GainType Ascent()
{
Node *t;
GainType BestW, W, W0, Alpha, MaxAlpha = INT_MAX;
int T, Period, P, InitialPhase, BestNorm;
Start:
/* Initialize Pi and BestPi */
t = FirstNode;
do
t->Pi = t->BestPi = 0;
while ((t = t->Suc) != FirstNode);
if (CandidateSetType == DELAUNAY)
CreateDelaunayCandidateSet();
else
AddTourCandidates();
/* Compute the cost of a minimum 1-tree */
W = Minimum1TreeCost(CandidateSetType == DELAUNAY
|| MaxCandidates == 0);
/* Return this cost
if either
(1) subgradient optimization is not wanted, or
(2) the norm of the tree (its deviation from a tour) is zero
(in that case the true optimum has been found).
*/
if (!Subgradient || !Norm)
return W;
if (Optimum != MINUS_INFINITY && (Alpha = Optimum * Precision - W) > 0)
MaxAlpha = Alpha;
if (MaxCandidates > 0) {
/* Generate symmetric candididate sets for all nodes */
if (CandidateSetType != DELAUNAY)
GenerateCandidates(AscentCandidates, MaxAlpha, 1);
else {
OrderCandidateSet(AscentCandidates, MaxAlpha, 1);
W = Minimum1TreeCost(1);
if (!Norm || W / Precision == Optimum)
return W;
}
}
if (ExtraCandidates > 0)
AddExtraCandidates(ExtraCandidates, ExtraCandidateSetType,
ExtraCandidateSetSymmetric);
if (TraceLevel >= 2) {
CandidateReport();
printff("Subgradient optimization ...\n");
}
/* Set LastV of every node to V (the node's degree in the 1-tree) */
t = FirstNode;
do
t->LastV = t->V;
while ((t = t->Suc) != FirstNode);
BestW = W0 = W;
BestNorm = Norm;
InitialPhase = 1;
/* Perform subradient optimization with decreasing period length
and decreasing step size */
for (Period = InitialPeriod, T = InitialStepSize * Precision;
Period > 0 && T > 0 && Norm != 0; Period /= 2, T /= 2) {
/* Period and step size are halved at each iteration */
if (TraceLevel >= 2)
printff
(" T = %d, Period = %d, BestW = %0.1f, Norm = %d\n",
T, Period, (double) BestW / Precision, Norm);
for (P = 1; T && P <= Period && Norm != 0; P++) {
/* Adjust the Pi-values */
t = FirstNode;
do {
if (t->V != 0) {
t->Pi += T * (7 * t->V + 3 * t->LastV) / 10;
if (t->Pi > INT_MAX / 4)
t->Pi = INT_MAX / 4;
else if (t->Pi < -INT_MAX / 4)
t->Pi = -INT_MAX / 4;
}
t->LastV = t->V;
}
while ((t = t->Suc) != FirstNode);
/* Compute a minimum 1-tree in the sparse graph */
W = Minimum1TreeCost(1);
/* Test if an improvement has been found */
if (W > BestW || (W == BestW && Norm < BestNorm)) {
/* If the lower bound becomes greater than twice its
initial value it is taken as a sign that the graph might be
too sparse */
if (W - W0 > (W0 >= 0 ? W0 : -W0) && AscentCandidates > 0
&& AscentCandidates < Dimension) {
W = Minimum1TreeCost(CandidateSetType == DELAUNAY
|| MaxCandidates == 0);
if (W < W0) {
/* Double the number of candidate edges
and start all over again */
if (TraceLevel >= 2)
printff("Warning: AscentCandidates doubled\n");
if ((AscentCandidates *= 2) > Dimension)
AscentCandidates = Dimension;
goto Start;
}
W0 = W;
}
BestW = W;
BestNorm = Norm;
/* Update the BestPi-values */
t = FirstNode;
do
t->BestPi = t->Pi;
while ((t = t->Suc) != FirstNode);
if (TraceLevel >= 2)
printff
("* T = %d, Period = %d, P = %d, BestW = %0.1f, Norm = %d\n",
T, Period, P, (double) BestW / Precision, Norm);
/* If in the initial phase, the step size is doubled */
if (InitialPhase && T * sqrt((double) Norm) > 0)
T *= 2;
/* If the improvement was found at the last iteration of the
current period, then double the period */
if (CandidateSetType != DELAUNAY && P == Period
&& (Period *= 2) > InitialPeriod)
Period = InitialPeriod;
} else {
if (TraceLevel >= 3)
printff
(" T = %d, Period = %d, P = %d, W = %0.1f, Norm = %d\n",
T, Period, P, (double) W / Precision, Norm);
if (InitialPhase && P > Period / 2) {
/* Conclude the initial phase */
InitialPhase = 0;
P = 0;
T = 3 * T / 4;
}
}
}
}
t = FirstNode;
do {
t->Pi = t->BestPi;
t->BestPi = 0;
} while ((t = t->Suc) != FirstNode);
/* Compute a minimum 1-tree */
W = BestW = Minimum1TreeCost(CandidateSetType == DELAUNAY
|| MaxCandidates == 0);
if (MaxCandidates > 0) {
FreeCandidateSets();
if (CandidateSetType == DELAUNAY)
CreateDelaunayCandidateSet();
} else {
Candidate *Nt;
t = FirstNode;
do {
for (Nt = t->CandidateSet; Nt && Nt->To; Nt++)
Nt->Cost += t->Pi + Nt->To->Pi;
}
while ((t = t->Suc) != FirstNode);
}
if (TraceLevel >= 2)
printff("Ascent: BestW = %0.1f, Norm = %d\n",
(double) BestW / Precision, Norm);
return W;
}
void LKH::LKHAlg::CreateCandidateSet()
{
GainType Cost, MaxAlpha, A;
Node *Na;
int CandidatesRead = 0, i;
double EntryTime = GetTime();
Norm = 9999;
if (C == &LKH::LKHAlg::C_EXPLICIT) {
Na = FirstNode;
do {
for (i = 1; i < Na->Id; i++)
Na->C[i] *= Precision;
}
while ((Na = Na->Suc) != FirstNode);
}
if (Distance == &LKH::LKHAlg::Distance_1 ||
(MaxTrials == 0 &&
(FirstNode->InitialSuc || InitialTourAlgorithm == SIERPINSKI ||
InitialTourAlgorithm == MOORE))) {
ReadCandidates(MaxCandidates);
AddTourCandidates();
if (ProblemType == HCP || ProblemType == HPP)
Ascent();
goto End_CreateCandidateSet;
}
if (TraceLevel >= 2)
printff("Creating candidates ...\n");
if (MaxCandidates > 0 &&
(CandidateSetType == QUADRANT || CandidateSetType == NN)) {
ReadPenalties();
if (!(CandidatesRead = ReadCandidates(MaxCandidates)) &&
MaxCandidates > 0) {
if (CandidateSetType == QUADRANT)
CreateQuadrantCandidateSet(MaxCandidates);
else if (CandidateSetType == NN)
CreateNearestNeighborCandidateSet(MaxCandidates);
} else {
AddTourCandidates();
if (CandidateSetSymmetric)
SymmetrizeCandidateSet();
}
goto End_CreateCandidateSet;
}
if (!ReadPenalties()) {
/* No PiFile specified or available */
Na = FirstNode;
do
Na->Pi = 0;
while ((Na = Na->Suc) != FirstNode);
CandidatesRead = ReadCandidates(MaxCandidates);
Cost = Ascent();
if (Subgradient && SubproblemSize == 0) {
WritePenalties();
PiFile = 0;
}
} else if ((CandidatesRead = ReadCandidates(MaxCandidates)) ||
MaxCandidates == 0) {
AddTourCandidates();
if (CandidateSetSymmetric)
SymmetrizeCandidateSet();
goto End_CreateCandidateSet;
} else {
if (CandidateSetType != DELAUNAY && MaxCandidates > 0) {
if (TraceLevel >= 2)
printff("Computing lower bound ... ");
Cost = Minimum1TreeCost(0);
if (TraceLevel >= 2)
printff("done\n");
} else {
CreateDelaunayCandidateSet();
Na = FirstNode;
do {
Na->BestPi = Na->Pi;
Na->Pi = 0;
}
while ((Na = Na->Suc) != FirstNode);
if (TraceLevel >= 2)
printff("Computing lower bound ... ");
Cost = Minimum1TreeCost(1);
if (TraceLevel >= 2)
printff("done\n");
Na = FirstNode;
do {
Na->Pi = Na->BestPi;
Cost -= 2 * Na->Pi;
}
while ((Na = Na->Suc) != FirstNode);
}
}
LowerBound = (double) Cost / Precision;
if (TraceLevel >= 1) {
/* printff("Lower bound = %0.1f", LowerBound);
if (Optimum != MINUS_INFINITY && Optimum != 0)
printff(", Gap = %0.2f%%",
100.0 * (Optimum - LowerBound) / Optimum);
if (!PiFile)
printff(", Ascent time = %0.2f sec.",
fabs(GetTime() - EntryTime));
printff("\n"); */
if (Optimum != MINUS_INFINITY && Optimum != 0)
m_Gap=100.0 * (Optimum - LowerBound) / Optimum;
if (!PiFile)
m_AscentTime=fabs(GetTime() - EntryTime);
}
MaxAlpha = (GainType) fabs(Excess * Cost);
if ((A = Optimum * Precision - Cost) > 0 && A < MaxAlpha)
MaxAlpha = A;
if (CandidateSetType == DELAUNAY || MaxCandidates == 0)
OrderCandidateSet(MaxCandidates, MaxAlpha, CandidateSetSymmetric);
else
GenerateCandidates(MaxCandidates, MaxAlpha, CandidateSetSymmetric);
End_CreateCandidateSet:
if (ExtraCandidates > 0) {
AddExtraCandidates(ExtraCandidates,
ExtraCandidateSetType,
ExtraCandidateSetSymmetric);
AddTourCandidates();
}
ResetCandidateSet();
Na = FirstNode;
do {
if (!Na->CandidateSet || !Na->CandidateSet[0].To) {
if (MaxCandidates == 0)
eprintf("MAX_CANDIDATES = 0: Node %d has no candidates",
Na->Id);
else
eprintf("Node %d has no candidates", Na->Id);
}
}
while ((Na = Na->Suc) != FirstNode);
if (!CandidatesRead && SubproblemSize == 0)
WriteCandidates();
if (C == &LKH::LKHAlg::C_EXPLICIT) {
Na = FirstNode;
do
for (i = 1; i < Na->Id; i++)
Na->C[i] += Na->Pi + NodeSet[i].Pi;
while ((Na = Na->Suc) != FirstNode);
}
if (TraceLevel >= 1) {
CandidateReport();
// printff("Preprocessing time = %0.2f sec.\n",
// fabs(GetTime() - EntryTime));
}
}
GainType LKH::LKHAlg::FindTour()
{
GainType Cost;
Node *t;
int i;
double EntryTime = GetTime();
if(!OrdinalTourCost.get())
OrdinalTourCost.reset(new GainType(0));
t = FirstNode;
do
t->OldPred = t->OldSuc = t->NextBestSuc = t->BestSuc = 0;
while ((t = t->Suc) != FirstNode);
if (Run == 1 && Dimension == DimensionSaved) {
*OrdinalTourCost = 0;
for (i = 1; i < Dimension; i++)
*OrdinalTourCost += (this->*C)(&NodeSet[i], &NodeSet[i + 1])
- NodeSet[i].Pi - NodeSet[i + 1].Pi;
*OrdinalTourCost += (this->*C)(&NodeSet[Dimension], &NodeSet[1])
- NodeSet[Dimension].Pi - NodeSet[1].Pi;
*OrdinalTourCost /= Precision;
}
BetterCost = PLUS_INFINITY;
if (MaxTrials > 0)
HashInitialize(HTable);
else {
Trial = 1;
ChooseInitialTour();
}
for (Trial = 1; Trial <= MaxTrials; Trial++) {
if (GetTime() - EntryTime >= TimeLimit) {
if (TraceLevel >= 1)
printff("*** Time limit exceeded ***\n");
break;
}
/* Choose FirstNode at random */
if (Dimension == DimensionSaved)
FirstNode = &NodeSet[1 + Random() % Dimension];
else
for (i = Random() % Dimension; i > 0; i--)
FirstNode = FirstNode->Suc;
ChooseInitialTour();
Cost = LinKernighan();
if (FirstNode->BestSuc) {
/* Merge tour with current best tour */
t = FirstNode;
while ((t = t->Next = t->BestSuc) != FirstNode);
Cost = MergeWithTour();
}
if (Dimension == DimensionSaved && Cost >= *OrdinalTourCost &&
BetterCost > *OrdinalTourCost) {
/* Merge tour with ordinal tour */
for (i = 1; i < Dimension; i++)
NodeSet[i].Next = &NodeSet[i + 1];
NodeSet[Dimension].Next = &NodeSet[1];
Cost = MergeWithTour();
}
if (Cost < BetterCost) {
if (TraceLevel >= 1) {
/* printff("* %d: Cost = " GainFormat, Trial, Cost);
if (Optimum != MINUS_INFINITY && Optimum != 0)
printff(", Gap = %0.4f%%",
100.0 * (Cost - Optimum) / Optimum);
printff(", Time = %0.2f sec. %s\n",
fabs(GetTime() - EntryTime),
Cost < Optimum ? "<" : Cost == Optimum ? "=" : ""); */
}
BetterCost = Cost;
RecordBetterTour();
if (Dimension == DimensionSaved && BetterCost < BestCost)
WriteTour(OutputTourFileName, BetterTour, BetterCost);
if (StopAtOptimum && BetterCost == Optimum)
break;
AdjustCandidateSet();
HashInitialize(HTable);
HashInsert(HTable, Hash, Cost);
} else if (TraceLevel >= 2)
printff(" %d: Cost = " GainFormat ", Time = %0.2f sec.\n",
Trial, Cost, fabs(GetTime() - EntryTime));
/* Record backbones if wanted */
if (Trial <= BackboneTrials && BackboneTrials < MaxTrials) {
SwapCandidateSets(this);
AdjustCandidateSet();
if (Trial == BackboneTrials) {
if (TraceLevel >= 1) {
printff("# %d: Backbone candidates ->\n", Trial);
CandidateReport();
}
} else
SwapCandidateSets(this);
}
}
if (BackboneTrials > 0 && BackboneTrials < MaxTrials) {
if (Trial > BackboneTrials ||
(Trial == BackboneTrials &&
(!StopAtOptimum || BetterCost != Optimum)))
SwapCandidateSets(this);
t = FirstNode;
do {
free(t->BackboneCandidateSet);
t->BackboneCandidateSet = 0;
} while ((t = t->Suc) != FirstNode);
}
t = FirstNode;
if (Norm == 0) {
do
t = t->BestSuc = t->Suc;
while (t != FirstNode);
}
do
(t->Suc = t->BestSuc)->Pred = t;
while ((t = t->BestSuc) != FirstNode);
if (Trial > MaxTrials)
Trial = MaxTrials;
ResetCandidateSet();
return BetterCost;
}
