void LKH::LKHAlg::Connect(Node * N1, int Max, int Sparse)
{
Node *N;
Candidate *NN1;
int d;
N1->Next = 0;
N1->NextCost = INT_MAX;
if (!Sparse || N1->CandidateSet == 0 ||
N1->CandidateSet[0].To == 0 || N1->CandidateSet[1].To == 0) {
/* Find the requested edge in a dense graph */
N = FirstNode;
do {
if (N == N1 || N == N1->Dad || N1 == N->Dad)
continue;
if (FixedOrCommon(N1, N)) {
N1->NextCost = (this->*D)(N1, N);
N1->Next = N;
return;
}
if (!N1->FixedTo2 && !N->FixedTo2 &&
!Forbidden(N1, N) &&
(!c || (this->*c)(N1, N) < N1->NextCost) &&
(d = (this->*D)(N1, N)) < N1->NextCost) {
N1->NextCost = d;
if (d <= Max)
return;
N1->Next = N;
}
}
while ((N = N->Suc) != FirstNode);
} else {
/* Find the requested edge in a sparse graph */
for (NN1 = N1->CandidateSet; (N = NN1->To); NN1++) {
if (N == N1->Dad || N1 == N->Dad)
continue;
if (FixedOrCommon(N1, N)) {
N1->NextCost = NN1->Cost + N1->Pi + N->Pi;
N1->Next = N;
return;
}
if (!N1->FixedTo2 && !N->FixedTo2 &&
(d = NN1->Cost + N1->Pi + N->Pi) < N1->NextCost) {
N1->NextCost = d;
if (d <= Max)
return;
N1->Next = N;
}
}
}
}
int IsPossibleCandidate(Node * From, Node * To)
{
Node *Na, *Nb, *Nc, *N;
if (InInitialTour(From, To) ||
From->SubproblemSuc == To || To->SubproblemSuc == From ||
FixedOrCommon(From, To))
return 1;
if (From->FixedTo2 || To->FixedTo2)
return 0;
if (MergeTourFiles < 2)
return 1;
if (!From->Head) {
Nb = FirstNode;
do {
Na = Nb;
Nb = Na->MergeSuc[0];
} while (Nb != FirstNode && FixedOrCommon(Na, Nb));
if (Nb != FirstNode) {
N = Nb;
do {
Nc = Nb;
do {
Na = Nb;
Na->Head = Nc;
Nb = Na->MergeSuc[0];
} while (FixedOrCommon(Na, Nb));
do
Nc->Tail = Na;
while ((Nc = Nc->MergeSuc[0]) != Nb);
} while (Nb != N);
} else {
do
Nb->Head = Nb->Tail = FirstNode;
while ((Nb = Nb->Suc) != FirstNode);
}
}
if (From->Head == To->Head ||
(From->Head != From && From->Tail != From) ||
(To->Head != To && To->Tail != To))
return 0;
return 1;
}
static int FixedOrCommonCandidates(Node * N)
{
int Count = 0;
Candidate *NN;
if (N->FixedTo2)
return 2;
if (!N->FixedTo1 && MergeTourFiles == 0)
return 0;
for (NN = N->CandidateSet; NN->To; NN++)
if (FixedOrCommon(N, NN->To))
Count++;
return Count;
}
int FixedOrCommonCandidates(Node * N)
{
int Count = 0;
Candidate *NN;
if (N->FixedTo2)
return 2;
if (!N->FixedTo1 && MergeTourFiles < 2)
return 0;
for (NN = N->CandidateSet; NN && NN->To; NN++)
if (FixedOrCommon(N, NN->To))
Count++;
if (Count > 2)
eprintf("Node %d has more than two required candidate edges", N->Id);
return Count;
}
GainType LKH::LKHAlg::PatchCycles(int k, GainType Gain)
{
Node *s1, *s2, *sStart, *sStop;
GainType NewGain;
int M, i;
if(!CurrentCycle.get())
{
CurrentCycle.reset(new int(0));
Patchwork.reset(new int(0));
RecLevel.reset(new int(0));
}
FindPermutation(k,this);
M = Cycles(k);
if (M == 1 && Gain > 0) {
MakeKOptMove(k);
return Gain;
}
if (M == 1 || M > PatchingC || k + M > NonsequentialMoveType)
return 0;
if (*RecLevel == 0)
*Patchwork = 0;
*CurrentCycle = ShortestCycle(M, k,this);
for (i = 0; i < k; i++) {
if ((*cycle.get())[(*p.get())[2 * i]] != *CurrentCycle)
continue;
sStart = (*t.get())[(*p.get())[2 * i]];
sStop = (*t.get())[(*p.get())[2 * i + 1]];
for (s1 = sStart; s1 != sStop; s1 = s2) {
s2 = SUC(s1);
if (FixedOrCommon(s1, s2))
continue;
if (++(*Patchwork) > Dimension)
return 0;
(*t.get())[2 * k + 1] = s1;
(*t.get())[2 * k + 2] = s2;
MarkDeleted(s1, s2);
/* Find a set of gainful alternating cycles */
NewGain = PatchCyclesRec(k, 2, M, Gain + (this->*C)(s1, s2),this);
UnmarkDeleted(s1, s2);
if (NewGain > 0)
return NewGain;
}
}
return 0;
}
GainType SFCTour(int CurveType)
{
double XMin, XMax, YMin, YMax;
Node *N, **Perm;
int i;
IndexFunction Index;
GainType Cost;
double EntryTime = GetTime();
if (CurveType == SIERPINSKI) {
if (TraceLevel >= 1)
printff("Sierpinski = ");
Index = SierpinskiIndex;
} else {
if (TraceLevel >= 1)
printff("Moore = ");
Index = MooreIndex;
}
N = FirstNode;
XMin = XMax = N->X;
YMin = YMax = N->Y;
N->V = 0;
while ((N = N->Suc) != 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 (XMax == XMin)
XMax = XMin + 1;
if (YMax == YMin)
YMax = YMin + 1;
assert(Perm = (Node **) malloc(Dimension * sizeof(Node *)));
for (i = 0, N = FirstNode; i < Dimension; i++, N = N->Suc)
(Perm[i] = N)->V =
Index((N->X - XMin) / (XMax - XMin),
(N->Y - YMin) / (YMax - YMin));
qsort(Perm, Dimension, sizeof(Node *), compare);
for (i = 1; i < Dimension; i++)
Follow(Perm[i], Perm[i - 1]);
free(Perm);
/* Assure that all fixed or common edges belong to the tour */
N = FirstNode;
do {
N->LastV = 1;
if (!FixedOrCommon(N, N->Suc) && N->CandidateSet) {
Candidate *NN;
for (NN = N->CandidateSet; NN->To; NN++) {
if (!NN->To->LastV && FixedOrCommon(N, NN->To)) {
Follow(NN->To, N);
break;
}
}
}
} while ((N = N->Suc) != FirstNode);
Cost = 0;
N = FirstNode;
do
if (!Fixed(N, N->Suc))
Cost += Distance(N, N->Suc);
while ((N = N->Suc) != FirstNode);
if (TraceLevel >= 1) {
printff(GainFormat, Cost);
if (Optimum != MINUS_INFINITY && Optimum != 0)
printff(", Gap = %0.1f%%", 100.0 * (Cost - Optimum) / Optimum);
printff(", Time = %0.2f sec.\n", fabs(GetTime() - EntryTime));
}
return Cost;
}
void CreateQuadrantCandidateSet(int K)
{
Node *From, *To;
Candidate *NFrom;
int L, Q, CandPerQ, Added, Count, i;
if (K <= 0)
return;
if (TraceLevel >= 2)
printff("Creating quadrant candidate set ... ");
KDTree = BuildKDTree(1);
assert(XMin =
(double *) malloc((1 + DimensionSaved) * sizeof(double)));
assert(XMax =
(double *) malloc((1 + DimensionSaved) * sizeof(double)));
assert(YMin =
(double *) malloc((1 + DimensionSaved) * sizeof(double)));
assert(YMax =
(double *) malloc((1 + DimensionSaved) * sizeof(double)));
if (CoordType == THREED_COORDS) {
assert(ZMin =
(double *) malloc((1 + DimensionSaved) * sizeof(double)));
assert(ZMax =
(double *) malloc((1 + DimensionSaved) * sizeof(double)));
}
ComputeBounds(0, Dimension - 1);
Contains = CoordType == THREED_COORDS ? Contains3D : Contains2D;
BoxOverlaps =
CoordType == THREED_COORDS ? BoxOverlaps3D : BoxOverlaps2D;
L = CoordType == THREED_COORDS ? 8 : 4;
CandPerQ = K / L;
assert(CandidateSet =
(Candidate *) malloc((K + 1) * sizeof(Candidate)));
From = FirstNode;
do {
Count = 0;
for (NFrom = From->CandidateSet; NFrom && NFrom->To; NFrom++)
if (FixedOrCommon(From, NFrom->To) && ++Count == 2)
break;
if (Count == 2)
continue;
Added = 0;
for (Q = 1; Q <= L; Q++) {
NearestQuadrantNeighbors(From, Q, CandPerQ);
for (i = 0; i < Candidates; i++) {
To = CandidateSet[i].To;
if (AddCandidate(From, To, D(From, To), 1))
Added++;
}
}
if (K > Added) {
NearestQuadrantNeighbors(From, 0, K - Added);
for (i = 0; i < Candidates; i++) {
To = CandidateSet[i].To;
AddCandidate(From, To, D(From, To), 2);
}
}
} while ((From = From->Suc) != FirstNode);
free(CandidateSet);
free(KDTree);
free(XMin);
free(XMax);
free(YMin);
free(YMax);
if (CoordType == THREED_COORDS) {
free(ZMin);
free(ZMax);
}
if (Level == 0 &&
(WeightType == GEO || WeightType == GEOM ||
WeightType == GEO_MEEUS || WeightType == GEOM_MEEUS)) {
Candidate **SavedCandidateSet;
assert(SavedCandidateSet =
(Candidate **) malloc((1 + DimensionSaved) *
sizeof(Candidate *)));
if (TraceLevel >= 2)
printff("done\n");
From = FirstNode;
while ((From = From->Suc) != FirstNode)
if ((From->Y > 0) != (FirstNode->Y > 0))
break;
if (From != FirstNode) {
/* Transform longitude (180 and -180 map to 0) */
From = FirstNode;
do {
SavedCandidateSet[From->Id] = From->CandidateSet;
From->CandidateSet = 0;
From->Zc = From->Y;
if (WeightType == GEO || WeightType == GEO_MEEUS)
From->Y =
(int) From->Y + 5.0 * (From->Y -
(int) From->Y) / 3.0;
From->Y += From->Y > 0 ? -180 : 180;
if (WeightType == GEO || WeightType == GEO_MEEUS)
From->Y =
(int) From->Y + 3.0 * (From->Y -
(int) From->Y) / 5.0;
} while ((From = From->Suc) != FirstNode);
Level++;
CreateQuadrantCandidateSet(K);
Level--;
From = FirstNode;
do
From->Y = From->Zc;
while ((From = From->Suc) != FirstNode);
do {
Candidate *QCandidateSet = From->CandidateSet;
From->CandidateSet = SavedCandidateSet[From->Id];
for (NFrom = QCandidateSet; (To = NFrom->To); NFrom++)
AddCandidate(From, To, NFrom->Cost, NFrom->Alpha);
free(QCandidateSet);
} while ((From = From->Suc) != FirstNode);
free(SavedCandidateSet);
}
}
if (Level == 0) {
ResetCandidateSet();
AddTourCandidates();
if (CandidateSetSymmetric)
SymmetrizeCandidateSet();
if (TraceLevel >= 2)
printff("done\n");
}
}
void LKH::LKHAlg::ChooseInitialTour()
{
Node *N, *NextN, *FirstAlternative, *Last;
Candidate *NN;
int Alternatives, Count = 0, i;
if (KickType > 0 && Kicks > 0 && Trial > 1) {
for (Last = FirstNode; (N = Last->BestSuc) != FirstNode; Last = N)
Follow(N, Last);
for (i = 1; i <= Kicks; i++)
KSwapKick(KickType);
return;
}
if (Trial == 1 && (!FirstNode->InitialSuc || InitialTourFraction < 1)) {
if (InitialTourAlgorithm == BORUVKA ||
InitialTourAlgorithm == GREEDY ||
InitialTourAlgorithm == MOORE ||
InitialTourAlgorithm == NEAREST_NEIGHBOR ||
InitialTourAlgorithm == QUICK_BORUVKA ||
InitialTourAlgorithm == SIERPINSKI) {
GainType Cost = InitialTourAlgorithm == MOORE ||
InitialTourAlgorithm == SIERPINSKI ?
SFCTour(InitialTourAlgorithm) : GreedyTour();
if (MaxTrials == 0) {
BetterCost = Cost;
RecordBetterTour();
}
if (!FirstNode->InitialSuc)
return;
}
}
Start:
/* Mark all nodes as "not chosen" by setting their V field to zero */
N = FirstNode;
do
N->V = 0;
while ((N = N->Suc) != FirstNode);
/* Choose FirstNode without two incident fixed or common candidate edges */
do {
if (FixedOrCommonCandidates(N,this) < 2)
break;
}
while ((N = N->Suc) != FirstNode);
FirstNode = N;
/* Move nodes with two incident fixed or common candidate edges in
front of FirstNode */
for (Last = FirstNode->Pred; N != Last; N = NextN) {
NextN = N->Suc;
if (FixedOrCommonCandidates(N,this) == 2)
Follow(N, Last);
}
/* Mark FirstNode as chosen */
FirstNode->V = 1;
N = FirstNode;
/* Loop as long as not all nodes have been chosen */
while (N->Suc != FirstNode) {
FirstAlternative = 0;
Alternatives = 0;
Count++;
/* Case A */
for (NN = N->CandidateSet; (NextN = NN->To); NN++) {
if (!NextN->V && FixedOrCommon(N, NextN)) {
Alternatives++;
NextN->Next = FirstAlternative;
FirstAlternative = NextN;
}
}
if (Alternatives == 0 && FirstNode->InitialSuc && Trial == 1 &&
Count <= InitialTourFraction * Dimension) {
/* Case B */
for (NN = N->CandidateSet; (NextN = NN->To); NN++) {
if (!NextN->V && InInitialTour(N, NextN)) {
Alternatives++;
NextN->Next = FirstAlternative;
FirstAlternative = NextN;
}
}
}
if (Alternatives == 0 && Trial > 1 &&
ProblemType != HCP && ProblemType != HPP) {
/* Case C */
for (NN = N->CandidateSet; (NextN = NN->To); NN++) {
if (!NextN->V && FixedOrCommonCandidates(NextN,this) < 2 &&
NN->Alpha == 0 && (InBestTour(N, NextN) ||
InNextBestTour(N, NextN))) {
Alternatives++;
NextN->Next = FirstAlternative;
FirstAlternative = NextN;
}
}
}
if (Alternatives == 0) {
/* Case D */
for (NN = N->CandidateSet; (NextN = NN->To); NN++) {
if (!NextN->V && FixedOrCommonCandidates(NextN,this) < 2) {
Alternatives++;
NextN->Next = FirstAlternative;
FirstAlternative = NextN;
}
}
}
if (Alternatives == 0) {
/* Case E (actually not really a random choice) */
NextN = N->Suc;
while ((FixedOrCommonCandidates(NextN,this) == 2 || Forbidden(N, NextN))
&& NextN->Suc != FirstNode)
NextN = NextN->Suc;
if (FixedOrCommonCandidates(NextN,this) == 2 || Forbidden(N, NextN)) {
FirstNode = FirstNode->Suc;
goto Start;
}
} else {
NextN = FirstAlternative;
if (Alternatives > 1) {
/* Select NextN at random among the alternatives */
i = Random() % Alternatives;
while (i--)
NextN = NextN->Next;
}
}
/* Include NextN as the successor of N */
Follow(NextN, N);
N = NextN;
N->V = 1;
}
if (Forbidden(N, N->Suc)) {
FirstNode = FirstNode->Suc;
goto Start;
}
if (MaxTrials == 0) {
GainType Cost = 0;
N = FirstNode;
do
Cost += (this->*C)(N, N->Suc) - N->Pi - N->Suc->Pi;
while ((N = N->Suc) != FirstNode);
Cost /= Precision;
if (Cost < BetterCost) {
BetterCost = Cost;
RecordBetterTour();
}
}
}
static int DelaunayClustering(int MaxClusterSize)
{
int Count = 0, Count1, Count2 = 0, i, j = 0;
Edge *EdgeSet, Key;
Node *From, *To, *N, *F, *T;
point *u, *v;
edge *e_start, *e;
delaunay(Dimension);
for (i = 0; i < Dimension; i++) {
u = &p_array[i];
e_start = e = u->entry_pt;
do {
v = Other_point(e, u);
if (u->id < v->id)
Count++;
} while ((e = Next(e, u)) != e_start);
}
assert(EdgeSet = (Edge *) malloc(Count * sizeof(Edge)));
for (i = 0; i < Dimension; i++) {
u = &p_array[i];
e_start = e = u->entry_pt;
do {
v = Other_point(e, u);
if (u->id < v->id) {
EdgeSet[j].From = From = &NodeSet[u->id];
EdgeSet[j].To = To = &NodeSet[v->id];
EdgeSet[j++].Cost = FixedOrCommon(From, To) ? INT_MIN :
Distance(From, To) * Precision + From->Pi + To->Pi;
}
} while ((e = Next(e, u)) != e_start);
}
free_memory();
if (WeightType == GEO || WeightType == GEOM ||
WeightType == GEO_MEEUS || WeightType == GEOM_MEEUS) {
N = FirstNode;
while ((N = N->Suc) != FirstNode)
if ((N->Y > 0) != (FirstNode->Y > 0))
break;
if (N != FirstNode) {
N = FirstNode;
do
N->Zc = N->Y;
while ((N = N->Suc) != FirstNode);
/* Transform longitude (180 and -180 map to 0) */
From = FirstNode;
do {
From->Zc = From->Y;
if (WeightType == GEO || WeightType == GEO_MEEUS)
From->Y =
(int) From->Y + 5.0 * (From->Y -
(int) From->Y) / 3.0;
From->Y += From->Y > 0 ? -180 : 180;
if (WeightType == GEO || WeightType == GEO_MEEUS)
From->Y =
(int) From->Y + 3.0 * (From->Y -
(int) From->Y) / 5.0;
} while ((From = From->Suc) != FirstNode);
delaunay(Dimension);
do
From->Y = From->Zc;
while ((From = From->Suc) != FirstNode);
qsort(EdgeSet, Count, sizeof(Edge), compareFromTo);
for (i = 0; i < Dimension; i++) {
u = &p_array[i];
e_start = e = u->entry_pt;
do {
v = Other_point(e, u);
if (u->id < v->id)
Count2++;
} while ((e = Next(e, u)) != e_start);
}
Count1 = Count;
assert(EdgeSet =
(Edge *) realloc(EdgeSet,
(Count1 + Count2) * sizeof(Edge)));
for (i = 0; i < Dimension; i++) {
u = &p_array[i];
e_start = e = u->entry_pt;
do {
v = Other_point(e, u);
if (u->id > v->id)
continue;
Key.From = From = &NodeSet[u->id];
Key.To = To = &NodeSet[v->id];
if (!bsearch
(&Key, EdgeSet, Count1, sizeof(Edge),
compareFromTo)) {
EdgeSet[Count].From = From;
EdgeSet[Count].To = To;
EdgeSet[Count].Cost =
FixedOrCommon(From, To) ? INT_MIN :
Distance(From,
To) * Precision + From->Pi + To->Pi;
Count++;
}
} while ((e = Next(e, u)) != e_start);
}
free_memory();
}
}
qsort(EdgeSet, Count, sizeof(Edge), compareCost);
/* Union-Find with path compression */
N = FirstNode;
do {
N->Next = N;
N->Size = 1;
} while ((N = N->Suc) != FirstNode);
for (i = 0; i < Count; i++) {
for (F = EdgeSet[i].From; F != F->Next;)
F = F->Next = F->Next->Next;
for (T = EdgeSet[i].To; T != T->Next;)
T = T->Next = T->Next->Next;
if (F != T && F->Size + T->Size <= MaxClusterSize) {
if (F->Size < T->Size) {
F->Next = T;
T->Size += F->Size;
} else {
T->Next = F;
F->Size += T->Size;
}
}
}
free(EdgeSet);
Count = 0;
N = FirstNode;
do {
if (N->Next == N && N->Size > 3)
N->Subproblem = ++Count;
} while ((N = N->Suc) != FirstNode);
do {
for (T = N; T != T->Next;)
T = T->Next = T->Next->Next;
N->Subproblem = T->Subproblem;
} while ((N = N->Suc) != FirstNode);
return Count;
}
Node *Best2OptMove(Node * t1, Node * t2, GainType * G0, GainType * Gain)
{
Node *t3, *t4, *T3 = 0, *T4 = 0;
Candidate *Nt2;
GainType G1, G2, BestG2 = MINUS_INFINITY;
int Breadth2 = 0;
if (SUC(t1) != t2)
Reversed ^= 1;
/*
* Determine (T3,T4) = (t3,t4)
* such that
*
* G4 = *G0 - C(t2,T3) + C(T3,T4)
*
* is maximum (= BestG2), and (T3,T4) has not previously been included.
* If during this process a legal move with *Gain > 0 is found, then make
* the move and exit Best2OptMove immediately
*/
/* Choose (t2,t3) as a candidate edge emanating from t2 */
for (Nt2 = t2->CandidateSet; (t3 = Nt2->To); Nt2++) {
if (t3 == t2->Pred || t3 == t2->Suc ||
((G1 = *G0 - Nt2->Cost) <= 0 && GainCriterionUsed &&
ProblemType != HCP && ProblemType != HPP))
continue;
/* Choose t4 (only one choice gives a closed tour) */
t4 = PRED(t3);
if (FixedOrCommon(t3, t4))
continue;
G2 = G1 + C(t3, t4);
if (!Forbidden(t4, t1) &&
(!c || G2 - c(t4, t1) > 0) && (*Gain = G2 - C(t4, t1)) > 0) {
Swap1(t1, t2, t3);
*G0 = G2;
return 0;
}
if (++Breadth2 > MaxBreadth)
break;
if (GainCriterionUsed && G2 - Precision < t4->Cost)
continue;
if (!Backtracking || Swaps > 0) {
if (G2 > BestG2 &&
Swaps < MaxSwaps &&
Excludable(t3, t4) && (!InInputTour(t3, t4)
|| !Near(t3, t4))) {
T3 = t3;
T4 = t4;
BestG2 = G2;
}
} else if (MaxSwaps > 0) {
GainType G = G2;
Node *t = t4;
Make2OptMove(t1, t2, t3, t4);
Exclude(t1, t2);
Exclude(t3, t4);
while ((t = BestSubsequentMove(t1, t, &G, Gain)));
if (*Gain > 0)
return 0;
RestoreTour();
if (t2 != SUC(t1))
Reversed ^= 1;
}
}
*Gain = 0;
if (T4) {
/* Make the best 2-opt move */
Swap1(t1, t2, T3);
Exclude(t1, t2);
Exclude(T3, T4);
*G0 = BestG2;
}
return T4;
}
GainType LinKernighan()
{
Node *t1, *t2, *SUCt1;
GainType Gain, G0, Cost;
int X2, i, it = 0;
Candidate *Nt1;
Segment *S;
SSegment *SS;
double EntryTime = GetTime();
Reversed = 0;
S = FirstSegment;
i = 0;
do {
S->Size = 0;
S->Rank = ++i;
S->Reversed = 0;
S->First = S->Last = 0;
}
while ((S = S->Suc) != FirstSegment);
SS = FirstSSegment;
i = 0;
do {
SS->Size = 0;
SS->Rank = ++i;
SS->Reversed = 0;
SS->First = SS->Last = 0;
}
while ((SS = SS->Suc) != FirstSSegment);
FirstActive = LastActive = 0;
Swaps = 0;
/* Compute the cost of the initial tour, Cost.
Compute the corresponding hash value, Hash.
Initialize the segment list.
Make all nodes "active" (so that they can be used as t1). */
Cost = 0;
Hash = 0;
i = 0;
t1 = FirstNode;
do {
t2 = t1->OldSuc = t1->Suc;
t1->OldPred = t1->Pred;
t1->Rank = ++i;
Cost += (t1->SucCost = t2->PredCost = C(t1, t2)) - t1->Pi - t2->Pi;
Hash ^= Rand[t1->Id] * Rand[t2->Id];
t1->Cost = INT_MAX;
for (Nt1 = t1->CandidateSet; (t2 = Nt1->To); Nt1++)
if (t2 != t1->Pred && t2 != t1->Suc && Nt1->Cost < t1->Cost)
t1->Cost = Nt1->Cost;
t1->Parent = S;
S->Size++;
if (S->Size == 1)
S->First = t1;
S->Last = t1;
if (SS->Size == 0)
SS->First = S;
S->Parent = SS;
SS->Last = S;
if (S->Size == GroupSize) {
S = S->Suc;
SS->Size++;
if (SS->Size == SGroupSize)
SS = SS->Suc;
}
t1->OldPredExcluded = t1->OldSucExcluded = 0;
t1->Next = 0;
if (KickType == 0 || Kicks == 0 ||
!InBestTour(t1, t1->Pred) || !InBestTour(t1, t1->Suc))
Activate(t1);
}
while ((t1 = t1->Suc) != FirstNode);
if (S->Size < GroupSize)
SS->Size++;
Cost /= Precision;
if (TraceLevel >= 3 || (TraceLevel == 2 && Cost < BetterCost)) {
printff("Cost = " GainFormat, Cost);
if (Optimum != MINUS_INFINITY && Optimum != 0)
printff(", Gap = %0.4f%%", 100.0 * (Cost - Optimum) / Optimum);
printff(", Time = %0.1f sec. %s\n", fabs(GetTime() - EntryTime),
Cost < Optimum ? "<" : Cost == Optimum ? "=" : "");
}
PredSucCostAvailable = 1;
/* Loop as long as improvements are found */
do {
/* Choose t1 as the first "active" node */
while ((t1 = RemoveFirstActive())) {
/* t1 is now "passive" */
SUCt1 = SUC(t1);
if ((TraceLevel >= 3 || (TraceLevel == 2 && Trial == 1)) &&
++it % (Dimension >= 100000 ? 10000 :
Dimension >= 10000 ? 1000 : 100) == 0)
printff("#%d: Time = %0.1f sec.\n",
it, fabs(GetTime() - EntryTime));
/* Choose t2 as one of t1's two neighbors on the tour */
for (X2 = 1; X2 <= 2; X2++) {
t2 = X2 == 1 ? PRED(t1) : SUCt1;
if (FixedOrCommon(t1, t2) ||
(RestrictedSearch && Near(t1, t2) &&
(Trial == 1 ||
(Trial > BackboneTrials &&
(KickType == 0 || Kicks == 0)))))
continue;
G0 = C(t1, t2);
/* Try to find a tour-improving chain of moves */
do
t2 = Swaps == 0 ? BestMove(t1, t2, &G0, &Gain) :
BestSubsequentMove(t1, t2, &G0, &Gain);
while (t2);
if (Gain > 0) {
/* An improvement has been found */
assert(Gain % Precision == 0);
Cost -= Gain / Precision;
if (TraceLevel >= 3 ||
(TraceLevel == 2 && Cost < BetterCost)) {
printff("Cost = " GainFormat, Cost);
if (Optimum != MINUS_INFINITY && Optimum != 0)
printff(", Gap = %0.4f%%",
100.0 * (Cost - Optimum) / Optimum);
printff(", Time = %0.1f sec. %s\n",
fabs(GetTime() - EntryTime),
Cost < Optimum ? "<" : Cost ==
Optimum ? "=" : "");
}
StoreTour();
if (HashSearch(HTable, Hash, Cost))
goto End_LinKernighan;
/* Make t1 "active" again */
Activate(t1);
break;
}
RestoreTour();
}
}
if (HashSearch(HTable, Hash, Cost))
goto End_LinKernighan;
HashInsert(HTable, Hash, Cost);
/* Try to find improvements using non-sequential 4/5-opt moves */
Gain = 0;
if (Gain23Used && (Gain = Gain23()) > 0) {
/* An improvement has been found */
assert(Gain % Precision == 0);
Cost -= Gain / Precision;
StoreTour();
if (TraceLevel >= 3 || (TraceLevel == 2 && Cost < BetterCost)) {
printff("Cost = " GainFormat, Cost);
if (Optimum != MINUS_INFINITY && Optimum != 0)
printff(", Gap = %0.4f%%",
100.0 * (Cost - Optimum) / Optimum);
printff(", Time = %0.1f sec. + %s\n",
fabs(GetTime() - EntryTime),
Cost < Optimum ? "<" : Cost == Optimum ? "=" : "");
}
if (HashSearch(HTable, Hash, Cost))
goto End_LinKernighan;
}
}
while (Gain > 0);
End_LinKernighan:
PredSucCostAvailable = 0;
NormalizeNodeList();
NormalizeSegmentList();
return Cost;
}
Node *Best3OptMove(Node * t1, Node * t2, GainType * G0, GainType * Gain)
{
Node *t3, *t4, *t5, *t6, *T3 = 0, *T4 = 0, *T5 = 0, *T6 = 0;
Candidate *Nt2, *Nt4;
GainType G1, G2, G3, G4, BestG4 = MINUS_INFINITY;
int Case6, BestCase6 = 0, X4, X6;
int Breadth2 = 0, Breadth4;
if (SUC(t1) != t2)
Reversed ^= 1;
/*
* Determine (T3,T4,T5,T6) = (t3,t4,t5,t6)
* such that
*
* G4 = *G0 - C(t2,T3) + C(T3,T4)
* - C(T4,T5) + C(T5,T6)
*
* is maximum (= BestG4), and (T5,T6) has not previously been included.
* If during this process a legal move with *Gain > 0 is found, then make
* the move and exit Best3OptMove immediately.
*/
/* Choose (t2,t3) as a candidate edge emanating from t2 */
for (Nt2 = t2->CandidateSet; (t3 = Nt2->To); Nt2++) {
if (t3 == t2->Pred || t3 == t2->Suc ||
((G1 = *G0 - Nt2->Cost) <= 0 && GainCriterionUsed &&
ProblemType != HCP && ProblemType != HPP))
continue;
if (++Breadth2 > MaxBreadth)
break;
/* Choose t4 as one of t3's two neighbors on the tour */
for (X4 = 1; X4 <= 2; X4++) {
t4 = X4 == 1 ? PRED(t3) : SUC(t3);
if (FixedOrCommon(t3, t4))
continue;
G2 = G1 + C(t3, t4);
if (X4 == 1 &&
!Forbidden(t4, t1) &&
(!c || G2 - c(t4, t1) > 0) && (*Gain = G2 - C(t4, t1)) > 0)
{
Swap1(t1, t2, t3);
return 0;
}
if (Backtracking && !Excludable(t3, t4))
continue;
Breadth4 = 0;
/* Choose (t4,t5) as a candidate edge emanating from t4 */
for (Nt4 = t4->CandidateSet; (t5 = Nt4->To); Nt4++) {
if (t5 == t4->Pred || t5 == t4->Suc ||
((G3 = G2 - Nt4->Cost) <= 0 && GainCriterionUsed) ||
(X4 == 2 && !BETWEEN(t2, t5, t3)))
continue;
if (++Breadth4 > MaxBreadth)
break;
/* Choose t6 as one of t5's two neighbors on the tour */
for (X6 = 1; X6 <= X4; X6++) {
if (X4 == 1) {
Case6 = 1 + !BETWEEN(t2, t5, t4);
t6 = Case6 == 1 ? SUC(t5) : PRED(t5);
} else {
Case6 = 4 + X6;
t6 = X6 == 1 ? SUC(t5) : PRED(t5);
if (t6 == t1)
continue;
}
if (FixedOrCommon(t5, t6))
continue;
G4 = G3 + C(t5, t6);
if (!Forbidden(t6, t1) &&
(!c || G4 - c(t6, t1) > 0) &&
(*Gain = G4 - C(t6, t1)) > 0) {
Make3OptMove(t1, t2, t3, t4, t5, t6, Case6);
return 0;
}
if (GainCriterionUsed && G4 - Precision < t6->Cost)
continue;
if (!Backtracking || Swaps > 0) {
if (G4 > BestG4 &&
Swaps < MaxSwaps &&
Excludable(t5, t6) &&
(!InInputTour(t5, t6) || !Near(t5, t6))) {
/* Ignore the move if the gain does not vary */
if (RestrictedSearch &&
ProblemType != HCP &&
ProblemType != HPP &&
G2 - t4->Pi == G4 - t6->Pi &&
G3 + t5->Pi == G1 + t3->Pi)
continue;
T3 = t3;
T4 = t4;
T5 = t5;
T6 = t6;
BestCase6 = Case6;
BestG4 = G4;
}
} else if (MaxSwaps > 0) {
GainType G = G4;
Node *t = t6;
Make3OptMove(t1, t2, t3, t4, t5, t6, Case6);
Exclude(t1, t2);
Exclude(t3, t4);
Exclude(t5, t6);
while ((t = BestSubsequentMove(t1, t, &G, Gain)));
if (*Gain > 0)
return 0;
RestoreTour();
if (t2 != SUC(t1))
Reversed ^= 1;
}
}
}
}
}
*Gain = 0;
if (T6) {
/* Make the best 3-opt move */
Make3OptMove(t1, t2, T3, T4, T5, T6, BestCase6);
Exclude(t1, t2);
Exclude(T3, T4);
Exclude(T5, T6);
*G0 = BestG4;
}
return T6;
}
LKH::LKHAlg::Node * LKH::LKHAlg::Best5OptMove(Node * t1, Node * t2, GainType * G0, GainType * Gain)
{
Node *t3, *t4, *t5, *t6 = 0, *t7, *t8 = 0, *t9, *t10 = 0;
Node *T3 = 0, *T4 = 0, *T5 = 0, *T6 = 0, *T7 = 0, *T8 = 0, *T9 =
0, *T10 = 0;
Candidate *Nt2, *Nt4, *Nt6, *Nt8;
GainType G1, G2, G3, G4, G5, G6, G7, G8, BestG8 = MINUS_INFINITY;
int Case6 = 0, Case8 = 0, Case10 = 0, BestCase10 = 0, X4, X6, X8, X10,
BTW275 = 0, BTW674 = 0,
BTW571 = 0, BTW376 = 0, BTW574 = 0, BTW671 = 0,
BTW471 = 0, BTW673 = 0, BTW573 = 0, BTW273 = 0;
int Breadth2 = 0, Breadth4, Breadth6, Breadth8;
if (t2 != SUC(t1))
Reversed ^= 1;
/*
* Determine (T3,T4,T5,T6,T7,T8,T9,T10) = (t3,t4,t5,t6,t7,t8,t9,t10)
* such that
*
* G8 = *G0 - C(t2,T3) + C(T3,T4)
* - C(T4,T5) + C(T5,T6)
* - C(T6,T7) + C(T7,T8)
* - C(T8,T9) + C(T9,T10)
*
* is maximum (= BestG8), and (T9,T10) has not previously been included.
* If during this process a legal move with *Gain > 0 is found, then make
* the move and exit Best5OptMove immediately.
*/
/* Choose (t2,t3) as a candidate edge emanating from t2 */
for (Nt2 = t2->CandidateSet; (t3 = Nt2->To); Nt2++) {
if (t3 == t2->Pred || t3 == t2->Suc ||
((G1 = *G0 - Nt2->Cost) <= 0 && GainCriterionUsed &&
ProblemType != HCP && ProblemType != HPP))
continue;
if (++Breadth2 > MaxBreadth)
break;
/* Choose t4 as one of t3's two neighbors on the tour */
for (X4 = 1; X4 <= 2; X4++) {
t4 = X4 == 1 ? PRED(t3) : SUC(t3);
if (FixedOrCommon(t3, t4))
continue;
G2 = G1 + (this->*C)(t3, t4);
if (X4 == 1 &&
!Forbidden(t4, t1) &&
(!c || G2 - (this->*c)(t4, t1) > 0) && (*Gain = G2 - (this->*C)(t4, t1)) > 0)
{
Make2OptMove(t1, t2, t3, t4);
return 0;
}
if (Backtracking && !Excludable(t3, t4))
continue;
Breadth4 = 0;
/* Choose (t4,t5) as a candidate edge emanating from t4 */
for (Nt4 = t4->CandidateSet; (t5 = Nt4->To); Nt4++) {
if (t5 == t4->Pred || t5 == t4->Suc ||
((G3 = G2 - Nt4->Cost) <= 0 && GainCriterionUsed &&
ProblemType != HCP && ProblemType != HPP))
continue;
if (++Breadth4 > MaxBreadth)
break;
/* Choose t6 as one of t5's two neighbors on the tour */
for (X6 = 1; X6 <= 2; X6++) {
if (X4 == 1) {
if (X6 == 1) {
Case6 = 1 + !BETWEEN(t2, t5, t4);
t6 = Case6 == 1 ? SUC(t5) : PRED(t5);
} else {
t6 = t6 == t5->Pred ? t5->Suc : t5->Pred;
if ((t5 == t1 && t6 == t2) ||
(t5 == t2 && t6 == t1))
continue;
Case6 += 2;
}
} else if (BETWEEN(t2, t5, t3)) {
Case6 = 4 + X6;
t6 = X6 == 1 ? SUC(t5) : PRED(t5);
if (t6 == t1)
continue;
} else {
Case6 = 6 + X6;
t6 = X6 == 1 ? PRED(t5) : SUC(t5);
if (t6 == t2)
continue;
}
if (FixedOrCommon(t5, t6))
continue;
G4 = G3 + (this->*C)(t5, t6);
if ((Case6 <= 2 || Case6 == 5 || Case6 == 6) &&
!Forbidden(t6, t1) &&
(!c || G4 - (this->*c)(t6, t1) > 0) &&
(*Gain = G4 - (this->*C)(t6, t1)) > 0) {
Make3OptMove(t1, t2, t3, t4, t5, t6, Case6);
return 0;
}
if (Backtracking && !Excludable(t5, t6))
continue;
Breadth6 = 0;
/* Choose (t6,t7) as a candidate edge emanating from t6 */
for (Nt6 = t6->CandidateSet; (t7 = Nt6->To); Nt6++) {
if (t7 == t6->Pred || t7 == t6->Suc ||
(t6 == t2 && t7 == t3) ||
(t6 == t3 && t7 == t2) ||
((G5 = G4 - Nt6->Cost) <= 0 &&
GainCriterionUsed &&
ProblemType != HCP && ProblemType != HPP))
continue;
if (++Breadth6 > MaxBreadth)
break;
/* Choose t8 as one of t7's two neighbors on the tour */
for (X8 = 1; X8 <= 2; X8++) {
if (X8 == 1) {
Case8 = Case6;
switch (Case6) {
case 1:
if ((BTW275 = BETWEEN(t2, t7, t5)))
t8 = SUC(t7);
else {
t8 = PRED(t7);
BTW674 = BETWEEN(t6, t7, t4);
}
break;
case 2:
if ((BTW376 = BETWEEN(t3, t7, t6)))
t8 = SUC(t7);
else {
t8 = PRED(t7);
BTW571 = BETWEEN(t5, t7, t1);
}
break;
case 3:
t8 = SUC(t7);
BTW574 = BETWEEN(t5, t7, t4);
break;
case 4:
if ((BTW671 = BETWEEN(t6, t7, t1)))
t8 = PRED(t7);
else
t8 = BETWEEN(t2, t7,
t4) ? SUC(t7) :
PRED(t7);
break;
case 5:
t8 = PRED(t7);
BTW471 = BETWEEN(t4, t7, t1);
if (!BTW471)
BTW673 = BETWEEN(t6, t7, t3);
break;
case 6:
if ((BTW471 = BETWEEN(t4, t7, t1)))
t8 = PRED(t7);
else {
t8 = SUC(t7);
BTW573 = BETWEEN(t5, t7, t3);
}
break;
case 7:
case 8:
t8 = SUC(t7);
BTW273 = BETWEEN(t2, t7, t3);
break;
}
} else {
t8 = t8 == t7->Pred ? t7->Suc : t7->Pred;
Case8 += 8;
}
if ((t7 == t1 && t8 == t2) ||
(t7 == t2 && t8 == t1) ||
(t7 == t3 && t8 == t4) ||
(t7 == t4 && t8 == t3))
continue;
if (FixedOrCommon(t7, t8))
continue;
if (Case6 == 3 && !BTW574 &&
(X8 == 1) == BETWEEN(t3, t7, t1))
continue;
if (Case6 == 4 && BTW671 && X8 == 2)
break;
if (Case6 == 7 && !BTW273 &&
(X8 == 1) == BETWEEN(t5, t7, t1))
continue;
if (Case6 == 8 && !BTW273
&& !BETWEEN(t4, t7, t5))
break;
G6 = G5 + (this->*C)(t7, t8);
if (t8 != t1 &&
(Case6 == 3 ? BTW574 :
Case6 == 4 ? !BTW671 :
Case6 == 7 ? BTW273 :
Case6 != 8 && X8 == 1) &&
!Forbidden(t8, t1) &&
(!c || G6 - (this->*c)(t8, t1) > 0) &&
(*Gain = G6 - (this->*C)(t8, t1)) > 0) {
Make4OptMove(t1, t2, t3, t4, t5, t6, t7,
t8, Case8);
return 0;
}
if (Backtracking && !Excludable(t7, t8))
continue;
Breadth8 = 0;
/* Choose (t8,t9) as a candidate edge emanating
from t8 */
for (Nt8 = t8->CandidateSet; (t9 = Nt8->To);
Nt8++) {
if (t9 == t8->Pred || t9 == t8->Suc
|| t9 == t1 || (t8 == t2 && t9 == t3)
|| (t8 == t3 && t9 == t2) || (t8 == t4
&& t9 ==
t5)
|| (t8 == t5 && t9 == t4)
|| ((G7 = G6 - Nt8->Cost) <= 0
&& GainCriterionUsed
&& ProblemType != HCP
&& ProblemType != HPP))
continue;
if (++Breadth8 > MaxBreadth)
break;
/* Choose t10 as one of t9's two neighbors
on the tour */
for (X10 = 1; X10 <= 2; X10++) {
if (X10 == 1) {
t10 = 0;
switch (Case8) {
case 1:
t10 = (BTW275 ?
BETWEEN(t8, t9, t5)
|| BETWEEN(t3, t9,
t1) : BTW674
? BETWEEN(t7, t9,
t1) :
BETWEEN(t7, t9,
t5)) ? PRED(t9)
: SUC(t9);
Case10 = 22;
break;
case 2:
t10 = (BTW376 ?
BETWEEN(t8, t9, t4) :
BTW571 ?
BETWEEN(t7, t9, t1)
|| BETWEEN(t3, t9,
t6) :
BETWEEN(t7, t9,
t1)) ? PRED(t9)
: SUC(t9);
Case10 = 23;
break;
case 3:
if (BTW574) {
t10 = BETWEEN(t5, t9, t1) ?
PRED(t9) : SUC(t9);
Case10 = 24;
break;
}
if (!BETWEEN(t5, t9, t4))
break;
t10 = SUC(t9);
Case10 = 1;
break;
case 4:
if (BTW671) {
if (!BETWEEN(t2, t9, t5))
break;
t10 = SUC(t9);
Case10 = 2;
break;
}
t10 = BETWEEN(t6, t9, t4) ?
PRED(t9) : SUC(t9);
Case10 = 25;
break;
case 5:
t10 = (BTW471 ?
BETWEEN(t7, t9, t1) :
BTW673 ?
BETWEEN(t7, t9, t5) :
BETWEEN(t4, t9, t1)
|| BETWEEN(t7, t9,
t5)) ?
PRED(t9) : SUC(t9);
Case10 = 26;
break;
case 6:
t10 = (BTW471 ?
BETWEEN(t7, t9, t3) :
BTW573 ?
BETWEEN(t8, t9, t6) :
BETWEEN(t4, t9, t1)
|| BETWEEN(t8, t9,
t6)) ?
PRED(t9) : SUC(t9);
Case10 = 27;
break;
case 7:
if (BTW273) {
t10 = BETWEEN(t5, t9, t3) ?
PRED(t9) : SUC(t9);
Case10 = 28;
break;
}
if (!BETWEEN(t2, t9, t3))
break;
t10 = SUC(t9);
Case10 = 3;
break;
case 8:
if (BTW273) {
if (!BETWEEN(t4, t9, t5))
break;
Case10 = 4;
} else {
if (!BETWEEN(t2, t9, t3))
break;
Case10 = 5;
}
t10 = SUC(t9);
break;
case 9:
if (BTW275) {
if (!BETWEEN(t7, t9, t4))
break;
t10 = SUC(t9);
Case10 = 6;
break;
}
if (!BTW674) {
if (!BETWEEN(t2, t9, t7))
break;
t10 = SUC(t9);
Case10 = 7;
break;
}
if (!BETWEEN(t6, t9, t7))
break;
t10 = SUC(t9);
Case10 = 8;
break;
case 10:
if (BTW376) {
if (!BETWEEN(t7, t9, t6))
break;
t10 = SUC(t9);
Case10 = 9;
break;
}
if (BTW571) {
if (!BETWEEN(t2, t9, t7))
break;
t10 = SUC(t9);
Case10 = 10;
break;
}
if (!BETWEEN(t3, t9, t6) &&
!BETWEEN(t2, t9, t7))
break;
t10 = SUC(t9);
Case10 = 11;
break;
case 11:
if (BTW574) {
t10 = BETWEEN(t3, t9, t1) ?
PRED(t9) : SUC(t9);
Case10 = 29;
break;
}
if (!BETWEEN(t5, t9, t4))
break;
t10 = SUC(t9);
Case10 = 12;
break;
case 12:
t10 = BETWEEN(t3, t9, t1) ?
PRED(t9) : SUC(t9);
Case10 = 30;
break;
case 13:
if (BTW471) {
if (!BETWEEN(t2, t9, t7))
break;
t10 = SUC(t9);
Case10 = 13;
break;
}
if (BTW673) {
if (!BETWEEN(t6, t9, t7))
break;
t10 = SUC(t9);
Case10 = 14;
break;
}
if (!BETWEEN(t6, t9, t3) &&
!BETWEEN(t2, t9, t7))
break;
t10 = SUC(t9);
Case10 = 15;
break;
case 14:
if (BTW471) {
if (!BETWEEN(t2, t9, t7))
break;
t10 = SUC(t9);
Case10 = 16;
break;
}
if (BTW573) {
if (!BETWEEN(t7, t9, t3) &&
!BETWEEN(t2, t9, t6))
break;
t10 = SUC(t9);
Case10 = 17;
break;
}
if (!BETWEEN(t7, t9, t6))
break;
t10 = SUC(t9);
Case10 = 18;
break;
case 15:
if (BTW273) {
t10 = BETWEEN(t5, t9, t1) ?
PRED(t9) : SUC(t9);
Case10 = 31;
break;
}
if (!BETWEEN(t2, t9, t3))
break;
t10 = SUC(t9);
Case10 = 19;
break;
case 16:
if (BTW273) {
if (!BETWEEN(t4, t9, t5))
break;
Case10 = 20;
} else {
if (!BETWEEN(t2, t9, t3))
break;
Case10 = 21;
}
t10 = SUC(t9);
break;
}
if (!t10)
break;
} else {
if (Case10 >= 22)
continue;
Case10 += 31;
t10 =
t10 ==
t9->Pred ? t9->Suc : t9->Pred;
}
if (t10 == t1 ||
(t9 == t3 && t10 == t4) ||
(t9 == t4 && t10 == t3) ||
(t9 == t5 && t10 == t6) ||
(t9 == t6 && t10 == t5))
continue;
if (FixedOrCommon(t9, t10))
continue;
G8 = G7 + (this->*C)(t9, t10);
if (!Forbidden(t10, t1) &&
(!c || G8 - (this->*c)(t10, t1) > 0) &&
(*Gain = G8 - (this->*C)(t10, t1)) > 0) {
Make5OptMove(t1, t2, t3, t4, t5,
t6, t7, t8, t9, t10,
Case10);
return 0;
}
if (GainCriterionUsed &&
G8 - Precision < t10->Cost)
continue;
if (!Backtracking || Swaps > 0) {
if ((G8 > BestG8 ||
(G8 == BestG8 && !Near(t9, t10)
&& Near(T9, T10)))
&& Swaps < MaxSwaps
&& Excludable(t9, t10)
&& !InInputTour(t9, t10)) {
/* Ignore the move if the gain does
not vary */
if (RestrictedSearch &&
ProblemType != HCP &&
ProblemType != HPP &&
G2 - t4->Pi == G4 - t6->Pi &&
G4 - t6->Pi == G6 - t8->Pi &&
G6 - t8->Pi == G8 - t10->Pi &&
G3 + t5->Pi == G1 + t3->Pi &&
G5 + t7->Pi == G3 + t5->Pi &&
G7 + t9->Pi == G5 + t7->Pi)
continue;
T3 = t3;
T4 = t4;
T5 = t5;
T6 = t6;
T7 = t7;
T8 = t8;
T9 = t9;
T10 = t10;
BestCase10 = Case10;
BestG8 = G8;
}
} else if (MaxSwaps > 0) {
GainType G = G8;
Node *t = t10;
Make5OptMove(t1, t2, t3, t4, t5,
t6, t7, t8, t9, t10,
Case10);
Exclude(t1, t2);
Exclude(t3, t4);
Exclude(t5, t6);
Exclude(t7, t8);
Exclude(t9, t10);
while ((t =
(this->*BestSubsequentMove)(t1, t,
&G,
Gain)));
if (*Gain > 0)
return 0;
RestoreTour();
if (t2 != SUC(t1))
Reversed ^= 1;
}
}
}
}
}
}
}
}
}
*Gain = 0;
if (T10) {
/* Make the best 5-opt move */
Make5OptMove(t1, t2, T3, T4, T5, T6, T7, T8, T9, T10, BestCase10);
Exclude(t1, t2);
Exclude(T3, T4);
Exclude(T5, T6);
Exclude(T7, T8);
Exclude(T9, T10);
*G0 = BestG8;
}
return T10;
}
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");
}
LKH::LKHAlg::Node * LKH::LKHAlg::Best4OptMove(Node * t1, Node * t2, GainType * G0, GainType * Gain)
{
Node *t3, *t4, *t5, *t6 = 0, *t7, *t8 = 0,
*T3 = 0, *T4 = 0, *T5 = 0, *T6 = 0, *T7 = 0, *T8 = 0;
Candidate *Nt2, *Nt4, *Nt6;
GainType G1, G2, G3, G4, G5, G6, BestG6 = MINUS_INFINITY;
int Case6 = 0, Case8 = 0, BestCase8 = 0, X4, X6, X8;
int Breadth2 = 0, Breadth4, Breadth6;
*Gain = 0;
if (SUC(t1) != t2)
Reversed ^= 1;
/*
* Determine (T3,T4,T5,T6,T7,T8) = (t3,t4,t5,t6,t7,t8)
* such that
*
* G8 = *G0 - C(t2,T3) + C(T3,T4)
* - C(T4,T5) + C(T5,T6)
* - C(T6,T7) + C(T7,T8)
*
* is maximum (= BestG6), and (T7,T8) has not previously been included.
* If during this process a legal move with *Gain > 0 is found, then make
* the move and exit Best4OptMove immediately.
*/
/* Choose (t2,t3) as a candidate edge emanating from t2 */
for (Nt2 = t2->CandidateSet; (t3 = Nt2->To); Nt2++) {
if (t3 == t2->Pred || t3 == t2->Suc ||
((G1 = *G0 - Nt2->Cost) <= 0 && GainCriterionUsed &&
ProblemType != HCP && ProblemType != HPP))
continue;
if (++Breadth2 > MaxBreadth)
break;
/* Choose t4 as one of t3's two neighbors on the tour */
for (X4 = 1; X4 <= 2; X4++) {
t4 = X4 == 1 ? PRED(t3) : SUC(t3);
if (FixedOrCommon(t3, t4))
continue;
G2 = G1 + (this->*C)(t3, t4);
if (X4 == 1 &&
!Forbidden(t4, t1) &&
(!c || G2 - (this->*c)(t4, t1) > 0) && (*Gain = G2 - (this->*C)(t4, t1)) > 0)
{
Swap1(t1, t2, t3);
return 0;
}
if (Backtracking && !Excludable(t3, t4))
continue;
Breadth4 = 0;
/* Choose (t4,t5) as a candidate edge emanating from t4 */
for (Nt4 = t4->CandidateSet; (t5 = Nt4->To); Nt4++) {
if (t5 == t4->Pred || t5 == t4->Suc ||
((G3 = G2 - Nt4->Cost) <= 0 && GainCriterionUsed &&
ProblemType != HCP && ProblemType != HPP))
continue;
if (++Breadth4 > MaxBreadth)
break;
/* Choose t6 as one of t5's two neighbors on the tour */
for (X6 = 1; X6 <= 2; X6++) {
if (X4 == 1) {
if (X6 == 1) {
Case6 = 1 + !BETWEEN(t2, t5, t4);
t6 = Case6 == 1 ? SUC(t5) : PRED(t5);
} else {
t6 = t6 == t5->Pred ? t5->Suc : t5->Pred;
if ((t5 == t1 && t6 == t2) ||
(t5 == t2 && t6 == t1))
continue;
Case6 += 2;
}
} else if (BETWEEN(t2, t5, t3)) {
Case6 = 4 + X6;
t6 = X6 == 1 ? SUC(t5) : PRED(t5);
if (t6 == t1)
continue;
} else {
if (X6 == 2)
break;
Case6 = 7;
t6 = PRED(t5);
if (t6 == t2)
continue;
}
if (FixedOrCommon(t5, t6))
continue;
G4 = G3 + (this->*C)(t5, t6);
if ((Case6 <= 2 || Case6 == 5 || Case6 == 6) &&
!Forbidden(t6, t1) &&
(!c || G4 - (this->*c)(t6, t1) > 0) &&
(*Gain = G4 - (this->*C)(t6, t1)) > 0) {
Make3OptMove(t1, t2, t3, t4, t5, t6, Case6);
return 0;
}
if (Backtracking && !Excludable(t5, t6))
continue;
Breadth6 = 0;
/* Choose (t6,t7) as a candidate edge emanating from t6 */
for (Nt6 = t6->CandidateSet; (t7 = Nt6->To); Nt6++) {
if (t7 == t6->Pred || t7 == t6->Suc ||
(t6 == t2 && t7 == t3) ||
(t6 == t3 && t7 == t2) ||
((G5 = G4 - Nt6->Cost) <= 0 &&
GainCriterionUsed &&
ProblemType != HCP && ProblemType != HPP))
continue;
if (++Breadth6 > MaxBreadth)
break;
/* Choose t8 as one of t7's two neighbors on the tour */
for (X8 = 1; X8 <= 2; X8++) {
if (X8 == 1) {
Case8 = Case6;
t8 = 0;
switch (Case6) {
case 1:
t8 = BETWEEN(t2, t7,
t5) ? SUC(t7) : PRED(t7);
break;
case 2:
t8 = BETWEEN(t3, t7,
t6) ? SUC(t7) : PRED(t7);
break;
case 3:
if (BETWEEN(t5, t7, t4))
t8 = SUC(t7);
break;
case 4:
if (BETWEEN(t2, t7, t5))
t8 = BETWEEN(t2, t7,
t4) ? SUC(t7) :
PRED(t7);
break;
case 5:
t8 = PRED(t7);
break;
case 6:
t8 = BETWEEN(t2, t7,
t3) ? SUC(t7) : PRED(t7);
break;
case 7:
if (BETWEEN(t2, t7, t3))
t8 = SUC(t7);
break;
}
if (t8 == 0)
break;
} else {
if (Case6 != 3 && Case6 != 4 && Case6 != 7)
break;
t8 = t8 == t7->Pred ? t7->Suc : t7->Pred;
Case8 += 8;
}
if (t8 == t1 ||
(t7 == t3 && t8 == t4) ||
(t7 == t4 && t8 == t3))
continue;
if (FixedOrCommon(t7, t8))
continue;
G6 = G5 + (this->*C)(t7, t8);
if (t8 != t1 &&
!Forbidden(t8, t1) &&
(!c || G6 - (this->*c)(t8, t1) > 0) &&
(*Gain = G6 - (this->*C)(t8, t1)) > 0) {
Make4OptMove(t1, t2, t3, t4, t5, t6, t7,
t8, Case8);
return 0;
}
if (GainCriterionUsed &&
G6 - Precision < t8->Cost)
continue;
if (!Backtracking || Swaps > 0) {
if ((G6 > BestG6 ||
(G6 == BestG6 && !Near(t7, t8) &&
Near(T7, T8))) &&
Swaps < MaxSwaps &&
Excludable(t7, t8) &&
!InInputTour(t7, t8)) {
/* Ignore the move if the gain does
not vary */
if (RestrictedSearch &&
ProblemType != HCP &&
ProblemType != HPP &&
G2 - t4->Pi == G4 - t6->Pi &&
G4 - t6->Pi == G6 - t8->Pi &&
G3 + t5->Pi == G1 + t3->Pi &&
G5 + t7->Pi == G3 + t5->Pi)
continue;
T3 = t3;
T4 = t4;
T5 = t5;
T6 = t6;
T7 = t7;
T8 = t8;
BestCase8 = Case8;
BestG6 = G6;
}
} else if (MaxSwaps > 0) {
GainType G = G6;
Node *t = t8;
Make4OptMove(t1, t2, t3, t4, t5, t6, t7,
t8, Case8);
Exclude(t1, t2);
Exclude(t3, t4);
Exclude(t5, t6);
Exclude(t7, t8);
while ((t =
(this->*BestSubsequentMove)(t1, t, &G,
Gain)));
if (*Gain > 0)
return 0;
RestoreTour();
if (t2 != SUC(t1))
Reversed ^= 1;
}
}
}
}
}
}
}
*Gain = 0;
if (T8) {
/* Make the best 4-opt move */
Make4OptMove(t1, t2, T3, T4, T5, T6, T7, T8, BestCase8);
Exclude(t1, t2), Exclude(T3, T4);
Exclude(T5, T6);
Exclude(T7, T8);
*G0 = BestG6;
}
return T8;
}
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::MinimumSpanningTree(int Sparse)
{
Node *Blue; /* Points to the last node included in the tree */
Node *NextBlue = 0; /* Points to the provisional next node to be included */
Node *N;
Candidate *NBlue;
int d;
Blue = N = FirstNode;
Blue->Dad = 0; /* The root of the tree has no father */
if (Sparse && Blue->CandidateSet) {
/* The graph is sparse */
/* Insert all nodes in the heap */
Blue->Loc = 0; /* A blue node is not in the heap */
while ((N = N->Suc) != FirstNode) {
N->Dad = Blue;
N->Cost = N->Rank = INT_MAX;
HeapLazyInsert(N,this);
}
/* Update all neighbors to the blue node */
for (NBlue = Blue->CandidateSet; (N = NBlue->To); NBlue++) {
if (FixedOrCommon(Blue, N)) {
N->Dad = Blue;
N->Cost = NBlue->Cost + Blue->Pi + N->Pi;
N->Rank = INT_MIN;
HeapSiftUp(N,this);
} else if (!Blue->FixedTo2 && !N->FixedTo2) {
N->Dad = Blue;
N->Cost = N->Rank = NBlue->Cost + Blue->Pi + N->Pi;
HeapSiftUp(N,this);
}
}
/* Loop as long as there are more nodes to include in the tree */
while ((NextBlue = HeapDeleteMin(this))) {
Follow(NextBlue, Blue);
Blue = NextBlue;
/* Update all neighbors to the blue node */
for (NBlue = Blue->CandidateSet; (N = NBlue->To); NBlue++) {
if (!N->Loc)
continue;
if (FixedOrCommon(Blue, N)) {
N->Dad = Blue;
N->Cost = NBlue->Cost + Blue->Pi + N->Pi;
N->Rank = INT_MIN;
HeapSiftUp(N,this);
} else if (!Blue->FixedTo2 && !N->FixedTo2 &&
(d = NBlue->Cost + Blue->Pi + N->Pi) < N->Cost)
{
N->Dad = Blue;
N->Cost = N->Rank = d;
HeapSiftUp(N,this);
}
}
}
} else {
/* The graph is dense */
while ((N = N->Suc) != FirstNode)
N->Cost = INT_MAX;
/* Loop as long as there a more nodes to include in the tree */
while ((N = Blue->Suc) != FirstNode) {
int Min = INT_MAX;
/* Update all non-blue nodes (the successors of Blue in the list) */
do {
if (FixedOrCommon(Blue, N)) {
N->Dad = Blue;
N->Cost = (this->*D)(Blue, N);
NextBlue = N;
Min = INT_MIN;
} else {
if (!Blue->FixedTo2 && !N->FixedTo2 &&
!Forbidden(Blue, N) &&
(!c || (this->*c)(Blue, N) < N->Cost) &&
(d = (this->*D)(Blue, N)) < N->Cost) {
N->Cost = d;
N->Dad = Blue;
}
if (N->Cost < Min) {
Min = N->Cost;
NextBlue = N;
}
}
}
while ((N = N->Suc) != FirstNode);
Follow(NextBlue, Blue);
Blue = NextBlue;
}
}
}