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lp_simplex.c
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lp_simplex.c
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/*
Core optimization drivers for lp_solve v5.0+
----------------------------------------------------------------------------------
Author: Michel Berkelaar (to lp_solve v3.2),
Kjell Eikland (v4.0 and forward)
Contact:
License terms: LGPL.
Requires: lp_lib.h, lp_simplex.h, lp_presolve.h, lp_pricerPSE.h
Release notes:
v5.0.0 1 January 2004 New unit applying stacked basis and bounds storage.
v5.0.1 31 January 2004 Moved B&B routines to separate file and implemented
a new runsolver() general purpose call method.
v5.0.2 1 May 2004 Changed routine names to be more intuitive.
v5.1.0 10 January 2005 Created modular stalling/cycling functions.
Rewrote dualloop() to optimize long dual and
also streamlined primloop() correspondingly.
v5.2.0 20 March 2005 Reimplemented primal phase 1 logic.
Made multiple pricing finally work (primal simplex).
----------------------------------------------------------------------------------
*/
#include <string.h>
#include "commonlib.h"
#include "lp_lib.h"
#include "lp_BFP.h"
#include "lp_simplex.h"
#include "lp_crash.h"
#include "lp_presolve.h"
#include "lp_price.h"
#include "lp_pricePSE.h"
#include "lp_report.h"
#ifdef FORTIFY
# include "lp_fortify.h"
#endif
STATIC void stallMonitor_update(lprec *lp, REAL newOF)
{
int newpos;
OBJmonrec *monitor = lp->monitor;
if(monitor->countstep < OBJ_STEPS)
monitor->countstep++;
else
monitor->startstep = mod(monitor->startstep + 1, OBJ_STEPS);
newpos = mod(monitor->startstep + monitor->countstep - 1, OBJ_STEPS);
monitor->objstep[newpos] = newOF;
monitor->idxstep[newpos] = monitor->Icount;
monitor->currentstep = newpos;
}
STATIC MYBOOL stallMonitor_creepingObj(lprec *lp)
{
OBJmonrec *monitor = lp->monitor;
if(monitor->countstep > 1) {
REAL deltaOF = (monitor->objstep[monitor->currentstep] -
monitor->objstep[monitor->startstep]) / monitor->countstep;
deltaOF /= MAX(1, (monitor->idxstep[monitor->currentstep] -
monitor->idxstep[monitor->startstep]));
deltaOF = my_chsign(monitor->isdual, deltaOF);
return( (MYBOOL) (deltaOF < monitor->epsvalue) );
}
else
return( FALSE );
}
STATIC MYBOOL stallMonitor_shortSteps(lprec *lp)
{
OBJmonrec *monitor = lp->monitor;
if(monitor->countstep == OBJ_STEPS) {
REAL deltaOF = MAX(1, (monitor->idxstep[monitor->currentstep] -
monitor->idxstep[monitor->startstep])) / monitor->countstep;
deltaOF = pow(deltaOF*OBJ_STEPS, 0.66);
return( (MYBOOL) (deltaOF > monitor->limitstall[TRUE]) );
}
else
return( FALSE );
}
STATIC void stallMonitor_reset(lprec *lp)
{
OBJmonrec *monitor = lp->monitor;
monitor->ruleswitches = 0;
monitor->Ncycle = 0;
monitor->Mcycle = 0;
monitor->Icount = 0;
monitor->startstep = 0;
monitor->objstep[monitor->startstep] = lp->infinite;
monitor->idxstep[monitor->startstep] = monitor->Icount;
monitor->prevobj = 0;
monitor->countstep = 1;
}
STATIC MYBOOL stallMonitor_create(lprec *lp, MYBOOL isdual, char *funcname)
{
OBJmonrec *monitor = NULL;
if(lp->monitor != NULL)
return( FALSE );
monitor = (OBJmonrec *) calloc(sizeof(*monitor), 1);
if(monitor == NULL)
return( FALSE );
monitor->lp = lp;
strcpy(monitor->spxfunc, funcname);
monitor->isdual = isdual;
monitor->pivdynamic = is_piv_mode(lp, PRICE_ADAPTIVE);
monitor->oldpivstrategy = lp->piv_strategy;
monitor->oldpivrule = get_piv_rule(lp);
if(MAX_STALLCOUNT <= 1)
monitor->limitstall[FALSE] = 0;
else
monitor->limitstall[FALSE] = MAX(MAX_STALLCOUNT,
(int) pow((REAL) (lp->rows+lp->columns)/2, 0.667));
#if 1
monitor->limitstall[FALSE] *= 2+2; /* Expand degeneracy/stalling tolerance range */
#endif
monitor->limitstall[TRUE] = monitor->limitstall[FALSE];
if(monitor->oldpivrule == PRICER_DEVEX) /* Increase tolerance since primal Steepest Edge is expensive */
monitor->limitstall[TRUE] *= 2;
if(MAX_RULESWITCH <= 0)
monitor->limitruleswitches = MAXINT32;
else
monitor->limitruleswitches = MAX(MAX_RULESWITCH,
lp->rows/MAX_RULESWITCH);
monitor->epsvalue = lp->epsprimal; /* lp->epsvalue; */
lp->monitor = monitor;
stallMonitor_reset(lp);
lp->suminfeas = lp->infinite;
return( TRUE );
}
STATIC MYBOOL stallMonitor_check(lprec *lp, int rownr, int colnr, int lastnr,
MYBOOL minit, MYBOOL approved, MYBOOL *forceoutEQ)
{
OBJmonrec *monitor = lp->monitor;
MYBOOL isStalled, isCreeping, acceptance = TRUE;
int altrule,
#ifdef Paranoia
msglevel = NORMAL;
#else
msglevel = DETAILED;
#endif
REAL deltaobj = lp->suminfeas;
/* Accept unconditionally if this is the first or second call */
monitor->active = FALSE;
if(monitor->Icount <= 1) {
if(monitor->Icount == 1) {
monitor->prevobj = lp->rhs[0];
monitor->previnfeas = deltaobj;
}
monitor->Icount++;
return( acceptance );
}
/* Define progress as primal objective less sum of (primal/dual) infeasibilities */
monitor->thisobj = lp->rhs[0];
monitor->thisinfeas = deltaobj;
if(lp->spx_trace &&
(lastnr > 0))
report(lp, NORMAL, "%s: Objective at iter %10.0f is " RESULTVALUEMASK " (%4d: %4d %s- %4d)\n",
monitor->spxfunc,
(double) get_total_iter(lp), monitor->thisobj, rownr, lastnr,
my_if(minit == ITERATE_MAJORMAJOR, "<","|"), colnr);
monitor->pivrule = get_piv_rule(lp);
/* Check if we have a stationary solution at selected tolerance level;
allow some difference in case we just refactorized the basis. */
deltaobj = my_reldiff(monitor->thisobj, monitor->prevobj);
deltaobj = fabs(deltaobj); /* Pre v5.2 version */
isStalled = (MYBOOL) (deltaobj < monitor->epsvalue);
/* Also require that we have a measure of infeasibility-stalling */
if(isStalled) {
REAL testvalue, refvalue = monitor->epsvalue;
#if 1
if(monitor->isdual)
refvalue *= 1000*log10(9.0+lp->rows);
else
refvalue *= 1000*log10(9.0+lp->columns);
#else
refvalue *= 1000*log10(9.0+lp->sum);
#endif
testvalue = my_reldiff(monitor->thisinfeas, monitor->previnfeas);
isStalled &= (fabs(testvalue) < refvalue);
/* Check if we should force "major" pivoting, i.e. no bound flips;
this is activated when we see the feasibility deteriorate */
/* if(!isStalled && (testvalue > 0) && (TRUE || is_action(lp->anti_degen, ANTIDEGEN_BOUNDFLIP))) */
#if !defined _PRICE_NOBOUNDFLIP
if(!isStalled && (testvalue > 0) && is_action(lp->anti_degen, ANTIDEGEN_BOUNDFLIP))
acceptance = AUTOMATIC;
}
#else
if(!isStalled && (testvalue > 0) && !ISMASKSET(lp->piv_strategy, PRICE_NOBOUNDFLIP)) {
SETMASK(lp->piv_strategy, PRICE_NOBOUNDFLIP);
acceptance = AUTOMATIC;
}
}
else
CLEARMASK(lp->piv_strategy, PRICE_NOBOUNDFLIP);
#endif
#if 1
isCreeping = FALSE;
#else
isCreeping |= stallMonitor_creepingObj(lp);
/* isCreeping |= stallMonitor_shortSteps(lp); */
#endif
if(isStalled || isCreeping) {
/* Update counters along with specific tolerance for bound flips */
#if 1
if(minit != ITERATE_MAJORMAJOR) {
if(++monitor->Mcycle > 2) {
monitor->Mcycle = 0;
monitor->Ncycle++;
}
}
else
#endif
monitor->Ncycle++;
/* Start to monitor for variable cycling if this is the initial stationarity */
if(monitor->Ncycle <= 1) {
monitor->Ccycle = colnr;
monitor->Rcycle = rownr;
}
/* Check if we should change pivoting strategy */
else if(isCreeping || /* We have OF creep */
(monitor->Ncycle > monitor->limitstall[monitor->isdual]) || /* KE empirical value */
((monitor->Ccycle == rownr) && (monitor->Rcycle == colnr))) { /* Obvious cycling */
monitor->active = TRUE;
/* Try to force out equality slacks to combat degeneracy */
if((lp->fixedvars > 0) && (*forceoutEQ != TRUE)) {
*forceoutEQ = TRUE;
goto Proceed;
}
/* Our options are now to select an alternative rule or to do bound perturbation;
check if these options are available to us or if we must signal failure and break out. */
approved &= monitor->pivdynamic && (monitor->ruleswitches < monitor->limitruleswitches);
if(!approved && !is_anti_degen(lp, ANTIDEGEN_STALLING)) {
lp->spx_status = DEGENERATE;
report(lp, msglevel, "%s: Stalling at iter %10.0f; no alternative strategy left.\n",
monitor->spxfunc, (double) get_total_iter(lp));
acceptance = FALSE;
return( acceptance );
}
/* See if we can do the appropriate alternative rule. */
switch (monitor->oldpivrule) {
case PRICER_FIRSTINDEX: altrule = PRICER_DEVEX;
break;
case PRICER_DANTZIG: altrule = PRICER_DEVEX;
break;
case PRICER_DEVEX: altrule = PRICER_STEEPESTEDGE;
break;
case PRICER_STEEPESTEDGE: altrule = PRICER_DEVEX;
break;
default: altrule = PRICER_FIRSTINDEX;
}
if(approved &&
(monitor->pivrule != altrule) && (monitor->pivrule == monitor->oldpivrule)) {
/* Switch rule to combat degeneracy. */
monitor->ruleswitches++;
lp->piv_strategy = altrule;
monitor->Ccycle = 0;
monitor->Rcycle = 0;
monitor->Ncycle = 0;
monitor->Mcycle = 0;
report(lp, msglevel, "%s: Stalling at iter %10.0f; changed to '%s' rule.\n",
monitor->spxfunc, (double) get_total_iter(lp),
get_str_piv_rule(get_piv_rule(lp)));
if((altrule == PRICER_DEVEX) || (altrule == PRICER_STEEPESTEDGE))
restartPricer(lp, AUTOMATIC);
}
/* If not, code for bound relaxation/perturbation */
else {
report(lp, msglevel, "%s: Stalling at iter %10.0f; proceed to bound relaxation.\n",
monitor->spxfunc, (double) get_total_iter(lp));
acceptance = FALSE;
lp->spx_status = DEGENERATE;
return( acceptance );
}
}
}
/* Otherwise change back to original selection strategy as soon as possible */
else {
if(monitor->pivrule != monitor->oldpivrule) {
lp->piv_strategy = monitor->oldpivstrategy;
altrule = monitor->oldpivrule;
if((altrule == PRICER_DEVEX) || (altrule == PRICER_STEEPESTEDGE))
restartPricer(lp, AUTOMATIC);
report(lp, msglevel, "...returned to original pivot selection rule at iter %.0f.\n",
(double) get_total_iter(lp));
}
stallMonitor_update(lp, monitor->thisobj);
monitor->Ccycle = 0;
monitor->Rcycle = 0;
monitor->Ncycle = 0;
monitor->Mcycle = 0;
}
/* Update objective progress tracker */
Proceed:
monitor->Icount++;
if(deltaobj >= monitor->epsvalue)
monitor->prevobj = monitor->thisobj;
monitor->previnfeas = monitor->thisinfeas;
return( acceptance );
}
STATIC void stallMonitor_finish(lprec *lp)
{
OBJmonrec *monitor = lp->monitor;
if(monitor == NULL)
return;
if(lp->piv_strategy != monitor->oldpivstrategy)
lp->piv_strategy = monitor->oldpivstrategy;
FREE(monitor);
lp->monitor = NULL;
}
STATIC MYBOOL add_artificial(lprec *lp, int forrownr, REAL *nzarray, int *idxarray)
/* This routine is called for each constraint at the start of
primloop and the primal problem is infeasible. Its
purpose is to add artificial variables and associated
objective function values to populate primal phase 1. */
{
MYBOOL add;
/* Make sure we don't add unnecessary artificials, i.e. avoid
cases where the slack variable is enough */
add = !isBasisVarFeasible(lp, lp->epspivot, forrownr);
if(add) {
int *rownr = NULL, i, bvar, ii;
REAL *avalue = NULL, rhscoef, acoef;
MATrec *mat = lp->matA;
/* Check the simple case where a slack is basic */
for(i = 1; i <= lp->rows; i++) {
if(lp->var_basic[i] == forrownr)
break;
}
acoef = 1;
/* If not, look for any basic user variable that has a
non-zero coefficient in the current constraint row */
if(i > lp->rows) {
for(i = 1; i <= lp->rows; i++) {
ii = lp->var_basic[i] - lp->rows;
if((ii <= 0) || (ii > (lp->columns-lp->P1extraDim)))
continue;
ii = mat_findelm(mat, forrownr, ii);
if(ii >= 0) {
acoef = COL_MAT_VALUE(ii);
break;
}
}
}
/* If no candidate was found above, gamble on using the densest column available */
#if 0
if(i > lp->rows) {
int len = 0;
bvar = 0;
for(i = 1; i <= lp->rows; i++) {
ii = lp->var_basic[i] - lp->rows;
if((ii <= 0) || (ii > (lp->columns-lp->P1extraDim)))
continue;
if(mat_collength(mat, ii) > len) {
len = mat_collength(mat, ii);
bvar = i;
}
}
i = bvar;
acoef = 1;
}
#endif
bvar = i;
add = (MYBOOL) (bvar <= lp->rows);
if(add) {
rhscoef = lp->rhs[forrownr];
/* Create temporary sparse array storage */
if(nzarray == NULL)
allocREAL(lp, &avalue, 2, FALSE);
else
avalue = nzarray;
if(idxarray == NULL)
allocINT(lp, &rownr, 2, FALSE);
else
rownr = idxarray;
/* Set the objective coefficient */
rownr[0] = 0;
avalue[0] = my_chsign(is_chsign(lp, 0), 1);
/* Set the constraint row coefficient */
rownr[1] = forrownr;
avalue[1] = my_chsign(is_chsign(lp, forrownr), my_sign(rhscoef/acoef));
/* Add the column of artificial variable data to the user data matrix */
add_columnex(lp, 2, avalue, rownr);
/* Free the temporary sparse array storage */
if(idxarray == NULL)
FREE(rownr);
if(nzarray == NULL)
FREE(avalue);
/* Now set the artificial variable to be basic */
set_basisvar(lp, bvar, lp->sum);
lp->P1extraDim++;
}
else {
report(lp, CRITICAL, "add_artificial: Could not find replacement basis variable for row %d\n",
forrownr);
lp->basis_valid = FALSE;
}
}
return(add);
}
STATIC int get_artificialRow(lprec *lp, int colnr)
{
MATrec *mat = lp->matA;
#ifdef Paranoia
if((colnr <= lp->columns-abs(lp->P1extraDim)) || (colnr > lp->columns))
report(lp, SEVERE, "get_artificialRow: Invalid column index %d\n", colnr);
if(mat->col_end[colnr] - mat->col_end[colnr-1] != 1)
report(lp, SEVERE, "get_artificialRow: Invalid column non-zero count\n");
#endif
/* Return the row index of the singleton */
colnr = mat->col_end[colnr-1];
colnr = COL_MAT_ROWNR(colnr);
return( colnr );
}
STATIC int findAnti_artificial(lprec *lp, int colnr)
/* Primal simplex: Find a basic artificial variable to swap
against the non-basic slack variable, if possible */
{
int i, k, rownr = 0, P1extraDim = abs(lp->P1extraDim);
if((P1extraDim == 0) || (colnr > lp->rows) || !lp->is_basic[colnr])
return( rownr );
for(i = 1; i <= lp->rows; i++) {
k = lp->var_basic[i];
if((k > lp->sum-P1extraDim) && (lp->rhs[i] == 0)) {
rownr = get_artificialRow(lp, k-lp->rows);
/* Should we find the artificial's slack direct "antibody"? */
if(rownr == colnr)
break;
rownr = 0;
}
}
return( rownr );
}
STATIC int findBasicArtificial(lprec *lp, int before)
{
int i = 0, P1extraDim = abs(lp->P1extraDim);
if(P1extraDim > 0) {
if(before > lp->rows || before <= 1)
i = lp->rows;
else
i = before;
while((i > 0) && (lp->var_basic[i] <= lp->sum-P1extraDim))
i--;
}
return(i);
}
STATIC void eliminate_artificials(lprec *lp, REAL *prow)
{
int i, j, colnr, rownr, P1extraDim = abs(lp->P1extraDim);
for(i = 1; (i <= lp->rows) && (P1extraDim > 0); i++) {
j = lp->var_basic[i];
if(j <= lp->sum-P1extraDim)
continue;
j -= lp->rows;
rownr = get_artificialRow(lp, j);
colnr = find_rowReplacement(lp, rownr, prow, NULL);
#if 0
performiteration(lp, rownr, colnr, 0.0, TRUE, FALSE, prow, NULL,
NULL, NULL, NULL);
#else
set_basisvar(lp, rownr, colnr);
#endif
del_column(lp, j);
P1extraDim--;
}
lp->P1extraDim = 0;
}
STATIC void clear_artificials(lprec *lp)
{
int i, j, n, P1extraDim;
/* Substitute any basic artificial variable for its slack counterpart */
n = 0;
P1extraDim = abs(lp->P1extraDim);
for(i = 1; (i <= lp->rows) && (n < P1extraDim); i++) {
j = lp->var_basic[i];
if(j <= lp->sum-P1extraDim)
continue;
j = get_artificialRow(lp, j-lp->rows);
set_basisvar(lp, i, j);
n++;
}
#ifdef Paranoia
if(n != lp->P1extraDim)
report(lp, SEVERE, "clear_artificials: Unable to clear all basic artificial variables\n");
#endif
/* Delete any remaining non-basic artificial variables */
while(P1extraDim > 0) {
i = lp->sum-lp->rows;
del_column(lp, i);
P1extraDim--;
}
lp->P1extraDim = 0;
if(n > 0) {
set_action(&lp->spx_action, ACTION_REINVERT);
lp->basis_valid = TRUE;
}
}
STATIC int primloop(lprec *lp, MYBOOL primalfeasible, REAL primaloffset)
{
MYBOOL primal = TRUE, bfpfinal = FALSE, changedphase = FALSE, forceoutEQ = AUTOMATIC,
primalphase1, pricerCanChange, minit, stallaccept, pendingunbounded;
int i, j, k, colnr = 0, rownr = 0, lastnr = 0,
candidatecount = 0, minitcount = 0, ok = TRUE;
LREAL theta = 0.0;
REAL epsvalue, xviolated = 0.0, cviolated = 0.0,
*prow = NULL, *pcol = NULL,
*drow = lp->drow;
int *workINT = NULL,
*nzdrow = lp->nzdrow;
if(lp->spx_trace)
report(lp, DETAILED, "Entered primal simplex algorithm with feasibility %s\n",
my_boolstr(primalfeasible));
/* Add sufficent number of artificial variables to make the problem feasible
through the first phase; delete when primal feasibility has been achieved */
lp->P1extraDim = 0;
if(!primalfeasible) {
lp->simplex_mode = SIMPLEX_Phase1_PRIMAL;
#ifdef Paranoia
if(!verify_basis(lp))
report(lp, SEVERE, "primloop: No valid basis for artificial variables\n");
#endif
#if 0
/* First check if we can get away with a single artificial variable */
if(lp->equalities == 0) {
i = (int) feasibilityOffset(lp, !primal);
add_artificial(lp, i, prow, (int *) pcol);
}
else
#endif
/* Otherwise add as many artificial variables as is necessary
to force primal feasibility. */
for(i = 1; i <= lp->rows; i++) {
add_artificial(lp, i, NULL, NULL);
}
/* Make sure we update the working objective */
if(lp->P1extraDim > 0) {
#if 1 /* v5.1 code: Not really necessary since we do not price the artificial
variables (stored at the end of the column list, they are initially
basic and are never allowed to enter the basis, once they exit) */
ok = allocREAL(lp, &(lp->drow), lp->sum+1, AUTOMATIC) &&
allocINT(lp, &(lp->nzdrow), lp->sum+1, AUTOMATIC);
if(!ok)
goto Finish;
lp->nzdrow[0] = 0;
drow = lp->drow;
nzdrow = lp->nzdrow;
#endif
mat_validate(lp->matA);
set_OF_p1extra(lp, 0.0);
}
if(lp->spx_trace)
report(lp, DETAILED, "P1extraDim count = %d\n", lp->P1extraDim);
simplexPricer(lp, (MYBOOL)!primal);
invert(lp, INITSOL_USEZERO, TRUE);
}
else {
lp->simplex_mode = SIMPLEX_Phase2_PRIMAL;
restartPricer(lp, (MYBOOL)!primal);
}
/* Create work arrays and optionally the multiple pricing structure */
ok = allocREAL(lp, &(lp->bsolveVal), lp->rows + 1, FALSE) &&
allocREAL(lp, &prow, lp->sum + 1, TRUE) &&
allocREAL(lp, &pcol, lp->rows + 1, TRUE);
if(is_piv_mode(lp, PRICE_MULTIPLE) && (lp->multiblockdiv > 1)) {
lp->multivars = multi_create(lp, FALSE);
ok &= (lp->multivars != NULL) &&
multi_resize(lp->multivars, lp->sum / lp->multiblockdiv, 2, FALSE, TRUE);
}
if(!ok)
goto Finish;
/* Initialize regular primal simplex algorithm variables */
lp->spx_status = RUNNING;
minit = ITERATE_MAJORMAJOR;
epsvalue = lp->epspivot;
pendingunbounded = FALSE;
ok = stallMonitor_create(lp, FALSE, "primloop");
if(!ok)
goto Finish;
lp->rejectpivot[0] = 0;
/* Iterate while we are successful; exit when the model is infeasible/unbounded,
or we must terminate due to numeric instability or user-determined reasons */
while((lp->spx_status == RUNNING) && !userabort(lp, -1)) {
primalphase1 = (MYBOOL) (lp->P1extraDim > 0);
clear_action(&lp->spx_action, ACTION_REINVERT | ACTION_ITERATE);
/* Check if we have stalling (from numerics or degenerate cycling) */
pricerCanChange = !primalphase1;
stallaccept = stallMonitor_check(lp, rownr, colnr, lastnr, minit, pricerCanChange, &forceoutEQ);
if(!stallaccept)
break;
/* Find best column to enter the basis */
RetryCol:
#if 0
if(verify_solution(lp, FALSE, "spx_loop") > 0)
i = 1; /* This is just a debug trap */
#endif
if(!changedphase) {
i = 0;
do {
i++;
colnr = colprim(lp, drow, nzdrow, (MYBOOL) (minit == ITERATE_MINORRETRY), i, &candidatecount, TRUE, &xviolated);
} while ((colnr == 0) && (i < partial_countBlocks(lp, (MYBOOL) !primal)) &&
partial_blockStep(lp, (MYBOOL) !primal));
/* Handle direct outcomes */
if(colnr == 0)
lp->spx_status = OPTIMAL;
if(lp->rejectpivot[0] > 0)
minit = ITERATE_MAJORMAJOR;
/* See if accuracy check during compute_reducedcosts flagged refactorization */
if(is_action(lp->spx_action, ACTION_REINVERT))
bfpfinal = TRUE;
}
/* Make sure that we do not erroneously conclude that an unbounded model is optimal */
#ifdef primal_UseRejectionList
if((colnr == 0) && (lp->rejectpivot[0] > 0)) {
lp->spx_status = UNBOUNDED;
if((lp->spx_trace && (lp->bb_totalnodes == 0)) ||
(lp->bb_trace && (lp->bb_totalnodes > 0)))
report(lp, DETAILED, "The model is primal unbounded.\n");
colnr = lp->rejectpivot[1];
rownr = 0;
lp->rejectpivot[0] = 0;
ok = FALSE;
break;
}
#endif
/* Check if we found an entering variable (indicating that we are still dual infeasible) */
if(colnr > 0) {
changedphase = FALSE;
fsolve(lp, colnr, pcol, NULL, lp->epsmachine, 1.0, TRUE); /* Solve entering column for Pi */
/* Do special anti-degeneracy column selection, if specified */
if(is_anti_degen(lp, ANTIDEGEN_COLUMNCHECK) && !check_degeneracy(lp, pcol, NULL)) {
if(lp->rejectpivot[0] < DEF_MAXPIVOTRETRY/3) {
i = ++lp->rejectpivot[0];
lp->rejectpivot[i] = colnr;
report(lp, DETAILED, "Entering column %d found to be non-improving due to degeneracy.\n",
colnr);
minit = ITERATE_MINORRETRY;
goto RetryCol;
}
else {
lp->rejectpivot[0] = 0;
report(lp, DETAILED, "Gave up trying to find a strictly improving entering column.\n");
}
}
/* Find the leaving variable that gives the most stringent bound on the entering variable */
theta = drow[colnr];
rownr = rowprim(lp, colnr, &theta, pcol, workINT, forceoutEQ, &cviolated);
#ifdef AcceptMarginalAccuracy
/* Check for marginal accuracy */
if((rownr > 0) && (xviolated+cviolated < lp->epspivot)) {
if(lp->bb_trace || (lp->bb_totalnodes == 0))
report(lp, DETAILED, "primloop: Assuming convergence with reduced accuracy %g.\n",
MAX(xviolated, cviolated));
rownr = 0;
colnr = 0;
goto Optimality;
}
else
#endif
/* See if we can do a straight artificial<->slack replacement (when "colnr" is a slack) */
if((lp->P1extraDim != 0) && (rownr == 0) && (colnr <= lp->rows))
rownr = findAnti_artificial(lp, colnr);
if(rownr > 0) {
pendingunbounded = FALSE;
lp->rejectpivot[0] = 0;
set_action(&lp->spx_action, ACTION_ITERATE);
if(!lp->obj_in_basis) /* We must manually copy the reduced cost for RHS update */
pcol[0] = my_chsign(!lp->is_lower[colnr], drow[colnr]);
lp->bfp_prepareupdate(lp, rownr, colnr, pcol);
}
/* We may be unbounded... */
else {
/* First make sure that we are not suffering from precision loss */
#ifdef primal_UseRejectionList
if(lp->rejectpivot[0] < DEF_MAXPIVOTRETRY) {
lp->spx_status = RUNNING;
lp->rejectpivot[0]++;
lp->rejectpivot[lp->rejectpivot[0]] = colnr;
report(lp, DETAILED, "...trying to recover via another pivot column.\n");
minit = ITERATE_MINORRETRY;
goto RetryCol;
}
else
#endif
/* Check that we are not having numerical problems */
if(!refactRecent(lp) && !pendingunbounded) {
bfpfinal = TRUE;
pendingunbounded = TRUE;
set_action(&lp->spx_action, ACTION_REINVERT);
}
/* Conclude that the model is unbounded */
else {
lp->spx_status = UNBOUNDED;
report(lp, DETAILED, "The model is primal unbounded.\n");
break;
}
}
}
/* We handle optimality and phase 1 infeasibility ... */
else {
Optimality:
/* Handle possible transition from phase 1 to phase 2 */
if(!primalfeasible || isP1extra(lp)) {
if(feasiblePhase1(lp, epsvalue)) {
lp->spx_status = RUNNING;
if(lp->bb_totalnodes == 0) {
report(lp, NORMAL, "Found feasibility by primal simplex after %10.0f iter.\n",
(double) get_total_iter(lp));
if((lp->usermessage != NULL) && (lp->msgmask & MSG_LPFEASIBLE))
lp->usermessage(lp, lp->msghandle, MSG_LPFEASIBLE);
}
changedphase = FALSE;
primalfeasible = TRUE;
lp->simplex_mode = SIMPLEX_Phase2_PRIMAL;
set_OF_p1extra(lp, 0.0);
/* We can do two things now;
1) delete the rows belonging to those variables, since they are redundant, OR
2) drive out the existing artificial variables via pivoting. */
if(lp->P1extraDim > 0) {
#ifdef Phase1EliminateRedundant
/* If it is not a MIP model we can try to delete redundant rows */
if((lp->bb_totalnodes == 0) && (MIP_count(lp) == 0)) {
while(lp->P1extraDim > 0) {
i = lp->rows;
while((i > 0) && (lp->var_basic[i] <= lp->sum-lp->P1extraDim))
i--;
#ifdef Paranoia
if(i <= 0) {
report(lp, SEVERE, "primloop: Could not find redundant artificial.\n");
break;
}
#endif
/* Obtain column and row indeces */
j = lp->var_basic[i]-lp->rows;
k = get_artificialRow(lp, j);
/* Delete row before column due to basis "compensation logic" */
if(lp->is_basic[k]) {
lp->is_basic[lp->rows+j] = FALSE;
del_constraint(lp, k);
}
else
set_basisvar(lp, i, k);
del_column(lp, j);
lp->P1extraDim--;
}
lp->basis_valid = TRUE;
}
/* Otherwise we drive out the artificials by elimination pivoting */
else
eliminate_artificials(lp, prow);
#else
/* Indicate phase 2 with artificial variables by negating P1extraDim */
lp->P1extraDim = my_flipsign(lp->P1extraDim);
#endif
}
/* We must refactorize since the OF changes from phase 1 to phase 2 */
set_action(&lp->spx_action, ACTION_REINVERT);
bfpfinal = TRUE;
}
/* We are infeasible in phase 1 */
else {
lp->spx_status = INFEASIBLE;
minit = ITERATE_MAJORMAJOR;
if(lp->spx_trace)
report(lp, NORMAL, "Model infeasible by primal simplex at iter %10.0f.\n",
(double) get_total_iter(lp));
}
}
/* Handle phase 1 optimality */
else {
/* (Do nothing special) */
}
/* Check if we are still primal feasible; the default assumes that this check
is not necessary after the relaxed problem has been solved satisfactorily. */
if((lp->bb_level <= 1) || (lp->improve & IMPROVE_BBSIMPLEX) /* || (lp->bb_rule & NODE_RCOSTFIXING) */) { /* NODE_RCOSTFIXING fix */
set_action(&lp->piv_strategy, PRICE_FORCEFULL);
i = rowdual(lp, lp->rhs, FALSE, FALSE, NULL);
clear_action(&lp->piv_strategy, PRICE_FORCEFULL);
if(i > 0) {
lp->spx_status = LOSTFEAS;
if(lp->total_iter == 0)
report(lp, DETAILED, "primloop: Lost primal feasibility at iter %10.0f: will try to recover.\n",
(double) get_total_iter(lp));
}
}
}
/* Pivot row/col and update the inverse */
if(is_action(lp->spx_action, ACTION_ITERATE)) {
lastnr = lp->var_basic[rownr];
if(refactRecent(lp) == AUTOMATIC)
minitcount = 0;
else if(minitcount > MAX_MINITUPDATES) {
recompute_solution(lp, INITSOL_USEZERO);
minitcount = 0;
}
minit = performiteration(lp, rownr, colnr, theta, primal,
(MYBOOL) (/*(candidatecount > 1) && */
(stallaccept != AUTOMATIC)),
NULL, NULL,
pcol, NULL, NULL);
if(minit != ITERATE_MAJORMAJOR)
minitcount++;
if((lp->spx_status == USERABORT) || (lp->spx_status == TIMEOUT))
break;
else if(minit == ITERATE_MINORMAJOR)
continue;
#ifdef UsePrimalReducedCostUpdate
/* Do a fast update of the reduced costs in preparation for the next iteration */
if(minit == ITERATE_MAJORMAJOR)
update_reducedcosts(lp, primal, lastnr, colnr, pcol, drow);
#endif
/* Detect if an auxiliary variable has left the basis and delete it; if
the non-basic variable only changed bound (a "minor iteration"), the
basic artificial variable did not leave and there is nothing to do */
if((minit == ITERATE_MAJORMAJOR) && (lastnr > lp->sum - abs(lp->P1extraDim))) {
#ifdef Paranoia
if(lp->is_basic[lastnr] || !lp->is_basic[colnr])
report(lp, SEVERE, "primloop: Invalid basis indicator for variable %d at iter %10.0f.\n",
lastnr, (double) get_total_iter(lp));
#endif
del_column(lp, lastnr-lp->rows);
if(lp->P1extraDim > 0)
lp->P1extraDim--;
else
lp->P1extraDim++;
if(lp->P1extraDim == 0) {
colnr = 0;
changedphase = TRUE;
stallMonitor_reset(lp);
}
}
}
if(lp->spx_status == SWITCH_TO_DUAL)
;
else if(!changedphase && lp->bfp_mustrefactorize(lp)) {
#ifdef ResetMinitOnReinvert
minit = ITERATE_MAJORMAJOR;
#endif
if(!invert(lp, INITSOL_USEZERO, bfpfinal))
lp->spx_status = SINGULAR_BASIS;
bfpfinal = FALSE;
}
}
/* Remove any remaining artificial variables (feasible or infeasible model) */
lp->P1extraDim = abs(lp->P1extraDim);
/* if((lp->P1extraDim > 0) && (lp->spx_status != DEGENERATE)) { */
if(lp->P1extraDim > 0) {
clear_artificials(lp);
if(lp->spx_status != OPTIMAL)
restore_basis(lp);
i = invert(lp, INITSOL_USEZERO, TRUE);
}
#ifdef Paranoia
if(!verify_basis(lp))
report(lp, SEVERE, "primloop: Invalid basis detected due to internal error\n");
#endif
/* Switch to dual phase 1 simplex for MIP models during
B&B phases, since this is typically far more efficient */
#ifdef ForceDualSimplexInBB
if((lp->bb_totalnodes == 0) && (MIP_count(lp) > 0) &&
((lp->simplex_strategy & SIMPLEX_Phase1_DUAL) == 0)) {
lp->simplex_strategy &= ~SIMPLEX_Phase1_PRIMAL;
lp->simplex_strategy += SIMPLEX_Phase1_DUAL;
}
#endif
Finish:
stallMonitor_finish(lp);
multi_free(&(lp->multivars));
FREE(prow);
FREE(pcol);
FREE(lp->bsolveVal);
return(ok);
} /* primloop */
STATIC int dualloop(lprec *lp, MYBOOL dualfeasible, int dualinfeasibles[], REAL dualoffset)
{
MYBOOL primal = FALSE, inP1extra, dualphase1 = FALSE, changedphase = TRUE,
pricerCanChange, minit, stallaccept, longsteps,
forceoutEQ = FALSE, bfpfinal = FALSE;
int i, colnr = 0, rownr = 0, lastnr = 0,
candidatecount = 0, minitcount = 0,
#ifdef FixInaccurateDualMinit
minitcolnr = 0,
#endif
ok = TRUE;
int *boundswaps = NULL;
LREAL theta = 0.0;
REAL epsvalue, xviolated, cviolated,
*prow = NULL, *pcol = NULL,
*drow = lp->drow;
int *nzprow = NULL, *workINT = NULL,