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* ûptimize the problem and obtain solution. */ status = SolveProb(env, Ip) ; if (scatus) { goto TERMI-WE; 1 /* Add the su-CO-one constraints for Lamda variables */ for(k=l; k CX, L, 11; Fnf 3 = pt-n_upkdcuble t LpSub [k] -wLY, Hf SFb-m [nb-subs j , l l ; i * Aad the sum <strong>of</strong> prknal proposals and add one col- to the subproblem *! LpSub[tl->CX += LpSub[4]->CX ;
status = CPXnewcols (env,lp, 1, &LpSub[2]->CX, &Lam-10, &L=up, NULL, m); if (status) fprintf (fp, ' =OR in defining a new column! ! ! \nu 1 ; for(i=HISPb,m[O]; i cHISPb,m[cur-block] ; i++) i status = CPXchgcoef (env, lp, i, LpS~(cur,blockj->n + HISPb-m[nb-subs]+ +iter,count-2+totlev2C. LpSubfZj->LY[ij); 1 for(i=LpSub[ll ->m - LOWSPb-m[ij -1; iml; i++) I status = ~PXchgcoef(env, Ip, i, LpSublcur-blockl->n+HISPbs[nb-subs] + iter-count-2 - totlev2C , LpSubt21 ->LY[~-LpSub[ll ->m - LOWSPb-m[l]+l+HISPb~[cu~:~block~ 1) ; 1 status = CPXchgcoef (env, lp, ( int (LpSub[cur-block] ->m-1) , LpSub[l~-~n+XISPb~[1]+LOWSPb~m(I~+iter~co~t-2+totlev2C, Lam,coef) ; /* Lower level iteration. 'exitlev2' Fs a signal coming from lower-uppex bound subproblem asking CO exit lower level iteration */ while(lev2-count < 150 && (objval[3] - objval[l] > 0.0001 1 1 lev2,count cl) && (lev2,counc c 1 II exitlev2 c= O 11 LpSub[cur-blockl->Pi3 = CompuPiB(LpSub); LpSub [ cur,block] - >OMeL = CompuOMet ( LpSub ; LpSub (-,block] ->PiD = CompuPiD (LpSubl ; 1 pvm-initsend(FvmDataRaw1; info = pvm-pkdouble (&LpSublcur-biockl-,PiS, i, 1); inf O = pvm_pkdouble (LpSub [cur-block] ->Pi& LSPb-n [cur-blockl , Il ; info = pvmgkdouble (LpSub [cur,block] ->OMeL, HISPb-n [nb-subs 1 , 1) ; Lnfo = pvmgkdouble (LpSub leur-blockl ->Ornega, LSPb,m[cur,blockj , 11 ; if(info < 0) fprintf ( fp, 'ERROR in packing data\nn ; gettime<strong>of</strong>day(&tvl, (struct tbezone*) 0 1 ; bufid = ptm_retv(tid[31, 2 ) ; rdtl = myseconds(rdtl); fgrincfifp, * Receiving Set up Data Time : S8f\nn, rdt~/~000000); , * Md a primai proposal from subproblem 3 (louer-upper bond s9roblem) */ status = C?Xnewcols(env,~p, 1, tLpSub[3]->a, &Lam,lo, &Lam,up, NUU, NUIL); if tstatus) fprincf ( fp, ' ERROR in defining a new col^ ! ! ! \na ) ;
Page 1 and 2:
A PARALLEL PRIMAL-DUAL DECOMPOSITIO
Page 3 and 4:
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
Page 9 and 10:
3.5 Sumary and Observations on the
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Table 4 . I Table 5.1 Table 5.2 Tab
Page 13 and 14:
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
Page 21 and 22:
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
Page 29 and 30:
angular linear programs by fixing t
Page 31 and 32:
Chapter 3 Paralle1 Decomposition of
Page 33 and 34:
ound constraints. The two parts are
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constnicted in the sarne way by res
Page 37 and 38:
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
Page 47 and 48:
(The "only if* part) If P is infeas
Page 49 and 50:
. - Thmm 3.6 Suppose (-ri. )Jik, VI
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the optimal value has ken reached.
Page 53 and 54:
spfl, we have have k .J< k PI -1 -
Page 55 and 56:
zi - $' 5 z+ - &J-[, and by Theorem
Page 57 and 58:
Chapter 4 Paraiiel Decomposition of
Page 59 and 60:
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
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Processor 2 Step O. Set level I cou
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- update and solve spi ; record opt
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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 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: * Use advanced basis at each iterat
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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