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LwatBal(hydro,u,K,predlevel) S(ord(K) GT I and pred(K) EQ predl(predlevel1) .. -(initial(hydro-u)S(pred(K) EQ O)+Llevel(hydro-u,predieveI)S(pred(~) GT O ) +(SUM(hydro-ul, links(hydroOul,hydroOu) * SUM (modes, (Ngen-f low (hydre-ul , modes. K 1 +NspillFlow(hydro~ul,modes,KI)) ! 1000000.0)) + inflow(hydro,u,K) (num,hour(K) * 3600-0 / 1000000.0~ - SIJM(modes,(Ngen,flow~hydro,u,rnodes,~l + NspillF~ow(hydro,u,modes,K) 1 / L000000.01) =L= -Llevel(hydro-u,K); OPTION LP =WATPAR: MODEL MFT iALL/; SOLE MFT USTNG LP WIMTZE COST; SETS them-u /therA, ...., theru/ hydro-u ihydrA, ...., hydrZ / 'C / 0'45 / periods / 1, 2, 3, 4 ! predlevel (KI /0*14/ mûdes ilglO/ areas / regleregla / ALIAS ( hydro-u , hydro-ul ALIAS (areas, areasl) , parame ters na-hour (KI Prab(K1 ; parameter unitCost(cherm,u) ; therA 0.8, . . . . , theru 0.8 1; Faramecer capacity(t5ezm-U) therA 9500, ,,,,. theru 21 i: parameter initiai(hydro-G) hydrA 650, , , , , , hydr~ 580 /; prameter conversion(hydro-u) , k,yà=A 4, . . . . , hydxZ 5 /; parameter Vnaxthyiro-u) / hy*A 2100, . . . . , hy&Z 2750 /; parameter Vmin ( h*o,u 1 / hyàrA 230, . . . ., hydrZ 210 /; parameter hydro,ef f (hydre-u)
hydrA 25, ...., hydrZ 1s /; parameter Fmax (hydre-u) / hydrA 21, ...., hydrZ 25 /; paramecer Fmin(hydro,u) / hydrA 5, . . . . , hydrZ 5 / ; table links(hy&o-u, hydro-ul) hy&A . . . . hydrL hydrA 0.5 .... 0.2 . . . . S . . . hydrZ 0.3 .... 0.1 ; parameter prob(K) / 1 1, 2 0-4, ...* 33 0.005, paramecer pred(K1 ! L O, 2'4 1, paramecer predl (KI : O O, I 8 8, 9 table demand(modes, K, pericas) 1.1 2'4.2 5'14.3 15'45.4 ? 4 9 19 28 39 ..-- .a.. 1 O 7 12 27 34 table duracion(nodes, R, periods) 1-1 2'4.2 5'14.3 LS'45.3 1 0.3 3.2 3-25 0.3 *. . * .... 10 0.2 0.3 3.23 0.24 table fracaea(modes, areas) regl reg2 .... reg15 reg16 1 0.05 0.38 .... 0.: 0.1 parameter impor=(areas) / reg1 cable hydre-içA (hydre-u, areas l 25000, ...., reg16 S?7CO / regl reg2 reg3 . -. . reg13 reg14 reg15 regL6 hydrA 1 hy&3 I ilyckc
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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
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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
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lower bound subproblem (parts 1 and
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&.',* and CI::;, are a 1 x (i - 1)
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from the same aggregated subproblem
Page 75 and 76: 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: APPENDIX A GAMS codes of the test m
Page 129 and 130: NwatBal(hydro,u,pericds,senarios1 .
Page 131 and 132: hydrEI 1100, hydrB 1200, ..... hydr
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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