void compute_thvec(void) /* simplest model */
{
compute_theta( nvec,xvec,yvec , ctvec,stvec ) ;
}
compute_thvim(void)
{
compute_theta( nvim,xvim,yvim , ctvim,stvim ) ;
}
STATIC int dualloop(lprec *lp, MYBOOL feasible)
{
int i, ok = TRUE;
LREAL theta = 0.0;
REAL *drow = NULL, *prow = NULL, *pcol = NULL, prevobj, epsvalue;
MYBOOL primal = FALSE, forceoutEQ = FALSE;
MYBOOL minit, pivdynamic, bfpfinal = FALSE;
int oldpivrule, oldpivmode, pivrule, Blandswitches,
colnr, rownr, lastnr, minitcount = 0;
int Rcycle = 0, Ccycle = 0, Ncycle = 0, changedphase = TRUE;
#ifdef FixInaccurateDualMinit
int minitcolnr = 0;
#endif
int *nzprow = NULL, *workINT = NULL;
if(lp->spx_trace)
report(lp, DETAILED, "Entering dual simplex algorithm\n");
/* Set Extrad value to force dual feasibility; reset when
"local optimality" has been achieved or a dual non-feasibility
has been encountered (no candidate for a first leaving variable) */
if(feasible)
lp->Extrad = 0;
else
lp->Extrad = feasibilityOffset(lp, (MYBOOL)!primal);
if(lp->spx_trace)
report(lp, DETAILED, "Extrad = %g\n", (double)lp->Extrad);
/* Allocate work arrays */
allocREAL(lp, &drow, lp->sum + 1, TRUE);
#ifdef UseSparseReducedCost
allocINT(lp, &nzprow, lp->sum + 1, FALSE);
#endif
allocREAL(lp, &prow, lp->sum + 1, TRUE);
allocREAL(lp, &pcol, lp->rows + 1, TRUE);
/* Refactorize the basis and set status variables */
i = my_if(is_bb_action(lp, ACTION_REBASE), INITSOL_SHIFTZERO, INITSOL_USEZERO);
if(((lp->spx_status == SWITCH_TO_DUAL) && !lp->justInverted) ||
(lp->Extrad != 0) ||
is_bb_action(lp, ACTION_REINVERT)) {
simplexPricer(lp, (MYBOOL)!primal);
/* Do basis crashing before refactorization, if specified */
invert(lp, (MYBOOL) i, TRUE);
}
else {
if(is_bb_action(lp, ACTION_RECOMPUTE))
recompute_solution(lp, (MYBOOL) i);
restartPricer(lp, (MYBOOL)!primal);
}
lp->bb_action = ACTION_NONE;
lp->spx_status = RUNNING;
lp->doIterate = FALSE;
minit = ITERATE_MAJORMAJOR;
prevobj = lp->rhs[0];
oldpivmode = lp->piv_strategy;
oldpivrule = get_piv_rule(lp);
pivdynamic = ANTICYCLEBLAND && is_piv_mode(lp, PRICE_ADAPTIVE);
epsvalue = lp->epspivot;
Blandswitches = 0;
rownr = 0;
colnr = -1; /* Used to detect infeasibility at the beginning of the dual loop */
lastnr = 0;
lp->rejectpivot[0] = 0;
if(feasible)
lp->simplex_mode = SIMPLEX_Phase2_DUAL;
else
lp->simplex_mode = SIMPLEX_Phase1_DUAL;
/* Check if we have equality slacks in the basis and we should try to
drive them out in order to reduce chance of degeneracy in Phase 1 */
if(!feasible && (lp->fixedvars > 0) && is_anti_degen(lp, ANTIDEGEN_FIXEDVARS)) {
forceoutEQ = AUTOMATIC;
}
while(lp->spx_status == RUNNING) {
if(lp->spx_trace)
if(lastnr > 0)
report(lp, NORMAL, "dualloop: Objective at iteration %8d is " RESULTVALUEMASK " (%4d: %4d %s- %4d)\n",
get_total_iter(lp), lp->rhs[0], rownr, lastnr,
my_if(minit == ITERATE_MAJORMAJOR, "<","|"), colnr);
pivrule = get_piv_rule(lp);
if(pivdynamic && ((pivrule != PRICER_FIRSTINDEX) ||
(pivrule != oldpivrule))
#if DualPivotStickiness==2
/* Stays with pricing rule as long as possible (also preserves accuracy) */
&& (lp->fixedvars == 0)
#elif DualPivotStickiness==1
/* Stays with pricing rule only if the model is infeasible */
&& feasible
#endif
) {
/* Check if we have a stationary solution */
if((minit == ITERATE_MAJORMAJOR) && !lp->justInverted &&
(fabs(my_reldiff(lp->rhs[0], prevobj)) < epsvalue)) {
Ncycle++;
/* Start to monitor for variable cycling if this is the initial stationarity */
if(Ncycle <= 1) {
Ccycle = colnr;
Rcycle = rownr;
}
/* Check if we should change pivoting strategy due to stationary variable cycling */
else if((pivrule == oldpivrule) && (((MAX_STALLCOUNT > 1) && (Ncycle > MAX_STALLCOUNT)) ||
(Ccycle == rownr) || (Rcycle == colnr))) {
/* First check if we should give up on Bland's rule and try perturbed bound
relaxation instead */
#ifdef EnableStallAntiDegen
if((MAX_BLANDSWITCH >= 0) && (Blandswitches >= MAX_BLANDSWITCH)) {
lp->spx_status = DEGENERATE;
break;
}
#endif
Blandswitches++;
lp->piv_strategy = PRICER_FIRSTINDEX; /* There is no advanced normalization for Bland's rule, restart at end */
Ccycle = 0;
Rcycle = 0;
Ncycle = 0;
if(lp->spx_trace)
report(lp, DETAILED, "dualloop: Detected cycling at iteration %d; changed to FIRST INDEX rule!\n",
get_total_iter(lp));
}
}
/* Handle cycling or stationary situations by switching to the primal simplex */
else if((pivrule == oldpivrule) && feasible && (lp->simplex_strategy & SIMPLEX_DYNAMIC)) {
lp->spx_status = SWITCH_TO_PRIMAL;
break;
}
/* Change back to original selection strategy as soon as possible */
else if((minit == ITERATE_MAJORMAJOR) && (pivrule != oldpivrule)) {
lp->piv_strategy = oldpivmode;
restartPricer(lp, AUTOMATIC); /* Pricer restart following Bland's rule */
Ccycle = 0;
Rcycle = 0;
Ncycle = 0;
if(lp->spx_trace)
report(lp, DETAILED, "...returned to original pivot selection rule at iteration %d.\n",
get_total_iter(lp));
}
}
/* Store current LP value for reference at next iteration */
changedphase = FALSE;
prevobj = lp->rhs[0];
lastnr = lp->var_basic[rownr];
lp->doInvert = FALSE;
/* Do minor iterations (non-basic variable bound switches) for as
long as possible since this is a cheap way of iterating */
#ifdef Phase1DualPriceEqualities
RetryRow:
#endif
if(minit != ITERATE_MINORRETRY) {
/* forceoutEQ
FALSE : Only eliminate assured "good" violated equality constraint slacks
AUTOMATIC: Seek more elimination of equality constraint slacks
(but not as aggressive as the rule used in lp_solve v4.0 and earlier)
TRUE: Force remaining equality slacks out of the basis */
i = 0;
do {
if(partial_countBlocks(lp, (MYBOOL) !primal) > 1)
partial_blockStep(lp, (MYBOOL) !primal);
rownr = rowdual(lp, forceoutEQ);
i++;
} while ((rownr == 0) && (i < partial_countBlocks(lp, (MYBOOL) !primal)));
lastnr = lp->var_basic[rownr];
}
if(rownr > 0) {
#ifdef UseRejectionList
RetryCol:
#endif
lp->doIterate = FALSE;
colnr = coldual(lp, rownr, (MYBOOL)(minit == ITERATE_MINORRETRY),
prow, nzprow, drow, NULL);
if(colnr > 0) {
lp->doIterate = TRUE;
fsolve(lp, colnr, pcol, workINT, lp->epsmachine, 1.0, TRUE);
#ifdef FixInaccurateDualMinit
/* Prevent bound flip-flops during minor iterations; used to detect
infeasibility after triggering of minor iteration accuracy management */
if(colnr != minitcolnr)
minitcolnr = 0;
#endif
/* Getting division by zero here; catch it and try to recover */
if(pcol[rownr] == 0) {
if(lp->spx_trace)
report(lp, DETAILED, "dualloop: Attempt to divide by zero (pcol[%d])\n", rownr);
lp->doIterate = FALSE;
if(!lp->justInverted) {
report(lp, DETAILED, "...trying to recover by reinverting!\n");
lp->doInvert = TRUE;
bfpfinal = FALSE;
}
#ifdef UseRejectionList
else if(lp->rejectpivot[0] < DEF_MAXPIVOTRETRY) {
lp->rejectpivot[0]++;
lp->rejectpivot[lp->rejectpivot[0]] = colnr;
if(lp->bb_totalnodes == 0)
report(lp, DETAILED, "...trying to recover via another pivot column!\n");
goto RetryCol;
}
#endif
else {
if(lp->bb_totalnodes == 0)
report(lp, DETAILED, "...cannot recover by reinverting.\n");
lp->spx_status = NUMFAILURE;
ok = FALSE;
}
}
else {
lp->rejectpivot[0] = 0;
theta = lp->bfp_prepareupdate(lp, rownr, colnr, pcol);
/* Verify numeric accuracy of the inverse and change to
the "theoretically" correct version of the theta */
if((lp->improve & IMPROVE_INVERSE) &&
(my_reldiff(fabs(theta),fabs(prow[colnr])) >
lp->epspivot*10.0*log(2.0+50.0*lp->rows))) {
lp->doInvert = TRUE;
bfpfinal = TRUE;
#ifdef IncreasePivotOnReducedAccuracy
if(lp->bfp_pivotcount(lp) < 2*DEF_MAXPIVOTRETRY)
lp->epspivot *= 2.0;
#endif
report(lp, DETAILED, "dualloop: Refactorizing at iteration %d due to loss of accuracy.\n",
get_total_iter(lp));
}
theta = prow[colnr];
compute_theta(lp, rownr, &theta, !lp->is_lower[colnr], 0, primal);
}
}
#ifdef FixInaccurateDualMinit
/* Reinvert and try another row if we did not find a bound-violated leaving column */
else if((minit != ITERATE_MAJORMAJOR) && (colnr != minitcolnr)) {
minitcolnr = colnr;
lp->doInvert = TRUE;
i = invert(lp, INITSOL_USEZERO, TRUE);
if((lp->spx_status == USERABORT) || (lp->spx_status == TIMEOUT))
break;
else if(!i) {
lp->spx_status = SINGULAR_BASIS;
break;
}
minit = ITERATE_MAJORMAJOR;
continue;
}
#endif
else {
if(lp->justInverted && (lp->simplex_mode == SIMPLEX_Phase2_DUAL))
lp->spx_status = LOSTFEAS;
#if 1
else if(!lp->justInverted && (lp->bb_level <= 1)) {
#else
else if(!lp->justInverted) {
#endif
lp->doIterate = FALSE;
lp->doInvert = TRUE;
bfpfinal = TRUE;
}
else {
if((lp->spx_trace && (lp->bb_totalnodes == 0)) ||
(lp->bb_trace && (lp->bb_totalnodes > 0)))
report(lp, DETAILED, "Model lost dual feasibility.\n");
lp->spx_status = INFEASIBLE;
ok = FALSE;
break;
}
}
}
else {
/* New code to solve to optimality using the dual, but only if the user
has specified a preference for the dual simplex - KE added 20030731 */
lp->doIterate = FALSE;
bfpfinal = TRUE;
if((lp->Extrad != 0) && (colnr < 0) && !isPrimalFeasible(lp, lp->epsprimal)) {
if(feasible) {
if(lp->bb_totalnodes == 0)
report(lp, DETAILED, "Model is dual infeasible and primal feasible\n");
lp->spx_status = SWITCH_TO_PRIMAL;
lp->doInvert = (MYBOOL) (lp->Extrad != 0);
lp->Extrad = 0;
}
else {
if(lp->bb_totalnodes == 0)
report(lp, NORMAL, "Model is primal and dual infeasible\n");
lp->spx_status = INFEASIBLE;
ok = FALSE;
}
break;
}
else if(lp->Extrad == 0) {
/* We are feasible (and possibly also optimal) */
feasible = TRUE;
lp->simplex_mode = SIMPLEX_Phase2_DUAL;
/* Check if we still have equality slacks stuck in the basis; drive them out? */
if((lp->fixedvars > 0) && lp->bb_totalnodes == 0)
#ifdef Paranoia
report(lp, NORMAL,
#else
report(lp, DETAILED,
#endif
"Found dual solution with %d fixed slack variables left basic\n",
lp->fixedvars);
#ifdef Phase1DualPriceEqualities
if(forceoutEQ != TRUE) {
forceoutEQ = TRUE;
goto RetryRow;
}
colnr = 0;
#else
#if 1
/* Problem: Check if we are dual degenerate and need to switch to the
primal simplex (there is a flaw in the dual simplex code) */
colnr = colprim(lp, FALSE, drow, nzprow);
#else
colnr = 0;
#endif
#endif
if(colnr == 0)
lp->spx_status = OPTIMAL;
else {
lp->spx_status = SWITCH_TO_PRIMAL;
if(lp->total_iter == 0)
report(lp, NORMAL, "Use primal simplex for finalization at iteration %8d\n",
get_total_iter(lp));
}
if((lp->total_iter == 0) && (lp->spx_status == OPTIMAL))
report(lp, NORMAL, "Optimal solution with dual simplex at iteration %8d\n",
get_total_iter(lp));
break;
}
else {
