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for i j=SPb-n [2 1 +LSPb3[2 1 +HISPb,n[I] ; j~SPb~n[21+LSPb~m~ZI+HISPb~n[nbnbsub~l-~SPb-n[2] ; j++) lstatus = CPXchgcoef (env, lp, (int) (SPb-m[21-LOWSPb,m[2] -HIS?b,m[ll -1-totlev2C+levS,count + (iter-count-2) l , j, LpS~[nb~subs1-~0MeL[j+H1SPbbnI21-SPb~nf21-~S~bbm[2~-~1~?b~n(1]]~ : 1 I lstatus = CPXchgcoef(env,lp, (=nt) (S?b-m[2]-LOWSPb-m[2] -HISPb-m[i] -l+cctlev2Ctlev2,count * titer-counc-2)1, j, LpSub[nb-subsl->OMeLIj+HfSPb-n[I!l); t Iscatus = CPXchgcoef (env. Ip, ( int) (SPb-m[2] -LOWSPb,m[S] -HISPb-n[l]-l~totlevZC+lev2,co~t + iter-counc-21, j, LpSub[nb,subs]-~PiD[j-S?b~n[2]-LSPbbm[2]-HISPb,n[~,s~s-l]+LSPb~n~2l 1 ) ; 1 lstatus = CPXchgcoef (env, Ip, ( int 1 (SPb-m [ 2 I -LOWSPb,m[2 ] -HISPbbm[ 11 -l+totlev2C+lev2,co~~t + iter-count-21, LpSub[Z]-~n+LSPb,m[2l+HISPbbn[nb_subs]-LSbn[2]+l, Theta-coef); short UpperBound (LpSubProb "LpSub) C ..., I3EFfNF IOCAL VARIiSLES AND XSKATE MPLFORIES ..... 1' Xeceive infonnacion of linking variables and constraints of other parts *I for(k=l; kLabjcoef, LSPb,n[k],T): info = pvm_rpkdauble (lpSub[k] ->LEP-bnds, LS?b,n [kl , 1) ; info = pvn_upkdouble(5pSub[k]-~L~o-bnds, LSPb,n[k],L); info = pvm-upklong(5pÇubikl -xLpfrcs, LSPb-n[k]rl, 1) ; Lnfo = pvn-upklong (LpSubik] ->mmmbs, LpSub[k] ->clpnts [LSPb,r?[kll, 1) ; info = pm-upkdo~le(lpSub[kl->coeffs, LpSub[k!->clpnts[SS?b,n[kII ,l); ... CO-T ORIGINAL DATA sense, objcoeffs and matcnt TO CONFORM CPLEX ..-. * Ncw copy the probkm data into the Lp '/ status=C?Xc3pylp (=v, lp, (kt) t~Sub[2] n , i n 5pSub[21 ->m. -I,cbjcoeffs, LpSub[2]->rbs,sense, tint*) (LpSub[2]->clpntsl, matcnt, (int*) LpSub[2]-~rwnmbs, LpS~[2i->c0eff~,LpSubI2]->I0~brrds, LpSub[2l->up,bnds, mu) ; l * Make the upper-~pper bomd sÿbproblem fo,?nat of the fizst iceration by deleting row zero and ocher partsr lickiog constraints. Md artificial
variables and add other part's linking variablese/ status = CPXdelrows lenv, lp, O, 0) ; if ( status ) { fprintf fstderr, "Failed to delete row O\nn); goto TERMINATE; 1 if (HISPb-mf 11 >= 11 status = CPXdelrows (env, lp, O, HISPb,m[ll-1) ; if (nb-subs > 2) status = CPXdelrows Lenv, lp, ( int) (SPb-m[2 1 -HISPb,m[l] -LOWSPb-m[2] -1) , (int) (SPb-n[2] -EISPb-m[L j-tl 1 ; status=CP.Ynewcols (env, lp, (int) LSPb-n[21, arti-obj , NULL, NULL, NULL, NEJLL) ; for (i=0: in) ri, arti-coef ; for (k=l; k 0) scatus = CP.uewcols cenv, lp, (int 1 LSPb-n[kl, LpSub[kJ ->Lobjcoef, LpSub [k] ->Llo,bnds, LpSub [k] ->Lup,bnds, NULL, N üUI ; ifiLpSub[kI -xwmbs[p] > SISPb-m[l] && LpSubIkI->rwnnbs[pj
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
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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
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The next result guarantees that in
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fonn a nondecreasing senes of lower
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one upper bound subproblem. The alg
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su, , for al1 i Note that when k= 1
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with proposals or cuts from other s
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- if t is an upper bound subproblem
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Proof : The Assumption guarantees t
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nNk-'. Proof : For i= 1.2. ... . N
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Chapter 5 Preliminary Implementatio
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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 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: short SolveProb(C3XEWptr env, CP.XL
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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