void SolveKCenterSubproblems()
{
Node *N;
GainType GlobalBestCost, OldGlobalBestCost;
double EntryTime = GetTime();
int CurrentSubproblem, Subproblems;
AllocateStructures();
ReadPenalties();
/* Compute upper bound for the original problem */
GlobalBestCost = 0;
N = FirstNode;
do {
if (!Fixed(N, N->SubproblemSuc))
GlobalBestCost += Distance(N, N->SubproblemSuc);
N->Subproblem = 0;
}
while ((N = N->SubproblemSuc) != FirstNode);
if (TraceLevel >= 1) {
if (TraceLevel >= 2)
printff("\n");
printff("*** K-center partitioning *** [Cost = " GainFormat "]\n",
GlobalBestCost);
}
Subproblems = (int) ceil((double) Dimension / SubproblemSize);
KCenterClustering(Subproblems);
for (CurrentSubproblem = 1;
CurrentSubproblem <= Subproblems; CurrentSubproblem++) {
OldGlobalBestCost = GlobalBestCost;
SolveSubproblem(CurrentSubproblem, Subproblems, &GlobalBestCost);
if (SubproblemsCompressed && GlobalBestCost == OldGlobalBestCost)
SolveCompressedSubproblem(CurrentSubproblem, Subproblems,
&GlobalBestCost);
}
printff("\nCost = " GainFormat, GlobalBestCost);
if (Optimum != MINUS_INFINITY && Optimum != 0)
printff(", Gap = %0.4f%%",
100.0 * (GlobalBestCost - Optimum) / Optimum);
printff(", Time = %0.2f sec. %s\n", fabs(GetTime() - EntryTime),
GlobalBestCost < Optimum ? "<" : GlobalBestCost ==
Optimum ? "=" : "");
if (SubproblemBorders && Subproblems > 1)
SolveSubproblemBorderProblems(Subproblems, &GlobalBestCost);
}
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));
}
}
void SolveKarpSubproblems()
{
Node *N;
int i;
double EntryTime = GetTime();
AllocateStructures();
ReadPenalties();
/* Compute upper bound for the original problem */
GlobalBestCost = 0;
N = FirstNode;
do {
if (!Fixed(N, N->SubproblemSuc))
GlobalBestCost += Distance(N, N->SubproblemSuc);
N->Subproblem = 0;
}
while ((N = N->BestSuc = N->SubproblemSuc) != FirstNode);
if (TraceLevel >= 1) {
if (TraceLevel >= 2)
printff("\n");
printff("*** Karp partitioning *** [Cost = " GainFormat "]\n",
GlobalBestCost);
}
if (WeightType == GEO || WeightType == GEOM ||
WeightType == GEO_MEEUS || WeightType == GEOM_MEEUS) {
N = FirstNode;
do {
N->Xc = N->X;
N->Yc = N->Y;
N->Zc = N->Z;
if (WeightType == GEO || WeightType == GEO_MEEUS)
GEO2XYZ(N->Xc, N->Yc, &N->X, &N->Y, &N->Z);
else
GEOM2XYZ(N->Xc, N->Yc, &N->X, &N->Y, &N->Z);
} while ((N = N->SubproblemSuc) != FirstNode);
CoordType = THREED_COORDS;
}
KDTree = BuildKDTree();
if (WeightType == GEO || WeightType == GEOM ||
WeightType == GEO_MEEUS || WeightType == GEOM_MEEUS) {
N = FirstNode;
do {
N->X = N->Xc;
N->Y = N->Yc;
N->Z = N->Zc;
} while ((N = N->SubproblemSuc) != FirstNode);
CoordType = TWOD_COORDS;
}
CurrentSubproblem = 0;
Subproblems = 1;
for (i = Dimension - 1; i > SubproblemSize; i /= 2)
Subproblems *= 2;
RestrictedSearchSaved = RestrictedSearch;
KarpPartition(0, Dimension - 1, 0);
free(KDTree);
printff("\nCost = " GainFormat, GlobalBestCost);
if (Optimum != MINUS_INFINITY && Optimum != 0)
printff(", Gap = %0.3f%%",
100.0 * (GlobalBestCost - Optimum) / Optimum);
printff(", Time = %0.1f sec. %s\n", fabs(GetTime() - EntryTime),
GlobalBestCost < Optimum ? "<" : GlobalBestCost ==
Optimum ? "=" : "");
if (SubproblemBorders && Subproblems > 1)
SolveSubproblemBorderProblems(Subproblems);
}
void SolveRoheSubproblems()
{
Node *N;
int CurrentSubproblem, Subproblems, Remaining, i;
GainType GlobalBestCost, OldGlobalBestCost;
double XMin, XMax, YMin, YMax, ZMin, ZMax, DX, DY, DZ, CLow, CMid,
CHigh;
double EntryTime = GetTime();
AllocateStructures();
ReadPenalties();
Subproblems = 0;
/* Compute upper bound for the original problem */
GlobalBestCost = 0;
N = FirstNode;
do {
if (!Fixed(N, N->SubproblemSuc))
GlobalBestCost += Distance(N, N->SubproblemSuc);
N->Subproblem = 0;
}
while ((N = N->SubproblemSuc) != FirstNode);
if (TraceLevel >= 1) {
if (TraceLevel >= 2)
printff("\n");
printff("*** Rohe partitioning *** [Cost = " GainFormat "]\n",
GlobalBestCost);
}
if (WeightType == GEO || WeightType == GEOM ||
WeightType == GEO_MEEUS || WeightType == GEOM_MEEUS) {
N = FirstNode;
do {
N->Xc = N->X;
N->Yc = N->Y;
N->Zc = N->Z;
if (WeightType == GEO || WeightType == GEO_MEEUS)
GEO2XYZ(N->Xc, N->Yc, &N->X, &N->Y, &N->Z);
else
GEOM2XYZ(N->Xc, N->Yc, &N->X, &N->Y, &N->Z);
} while ((N = N->SubproblemSuc) != FirstNode);
CoordType = THREED_COORDS;
}
N = FirstNode;
XMin = XMax = N->X;
YMin = YMax = N->Y;
ZMin = ZMax = N->Z;
while ((N = N->SubproblemSuc) != FirstNode) {
if (N->X < XMin)
XMin = N->X;
else if (N->X > XMax)
XMax = N->X;
if (N->Y < YMin)
YMin = N->Y;
else if (N->Y > YMax)
YMax = N->Y;
if (N->Z < ZMin)
ZMin = N->Z;
else if (N->Z > ZMax)
ZMax = N->Z;
}
KDTree = BuildKDTree(SubproblemSize);
Remaining = Dimension;
while (Remaining > SubproblemSize) {
N = FirstNode;
i = Random() % Remaining;
while (i--)
N = N->Suc;
DX = (0.5 + 0.5 * Random() / (PRANDMAX - 1)) * (XMax - XMin);
DY = (0.5 + 0.5 * Random() / (PRANDMAX - 1)) * (YMax - YMin);
DZ = (0.5 + 0.5 * Random() / (PRANDMAX - 1)) * (ZMax - ZMin);
CLow = 0;
CHigh = 2;
/* Binary search */
do {
CMid = (CLow + CHigh) / 2;
Size = 0;
WindowSize(N->X - CMid * DX, N->X + CMid * DX,
N->Y - CMid * DY, N->Y + CMid * DY,
N->Z - CMid * DZ, N->Z + CMid * DZ,
0, Dimension - 1);
if (Size >= 2.0 / 3 * SubproblemSize && Size <= SubproblemSize)
break;
if (Size < 2.0 / 3 * SubproblemSize)
CLow = CMid;
else
CHigh = CMid;
}
while (CHigh - CLow > DBL_EPSILON);
MakeSubproblem(N->X - CMid * DX, N->X + CMid * DX,
N->Y - CMid * DY, N->Y + CMid * DY,
N->Z - CMid * DZ, N->Z + CMid * DZ,
++Subproblems, 0, Dimension - 1);
Remaining -= Size;
}
if (Remaining > 3) {
Subproblems++;
N = FirstNode;
do
N->Subproblem = Subproblems;
while ((N = N->Suc) != FirstNode);
}
if (WeightType == GEO || WeightType == GEOM || WeightType == GEO_MEEUS
|| WeightType == GEOM_MEEUS) {
N = FirstNode;
do {
N->X = N->Xc;
N->Y = N->Yc;
N->Z = N->Zc;
} while ((N = N->SubproblemSuc) != FirstNode);
CoordType = TWOD_COORDS;
}
free(KDTree);
for (CurrentSubproblem = 1;
CurrentSubproblem <= Subproblems; CurrentSubproblem++) {
OldGlobalBestCost = GlobalBestCost;
SolveSubproblem(CurrentSubproblem, Subproblems, &GlobalBestCost);
if (SubproblemsCompressed && GlobalBestCost == OldGlobalBestCost)
SolveCompressedSubproblem(CurrentSubproblem, Subproblems,
&GlobalBestCost);
}
printff("\nCost = " GainFormat, GlobalBestCost);
if (Optimum != MINUS_INFINITY && Optimum != 0)
printff(", Gap = %0.4f%%",
100.0 * (GlobalBestCost - Optimum) / Optimum);
printff(", Time = %0.1f sec. %s\n", fabs(GetTime() - EntryTime),
GlobalBestCost < Optimum ? "<" : GlobalBestCost ==
Optimum ? "=" : "");
if (SubproblemBorders && Subproblems > 1)
SolveSubproblemBorderProblems(Subproblems, &GlobalBestCost);
}
