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stacus = CompuLY (LpSub) ; info = pvmqkdouble (&LpSub[2] -XX, 1,:) ; info = pvm~kdouble (LpSubi21->LY, ~ ISPb~nf~b~subs],~~; if (subtype [nb-subs] == 2 1 info = pvni~kdouble (alcy, HISPb-n[nb,subs] , 1) : info = pvm,senà(tid[lev2,bIockI ,SI; status = SolveProb if ( status 1 { goto TEFUYINATE; 1 env, Ip) ; (env. lp); pvm-iaitsena(RmDataRdwI ; inf O = pvn_~;kdo&le ( &ob jval [cur-block] , L , Il ; bufici = pi;m_sezd (cia[Levf-blockj,7); rdcl = myseccndsi=dtll; fprintf(fp, ' Receiving Sec up Data T he : i8f\nn, rdt1;lûOOOOO); .,.. Free up the prcblem as allccated by CPXcreaceprob, if necessary . - - .
C3 Proecssor 3 : Lower-Upper Bound SubproMem double *CompuLY(LpSubProb **LpSub, double *>oc) ..., COMPUTE BX AND LY .... return ( LpSub [cur-block] ->LY 1 ; 1 double CompuPiB(LpSubProb "LpSub, int *cscat, double 'pi, double *dj) C .... COMPUTE PIB .... return ( LpSub [cur,blockl ->PiB) ; 1 double *CompuPiD(LpSubProb **LpSub, double 'ppil t .... COMPüTE PID .... ret~n (LpSublcur,blockI ->PiD) ; 1 double *CompuOMeL(ipSubProb "LpSub, double *?pi) i .... COMPUTE OKEL .... return(LpSub[cur-blockl->OMeL); 1 /* Add initial columns of the linking variables of lower-loner bound subproblem of the first Fteration */ int LSecaddcok(LpSubProb "SpSub, CP.YENVptr env, CPXL?ptr lp) i int f, p, k. status=l; i iftLSPb-nIll > 0) status = ClL~ewcûls (env, lp, LSPb-n [l 1 , LpSub [l ! ->Lob jcoef , tpSub[lj->llo-bnds, LpSub[l]->Lup,bnds,h'UU, 2RLL) ; ? recu3 t status 1 ; : Add a lada colun fûr primai icfaraacion coming £rom aggregated upper bound subproblem *! izt Ad&arncols(LpSub?rob "LpSub, CXEWpcr eov, CPXLPptr Ip, int icer-count)
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
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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
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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
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NB,~,PEI 8 # Selectmg the rows ROWS
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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 and 154: short SolveProb(C3XEWptr env, CP.XL
Page 155 and 156: variables and add other part's link
Page 157: i* Add a cut for upper level iterat
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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