advanced basis at each iterat
Page 149 and 150: status = CPXnewcols (env,lp, 1, &Lp
Page 151 and 152: TERMINATE : ..,. Free up the proble
Page 153 and 154: short SolveProb(C3XEWptr env, CP.XL
Page 155 and 156: variables and add other part's link
Page 157 and 158: i* Add a cut for upper level iterat
Page 159 and 160: C3 Proecssor 3 : Lower-Upper Bound
Page 161 and 162: t for(k=l; k c icer-count; k+-1 sta
Page 163 and 164: { gectimeofday(&tvl, (struct cimezo
Page 165 and 166: i status = CPXchgcoef(env, lp, (int
Page 167 and 168: status = AddLamcols ( LpSub, env, I
Page 169 and 170: BIBLIOGRAPHY Aardal. K. And A. An.
Page 171 and 172: Computation". Mathematical Programm
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