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*Columbirb. prn Table inflow(hydro-u,K) 1 2 3 .**. 43 44 4s hydrA 52 66 81 . . . . 57 66 85 A.2 Hydro-Eletric Generation Planning Mode1 2 (HEGP2) written by J.R. Birge and C. Supatgiat, O. Michigan, 1998, Lasc modified H. Jin Park Sinclude "columbia.datN VARIABLES COST ; POSITIVE VARIABLES ~therm~en(therm,u,modes,periodç,senarios) therm production in each mode in each month (MWh1 Ngen~flow(hydro,u,rnodes,periodç,çenarios~ hydro water release for generation in each mode in each month (m3) Llevel(hydro,u,periods,senarios) water level ac the end <strong>of</strong> period (Mm31 Nspil~Flow(hydro,u,modes,periods,senarios~ * water spi11 over the period due to over capacity (m3) Nexchange(areas,areas,modes,periods,senarios~ amount power transfer from (1st) to (2nd) in each mode , each node (Mhlh) Nrat~~low(hydro,u,rnodes,perioas,senarios1: slack in minimum flow constraints. Ic gets penalty in the objective function EQUÀTIONS OBJECTIVE NexpCapa(areas,mcdes,periods,senarios) Nimp~capa(areas,modes,periods,senarios1 ~lmeet,load(areas,nodes,periods,ser,arias) Nwat9al(hydro~u,perFoas,senariost NhydraMinC(hy~o~u,modes.petlods,senarios) Lnon&zt(hydro,u,periods,senario~l Lno~ttl(hydro,u,periods,senarios1 Lnomt22 i hltdro-u, periods , senarias 1 LnoxAnt3 1 (hydre-u, periods , senarias t , LnonAnt32 (hydre-u, periods , senarias 1 LanIInc33 ihydro-u, periods , senarios 1 , Lnor~t34 (hydre-u, periods, senarios 1 OP-CTXVE .. COST =E= - (SUM(senarios, probtsenarios)*~~~(periods, ST;TMtmodes,duration(mdes,periods)* çUM(therm,u, unitCost(themrmu) Nthermgen(theni~u,des,periods,send2:iosl~~ 1 ) 116
NwatBal(hydro,u,pericds,senarios1 .. -(initial(hydro,u)S(ord(periods) EQ 1) + Llevel(hydro,u,periods-1, senarios) S (ord (periods 1 GT 11 + (~(hydro,ul, links (hydro-ul hydre-u) ' SUM(modes, (Ngen,f1ow(hydro~u~,modes,periads,senarios) + Nspillflow(hydro,u~,mc~es,periods,ssnarios1 / 1000000.01) + inflow(hydro,u,periods,senarios) (num,hour(periods,senarios) 3600.0 / 1000000.0) - SüM(modes, (~gen,flow(hybro,u,modes,periods,senarios~ t NspillFlow(hydro,u,modes,periods,.senarios) 1 / 1000000.0) =L= - Llevel(hydro,u,periods,senarios); Llevel(hydro,u,peri3,sen3) =1= Lievel (hydre-u, peri3, sen3++ll ; Llevel(hydro_u,peri3,sen4) =1= Llevel(hydro,u,peri3,sen4++1); Llevel(hydro,u,peri3,sen5) =1= Llevel(hydro-u,peri3,sen5++1); L~eve~(hydrc~u,peri3,sen6) =1= LlevelIhydro-~,peri3,sen6++11 ;
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
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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
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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: hydrA 25, ...., hydrZ 1s /; paramet
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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