void FreeStructures()
{
FreeCandidateSets();
FreeSegments();
if (NodeSet) {
int i;
for (i = 1; i <= Dimension; i++) {
Node *N = &NodeSet[i];
Free(N->MergeSuc);
N->C = 0;
}
Free(NodeSet);
}
Free(CostMatrix);
Free(BestTour);
Free(BetterTour);
Free(SwapStack);
Free(HTable);
Free(Rand);
Free(CacheSig);
Free(CacheVal);
Free(Name);
Free(Type);
Free(EdgeWeightType);
Free(EdgeWeightFormat);
Free(EdgeDataFormat);
Free(NodeCoordType);
Free(DisplayDataType);
Free(Heap);
Free(t);
Free(T);
Free(tSaved);
Free(p);
Free(q);
Free(incl);
Free(cycle);
Free(G);
FreePopulation();
}
int
SolveSubproblem(int CurrentSubproblem, int Subproblems,
GainType * GlobalBestCost)
{
Node *FirstNodeSaved = FirstNode, *N, *Next, *Last = 0;
GainType OptimumSaved = Optimum, Cost, Improvement, GlobalCost;
double LastTime, Time, ExcessSaved = Excess;
int NewDimension = 0, OldDimension = 0, Number, i, InitialTourEdges = 0,
AscentCandidatesSaved = AscentCandidates,
InitialPeriodSaved = InitialPeriod, MaxTrialsSaved = MaxTrials;
BestCost = PLUS_INFINITY;
FirstNode = 0;
N = FirstNodeSaved;
do {
if (N->Subproblem == CurrentSubproblem) {
if (SubproblemsCompressed &&
(((N->SubproblemPred == N->SubBestPred ||
FixedOrCommon(N, N->SubproblemPred) ||
(N->SubBestPred &&
(N->FixedTo1Saved == N->SubBestPred ||
N->FixedTo2Saved == N->SubBestPred))) &&
(N->SubproblemSuc == N->SubBestSuc ||
FixedOrCommon(N, N->SubproblemSuc) ||
(N->SubBestSuc &&
(N->FixedTo1Saved == N->SubBestSuc ||
N->FixedTo2Saved == N->SubBestSuc)))) ||
((N->SubproblemPred == N->SubBestSuc ||
FixedOrCommon(N, N->SubproblemPred) ||
(N->SubBestSuc &&
(N->FixedTo1Saved == N->SubBestSuc ||
N->FixedTo2Saved == N->SubBestSuc))) &&
(N->SubproblemSuc == N->SubBestPred ||
FixedOrCommon(N, N->SubproblemSuc) ||
(N->SubBestPred &&
(N->FixedTo1Saved == N->SubBestPred ||
N->FixedTo2Saved == N->SubBestPred))))))
N->Subproblem = -CurrentSubproblem;
else {
if (!FirstNode)
FirstNode = N;
NewDimension++;
}
N->Head = N->Tail = 0;
if (N->SubBestSuc)
OldDimension++;
}
N->SubBestPred = N->SubBestSuc = 0;
N->FixedTo1Saved = N->FixedTo1;
N->FixedTo2Saved = N->FixedTo2;
} while ((N = N->SubproblemSuc) != FirstNodeSaved);
if ((Number = CurrentSubproblem % Subproblems) == 0)
Number = Subproblems;
if (NewDimension <= 3 || NewDimension == OldDimension) {
if (TraceLevel >= 1 && NewDimension <= 3)
printff
("\nSubproblem %d of %d: Dimension = %d (too small)\n",
Number, Subproblems, NewDimension);
FirstNode = FirstNodeSaved;
return 0;
}
if (AscentCandidates > NewDimension - 1)
AscentCandidates = NewDimension - 1;
if (InitialPeriod < 0) {
InitialPeriod = NewDimension / 2;
if (InitialPeriod < 100)
InitialPeriod = 100;
}
if (Excess < 0)
Excess = 1.0 / NewDimension;
if (MaxTrials == -1)
MaxTrials = NewDimension;
N = FirstNode;
do {
Next = N->SubproblemSuc;
if (N->Subproblem == CurrentSubproblem) {
N->Pred = N->Suc = N;
if (N != FirstNode)
Follow(N, Last);
Last = N;
} else if (Next->Subproblem == CurrentSubproblem
&& !Fixed(Last, Next)) {
if (!Last->FixedTo1
|| Last->FixedTo1->Subproblem != CurrentSubproblem)
Last->FixedTo1 = Next;
else
Last->FixedTo2 = Next;
if (!Next->FixedTo1
|| Next->FixedTo1->Subproblem != CurrentSubproblem)
Next->FixedTo1 = Last;
else
Next->FixedTo2 = Last;
if (C == C_EXPLICIT) {
if (Last->Id > Next->Id)
Last->C[Next->Id] = 0;
else
Next->C[Last->Id] = 0;
}
}
}
while ((N = Next) != FirstNode);
Dimension = NewDimension;
AllocateSegments();
InitializeStatistics();
if (CacheSig)
for (i = 0; i <= CacheMask; i++)
CacheSig[i] = 0;
OptimumSaved = Optimum;
Optimum = 0;
N = FirstNode;
do {
if (N->SubproblemSuc == N->InitialSuc ||
N->SubproblemPred == N->InitialSuc)
InitialTourEdges++;
if (!Fixed(N, N->Suc))
Optimum += Distance(N, N->Suc);
if (N->FixedTo1 && N->Subproblem != N->FixedTo1->Subproblem)
eprintf("Illegal fixed edge (%d,%d)", N->Id, N->FixedTo1->Id);
if (N->FixedTo2 && N->Subproblem != N->FixedTo2->Subproblem)
eprintf("Illegal fixed edge (%d,%d)", N->Id, N->FixedTo2->Id);
}
while ((N = N->Suc) != FirstNode);
if (TraceLevel >= 1)
printff
("\nSubproblem %d of %d: Dimension = %d, Upper bound = "
GainFormat "\n", Number, Subproblems, Dimension, Optimum);
FreeCandidateSets();
CreateCandidateSet();
for (Run = 1; Run <= Runs; Run++) {
LastTime = GetTime();
Cost = Norm != 0 ? FindTour() : Optimum;
/* Merge with subproblem tour */
Last = 0;
N = FirstNode;
do {
if (N->Subproblem == CurrentSubproblem) {
if (Last)
Last->Next = N;
Last = N;
}
}
while ((N = N->SubproblemSuc) != FirstNode);
Last->Next = FirstNode;
Cost = MergeWithTour();
if (MaxPopulationSize > 1) {
/* Genetic algorithm */
for (i = 0; i < PopulationSize; i++)
Cost = MergeTourWithIndividual(i);
if (!HasFitness(Cost)) {
if (PopulationSize < MaxPopulationSize) {
AddToPopulation(Cost);
if (TraceLevel >= 1)
PrintPopulation();
} else if (Cost < Fitness[PopulationSize - 1]) {
ReplaceIndividualWithTour(PopulationSize - 1, Cost);
if (TraceLevel >= 1)
PrintPopulation();
}
}
}
if (Cost < BestCost) {
N = FirstNode;
do {
N->SubBestPred = N->Pred;
N->SubBestSuc = N->Suc;
} while ((N = N->Suc) != FirstNode);
BestCost = Cost;
}
if (Cost < Optimum || (Cost != Optimum && OutputTourFileName)) {
Improvement = Optimum - Cost;
if (Improvement > 0) {
BestCost = GlobalCost = *GlobalBestCost -= Improvement;
Optimum = Cost;
} else
GlobalCost = *GlobalBestCost - Improvement;
N = FirstNode;
do
N->Mark = 0;
while ((N = N->SubproblemSuc) != FirstNode);
do {
N->Mark = N;
if (!N->SubproblemSuc->Mark &&
(N->Subproblem != CurrentSubproblem ||
N->SubproblemSuc->Subproblem != CurrentSubproblem))
N->BestSuc = N->SubproblemSuc;
else if (!N->SubproblemPred->Mark &&
(N->Subproblem != CurrentSubproblem ||
N->SubproblemPred->Subproblem !=
CurrentSubproblem))
N->BestSuc = N->SubproblemPred;
else if (!N->Suc->Mark)
N->BestSuc = N->Suc;
else if (!N->Pred->Mark)
N->BestSuc = N->Pred;
else
N->BestSuc = FirstNode;
}
while ((N = N->BestSuc) != FirstNode);
Dimension = DimensionSaved;
i = 0;
do {
if (ProblemType != ATSP)
BetterTour[++i] = N->Id;
else if (N->Id <= Dimension / 2) {
i++;
if (N->BestSuc->Id != N->Id + Dimension / 2)
BetterTour[i] = N->Id;
else
BetterTour[Dimension / 2 - i + 1] = N->Id;
}
}
while ((N = N->BestSuc) != FirstNode);
BetterTour[0] =
BetterTour[ProblemType !=
ATSP ? Dimension : Dimension / 2];
WriteTour(OutputTourFileName, BetterTour, GlobalCost);
if (Improvement > 0) {
do
if (N->Subproblem != CurrentSubproblem)
break;
while ((N = N->SubproblemPred) != FirstNode);
if (N->SubproblemSuc == N->BestSuc) {
N = FirstNode;
do {
N->BestSuc->SubproblemPred = N;
N = N->SubproblemSuc = N->BestSuc;
}
while (N != FirstNode);
} else {
N = FirstNode;
do
(N->SubproblemPred = N->BestSuc)->SubproblemSuc =
N;
while ((N = N->BestSuc) != FirstNode);
}
RecordBestTour();
WriteTour(TourFileName, BestTour, GlobalCost);
}
Dimension = NewDimension;
if (TraceLevel >= 1) {
printff("*** %d: Cost = " GainFormat, Number, GlobalCost);
if (OptimumSaved != MINUS_INFINITY && OptimumSaved != 0)
printff(", Gap = %04f%%",
100.0 * (GlobalCost -
OptimumSaved) / OptimumSaved);
printff(", Time = %0.2f sec. %s\n",
fabs(GetTime() - LastTime),
GlobalCost < OptimumSaved ? "<" : GlobalCost ==
OptimumSaved ? "=" : "");
}
}
Time = fabs(GetTime() - LastTime);
UpdateStatistics(Cost, Time);
if (TraceLevel >= 1 && Cost != PLUS_INFINITY)
printff("Run %d: Cost = " GainFormat ", Time = %0.2f sec.\n\n",
Run, Cost, Time);
if (PopulationSize >= 2 &&
(PopulationSize == MaxPopulationSize
|| Run >= 2 * MaxPopulationSize) && Run < Runs) {
Node *N;
int Parent1, Parent2;
Parent1 = LinearSelection(PopulationSize, 1.25);
do
Parent2 = LinearSelection(PopulationSize, 1.25);
while (Parent1 == Parent2);
ApplyCrossover(Parent1, Parent2);
N = FirstNode;
do {
int d = C(N, N->Suc);
AddCandidate(N, N->Suc, d, INT_MAX);
AddCandidate(N->Suc, N, d, INT_MAX);
N = N->InitialSuc = N->Suc;
}
while (N != FirstNode);
}
SRandom(++Seed);
if (Norm == 0)
break;
}
if (TraceLevel >= 1)
PrintStatistics();
if (C == C_EXPLICIT) {
N = FirstNode;
do {
for (i = 1; i < N->Id; i++) {
N->C[i] -= N->Pi + NodeSet[i].Pi;
N->C[i] /= Precision;
}
if (N->FixedTo1 && N->FixedTo1 != N->FixedTo1Saved) {
if (N->Id > N->FixedTo1->Id)
N->C[N->FixedTo1->Id] = Distance(N, N->FixedTo1);
else
N->FixedTo1->C[N->Id] = Distance(N, N->FixedTo1);
}
if (N->FixedTo2 && N->FixedTo2 != N->FixedTo2Saved) {
if (N->Id > N->FixedTo2->Id)
N->C[N->FixedTo2->Id] = Distance(N, N->FixedTo2);
else
N->FixedTo2->C[N->Id] = Distance(N, N->FixedTo2);
}
}
while ((N = N->Suc) != FirstNode);
}
FreeSegments();
FreeCandidateSets();
FreePopulation();
if (InitialTourEdges == Dimension) {
do
N->InitialSuc = N->SubproblemSuc;
while ((N = N->SubproblemSuc) != FirstNode);
} else {
do
N->InitialSuc = 0;
while ((N = N->SubproblemSuc) != FirstNode);
}
Dimension = ProblemType != ATSP ? DimensionSaved : 2 * DimensionSaved;
N = FirstNode = FirstNodeSaved;
do {
N->Suc = N->BestSuc = N->SubproblemSuc;
N->Suc->Pred = N;
Next = N->FixedTo1;
N->FixedTo1 = N->FixedTo1Saved;
N->FixedTo1Saved = Next;
Next = N->FixedTo2;
N->FixedTo2 = N->FixedTo2Saved;
N->FixedTo2Saved = Next;
}
while ((N = N->Suc) != FirstNode);
Optimum = OptimumSaved;
Excess = ExcessSaved;
AscentCandidates = AscentCandidatesSaved;
InitialPeriod = InitialPeriodSaved;
MaxTrials = MaxTrialsSaved;
return 1;
}
void LKH::LKHAlg::GenerateCandidates(int MaxCandidates, GainType MaxAlpha,
int Symmetric)
{
Node *From, *To;
Candidate *NFrom, *NN;
int a, d, Count;
if (TraceLevel >= 2)
printff("Generating candidates ... ");
if (MaxAlpha < 0 || MaxAlpha > INT_MAX)
MaxAlpha = INT_MAX;
/* Initialize CandidateSet for each node */
FreeCandidateSets();
From = FirstNode;
do
From->Mark = 0;
while ((From = From->Suc) != FirstNode);
if (MaxCandidates > 0) {
do {
assert(From->CandidateSet =
(Candidate *) malloc((MaxCandidates + 1) *
sizeof(Candidate)));
From->CandidateSet[0].To = 0;
}
while ((From = From->Suc) != FirstNode);
} else {
AddTourCandidates();
do {
if (!From->CandidateSet)
eprintf("MAX_CANDIDATES = 0: No candidates");
} while ((From = From->Suc) != FirstNode);
return;
}
/* Loop for each node, From */
do {
NFrom = From->CandidateSet;
if (From != FirstNode) {
From->Beta = INT_MIN;
for (To = From; To->Dad != 0; To = To->Dad) {
To->Dad->Beta =
!FixedOrCommon(To, To->Dad) ?
Max(To->Beta, To->Cost) : To->Beta;
To->Dad->Mark = From;
}
}
Count = 0;
/* Loop for each node, To */
To = FirstNode;
do {
if (To == From)
continue;
d = c && !FixedOrCommon(From, To) ? (this->*c)(From, To) : (this->*D)(From, To);
if (From == FirstNode)
a = To == From->Dad ? 0 : d - From->NextCost;
else if (To == FirstNode)
a = From == To->Dad ? 0 : d - To->NextCost;
else {
if (To->Mark != From)
To->Beta =
!FixedOrCommon(To, To->Dad) ?
Max(To->Dad->Beta, To->Cost) : To->Dad->Beta;
a = d - To->Beta;
}
if (FixedOrCommon(From, To))
a = INT_MIN;
else {
if (From->FixedTo2 || To->FixedTo2 || Forbidden(From, To))
continue;
if (InInputTour(From, To)) {
a = 0;
if (c)
d = (this->*D)(From, To);
} else if (c) {
if (a > MaxAlpha ||
(Count == MaxCandidates &&
(a > (NFrom - 1)->Alpha ||
(a == (NFrom - 1)->Alpha
&& d >= (NFrom - 1)->Cost))))
continue;
if (To == From->Dad) {
d = From->Cost;
a = 0;
} else if (From == To->Dad) {
d = To->Cost;
a = 0;
} else {
a -= d;
a += (d = (this->*D)(From, To));
}
}
}
if (a <= MaxAlpha && IsPossibleCandidate(From, To)) {
/* Insert new candidate edge in From->CandidateSet */
NN = NFrom;
while (--NN >= From->CandidateSet) {
if (a > NN->Alpha || (a == NN->Alpha && d >= NN->Cost))
break;
*(NN + 1) = *NN;
}
NN++;
NN->To = To;
NN->Cost = d;
NN->Alpha = a;
if (Count < MaxCandidates) {
Count++;
NFrom++;
}
NFrom->To = 0;
}
}
while ((To = To->Suc) != FirstNode);
}
while ((From = From->Suc) != FirstNode);
AddTourCandidates();
if (Symmetric)
SymmetrizeCandidateSet();
if (TraceLevel >= 2)
printff("done\n");
}
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;
}
