bool LpSolve::solve() {
set_add_rowmode(lp, TRUE);
for (size_t c = 0; c < moduleIndexMap.size(); ++c) {
colno[c] = c + 1;
set_binary(lp, c + 1, TRUE);
}
for (auto &equation : equations) {
memset(row, 0, moduleIndexMap.size() * sizeof(*row));
for (auto const &module : equation->getModules()) {
row[moduleIndexMap.at(module->toString())] = 1;
}
add_constraintex(lp, moduleIndexMap.size(), row, colno, equation->getIsEqualityConstraint() ? EQ : LE, 1);
}
set_add_rowmode(lp, FALSE);
memset(row, 0, moduleIndexMap.size() * sizeof(*row));
set_obj_fnex(lp, moduleIndexMap.size(), row, colno);
if (::solve(lp) != OPTIMAL) {
return false;
}
get_variables(lp, row);
for (size_t j = 0; j < moduleIndexMap.size(); j++)
printf("%s: %f\n", get_col_name(lp, j + 1), row[j]);
return true;
}
// TODO there's a seriouxx need for refactoring here !
Solution LpsolveAdaptator::getAdmissibleSolution(LinearProblem * lp) {
lprec *lprec;
int nbCol = lp->getVariables().size();
lprec = make_lp(0, nbCol);
if (lprec == NULL) {
// TODO raise an exception
}
/* set variables name to ease debugging */
for (int i = 0; i < (int)lp->getVariables().size(); ++i) {
Variable * var = (lp->getVariables())[i];
set_col_name(lprec, i+1, var->getNameToChar());
if (var->isBinary()) {
set_binary(lprec, i+1, TRUE);
}
}
/* to build the model faster when adding constraints one at a time */
set_add_rowmode(lprec, TRUE);
for (int i = 0; i < (int)(lp->getConstraints().size()); ++i) {
// FIXME there's a bug here but I can't find it
Constraint c = (Constraint)(lp->getConstraints()[i]);
TermList terms = c.getTerms();
int col[terms.size()];
REAL row[terms.size()];
int j = 0;
for (TermList::const_iterator it = terms.begin(); it != terms.end();
++it, ++j) {
// TODO check if this is fixed
col[j] = ((Term)*it).getVariable().getPosition();
row[j] = ((Term)*it).getCoeff();
}
// WARNING the Consraint uses the same operator values than in lp_lib.h
if (!add_constraintex(lprec, j, row, col, c.getOperator(), c.getBound())) {
// TODO raise an exception
}
}
/* the objective function requires rowmode to be off */
set_add_rowmode(lprec, FALSE);
return getSolution(lprec);
}
int main ( int argv, char * argc[] )
{
# if defined ERROR
# undef ERROR
# endif
# define ERROR() { fprintf(stderr, "Error\n"); exit(1); }
lprec *lp;
int majorversion, minorversion, release, build;
#if defined FORTIFY
Fortify_EnterScope();
#endif
lp_solve_version(&majorversion, &minorversion, &release, &build);
printf("lp_solve %d.%d.%d.%d demo\n\n", majorversion, minorversion, release, build);
printf("This demo will show most of the features of lp_solve %d.%d.%d.%d\n", majorversion, minorversion, release, build);
press_ret();
printf("\nWe start by creating a new problem with 4 variables and 0 constraints\n");
printf("We use: lp=make_lp(0,4);\n");
if ((lp = make_lp(0,4)) == NULL)
ERROR();
press_ret();
printf("We can show the current problem with print_lp(lp)\n");
print_lp(lp);
press_ret();
printf("Now we add some constraints\n");
printf("add_constraint(lp, {0, 3, 2, 2, 1}, LE, 4)\n");
{
double row[] = {0, 3, 2, 2, 1};
if (!add_constraint(lp, row, LE, 4))
ERROR();
}
print_lp(lp);
press_ret();
printf("add_constraintex is now used to add a row. Only the npn-zero values must be specfied with this call.\n");
printf("add_constraintex(lp, 3, {4, 3, 1}, {2, 3, 4}, GE, 3)\n");
{
int colno[] = {2, 3, 4};
double row[] = {4, 3, 1};
if (!add_constraintex(lp, sizeof(colno) / sizeof(*colno), row, colno, GE, 3))
ERROR();
}
print_lp(lp);
press_ret();
printf("Set the objective function\n");
printf("set_obj_fn(lp, {0, 2, 3, -2, 3})\n");
{
double row[] = {0, 2, 3, -2, 3};
if (!set_obj_fn(lp, row))
ERROR();
}
print_lp(lp);
press_ret();
printf("Now solve the problem with printf(solve(lp));\n");
printf("%d",solve(lp));
press_ret();
printf("The value is 0, this means we found an optimal solution\n");
printf("We can display this solution with print_objective(lp) and print_solution(lp)\n");
print_objective(lp);
print_solution(lp, 1);
print_constraints(lp, 1);
press_ret();
printf("The dual variables of the solution are printed with\n");
printf("print_duals(lp);\n");
print_duals(lp);
press_ret();
printf("We can change a single element in the matrix with\n");
printf("set_mat(lp,2,1,0.5)\n");
if (!set_mat(lp,2,1,0.5))
ERROR();
print_lp(lp);
press_ret();
printf("If we want to maximize the objective function use set_maxim(lp);\n");
set_maxim(lp);
print_lp(lp);
press_ret();
printf("after solving this gives us:\n");
solve(lp);
print_objective(lp);
print_solution(lp, 1);
print_constraints(lp, 1);
print_duals(lp);
press_ret();
printf("Change the value of a rhs element with set_rh(lp,1,7.45)\n");
set_rh(lp,1,7.45);
print_lp(lp);
solve(lp);
print_objective(lp);
print_solution(lp, 1);
print_constraints(lp, 1);
press_ret();
printf("We change %s to the integer type with\n", get_col_name(lp, 4));
printf("set_int(lp, 4, TRUE)\n");
set_int(lp, 4, TRUE);
print_lp(lp);
printf("We set branch & bound debugging on with set_debug(lp, TRUE)\n");
set_debug(lp, TRUE);
printf("and solve...\n");
press_ret();
solve(lp);
print_objective(lp);
print_solution(lp, 1);
print_constraints(lp, 1);
press_ret();
printf("We can set bounds on the variables with\n");
printf("set_lowbo(lp,2,2); & set_upbo(lp,4,5.3)\n");
set_lowbo(lp,2,2);
set_upbo(lp,4,5.3);
print_lp(lp);
press_ret();
solve(lp);
print_objective(lp);
print_solution(lp, 1);
print_constraints(lp, 1);
press_ret();
printf("Now remove a constraint with del_constraint(lp, 1)\n");
del_constraint(lp,1);
print_lp(lp);
printf("Add an equality constraint\n");
{
double row[] = {0, 1, 2, 1, 4};
if (!add_constraint(lp, row, EQ, 8))
ERROR();
}
print_lp(lp);
press_ret();
printf("A column can be added with:\n");
printf("add_column(lp,{3, 2, 2});\n");
{
double col[] = {3, 2, 2};
if (!add_column(lp, col))
ERROR();
}
print_lp(lp);
press_ret();
printf("A column can be removed with:\n");
printf("del_column(lp,3);\n");
del_column(lp,3);
print_lp(lp);
press_ret();
printf("We can use automatic scaling with:\n");
printf("set_scaling(lp, SCALE_MEAN);\n");
set_scaling(lp, SCALE_MEAN);
print_lp(lp);
press_ret();
printf("The function get_mat(lprec *lp, int row, int column) returns a single\n");
printf("matrix element\n");
printf("%s get_mat(lp,2,3), get_mat(lp,1,1); gives\n","printf(\"%f %f\\n\",");
printf("%f %f\n", (double)get_mat(lp,2,3), (double)get_mat(lp,1,1));
printf("Notice that get_mat returns the value of the original unscaled problem\n");
press_ret();
printf("If there are any integer type variables, then only the rows are scaled\n");
printf("set_scaling(lp, SCALE_MEAN);\n");
set_scaling(lp, SCALE_MEAN);
printf("set_int(lp,3,FALSE);\n");
set_int(lp,3,FALSE);
print_lp(lp);
press_ret();
solve(lp);
printf("print_objective, print_solution gives the solution to the original problem\n");
print_objective(lp);
print_solution(lp, 1);
print_constraints(lp, 1);
press_ret();
printf("Scaling is turned off with unscale(lp);\n");
unscale(lp);
print_lp(lp);
press_ret();
printf("Now turn B&B debugging off and simplex tracing on with\n");
printf("set_debug(lp, FALSE), set_trace(lp, TRUE) and solve(lp)\n");
set_debug(lp, FALSE);
set_trace(lp, TRUE);
press_ret();
solve(lp);
printf("Where possible, lp_solve will start at the last found basis\n");
printf("We can reset the problem to the initial basis with\n");
printf("default_basis(lp). Now solve it again...\n");
press_ret();
default_basis(lp);
solve(lp);
printf("It is possible to give variables and constraints names\n");
printf("set_row_name(lp,1,\"speed\"); & set_col_name(lp,2,\"money\")\n");
if (!set_row_name(lp,1,"speed"))
ERROR();
if (!set_col_name(lp,2,"money"))
ERROR();
print_lp(lp);
printf("As you can see, all column and rows are assigned default names\n");
printf("If a column or constraint is deleted, the names shift place also:\n");
press_ret();
printf("del_column(lp,1);\n");
del_column(lp,1);
print_lp(lp);
press_ret();
write_lp(lp, "lp.lp");
delete_lp(lp);
printf("An lp structure can be created and read from a .lp file\n");
printf("lp = read_lp(\"lp.lp\", TRUE);\n");
printf("The verbose option is used\n");
if ((lp = read_LP("lp.lp", TRUE, "test")) == NULL)
ERROR();
press_ret();
printf("lp is now:\n");
print_lp(lp);
press_ret();
printf("solution:\n");
set_debug(lp, TRUE);
solve(lp);
set_debug(lp, FALSE);
print_objective(lp);
print_solution(lp, 1);
print_constraints(lp, 1);
press_ret();
delete_lp(lp);
#if defined FORTIFY
Fortify_LeaveScope();
#endif
return 0;
}
vector<PathPoint *> LPPath :: findPath(vertex *curr) {
lprec *lp;
int numDropoff = 0;
int numDropped = 0;
int numPickup = 0;
//find pairs for each dropoff point
for(int i = 0; i < points.size(); i++) {
if(points[i]->type == 1) {
bool foundPair = false;
for(int j = 0; j < points.size(); j++) {
if(j != i && points[j]->pairIndex == points[i]->pairIndex) {
pairIndex[i] = j;
foundPair = true;
break;
}
}
//sometimes, there's an error and the pair cannot be found
//in that case, print out some debugging information
if(!foundPair) {
cout << i << ":" << points[i]->pairIndex << " ";
for(int j = 0; j < points.size(); j++) {
cout << points[j]->type << ":" << points[j]->pairIndex << " ";
}
cout << endl;
}
}
}
//occasionally we encounter a model that takes hours or days to solve
//we set a timeout on the solve function, and then advance to the next iteration
//as the iteration increases, we introduce more randomness into the model
// (this is done via the getNonZero function)
for(int iteration = 0; ; iteration += 10) {
//calculate cost matrix
for(int i = 0; i < points.size(); i++) {
PathPoint *ipoint = points[i];
if(ipoint->type == 0) numPickup++;
else if(ipoint->type == 1) numDropoff++;
else if(ipoint->type == 2) numDropped++;
//from this point to itself
costMatrix[i + 1][i] = getNonZero(0, iteration);
//from this point to every other point
for(int j = 0; j < points.size(); j++) {
if(i != j)
costMatrix[i + 1][j] = getNonZero(length(ipoint, points[j]), iteration);
}
//from the current location to this point
costMatrix[0][i] = getNonZero(taxiPath->shortestPath(curr, ipoint->vert), iteration);
}
//calculate m matrix
//first, we have to find earliest and latest
//the current location must occur at time zero
latest[0] = 0;
for(int i = 0; i < points.size(); i++) {
if(points[i]->type == 0 || points[i]->type == 2) {
//this is a pickup or stand-alone dropoff point
//the earliest time occurs when we go directly
// from the current location to here
//the latest time is set by the pickup constraint
earliest[i] = costMatrix[0][i];
latest[i + 1] = points[i]->remaining;
} else if(points[i]->type == 1) {
//this is a dropoff point
//the earliest time occurs when we go directly
// to the pickup point, then here
//the latest time occurs when we get to the pickup
// point the latest, and then here the latest
// (stretch both pickup and service constraints)
earliest[i] = costMatrix[0][pairIndex[i]] + costMatrix[pairIndex[i] + 1][i];
latest[i + 1] = points[pairIndex[i]]->remaining + points[i]->remaining;
}
}
//calculate m
double test;
for(int i = 0; i < points.size() + 1; i++) {
for(int j = 0; j < points.size(); j++) {
test = latest[i] + costMatrix[i][j] - earliest[j];
if(test > 0) m[i][j] = test;
else m[i][j] = 0;
}
}
//find the number of binary columns
//each x_ij determines whether or not the taxi will move
// from i to j
//in the comments below these movements will be referred
// to as route segments (_from_ i _to_ j)
int ncol = (points.size() + 1) * points.size();
//find the total number of columns
//besides the binary ones, there are ones for the time
// at which the taxi will reach a point (B_i)
int ncol_total = ncol + points.size() + 1;
//create the lp instance
lp = make_lp(0, ncol_total);
//colno and row are used to define the constraints, and
// later row will store the result from lpsolve
//colno identifies the variable (column), and row identifies
// the constants (multiplied by the variable); then, a
// separate value determines the number of variables
// that will be read (since we are using a sparse matrix -
// otherwise we wouldn't need colno)
//note**: column numbers are labeled starting from 1, not 0
int *colno = new int[ncol_total];
REAL *row = new REAL[ncol_total];
//since we're going to be adding constraints equation
// by equation, we set add row mode to make it faster
set_add_rowmode(lp, TRUE);
//disable most output from lpsolve
set_verbose(lp, CRITICAL);
//set timeout of three seconds so we don't spend forever on this model
set_timeout(lp, 3);
//set up the binary constraints
for(int i = 0; i < ncol; i++) {
set_binary(lp, i + 1, TRUE);
}
//constraints 1 to 3
//these have one constraint per point
for(int i = 0; i < points.size(); i++) {
//1. the total number of route segments to here will
// be equal to one
for(int j = 0; j < points.size() + 1; j++) {
colno[j] = j * points.size() + i + 1;
row[j] = 1;
}
add_constraintex(lp, points.size() + 1, row, colno, EQ, 1);
//2. there will be no route segment from here to itself
colno[0] = (i + 1) * points.size() + i + 1;
row[0] = 1;
add_constraintex(lp, 1, row, colno, EQ, 0);
//3. the total number of route segments from here will
// be less than or equal to one (since the last point in
// the route will be zero)
for(int j = 0; j < points.size(); j++) {
colno[j] = (i + 1) * points.size() + j + 1;
row[j] = 1;
}
add_constraintex(lp, points.size(), row, colno, LE, 1);
}
//4. there will be exactly one route segment from the
// current location
for(int i = 0; i < points.size(); i++) {
colno[i] = i + 1;
row[i] = 1;
}
add_constraintex(lp, points.size(), row, colno, EQ, 1);
//5. the relative time that the taxi reaches the current
// location is zero
colno[0] = ncol + 1;
row[0] = 1;
add_constraintex(lp, 1, row, colno, EQ, 0);
//6. defined for each route segment (i, j)
//if the segment (i, j) exists, then the time B_j
// the taxi reaches j will be greater than
// B_i + time(i, j)
// (time is interchangeable with distance)
//in other words,
// B_j >= ( B_i + time(i, j) ) * x_ij
//
//**but that's non-linear (since B_i * x_ij)
//to achieve the if statement, we subtract a large
// number M from the right and M * x_ij on the left
//the equation becomes:
// B_j - B_i - M*x_ij >= time(i, j) - M
//
//m_ij that we found earlier is suitable for M, since
// if x_ij = 0 the equation reduces to
// B_j - B_i >= time(i, j) - M
// >> M >= B_i + time(i, j) - B_j
// we used the maximum possible value for B_i (latest[i])
// and the minimim for B_j (earliest[j]), so everything
// is good :)
for(int i = 0; i < points.size() + 1; i++) {
for(int j = 0; j < points.size(); j++) {
colno[0] = ncol + 1 + i;
colno[1] = ncol + 1 + j + 1; //make sure to add an extra 1 because we're not including current location
colno[2] = i * points.size() + j + 1;
double constant = costMatrix[i][j] - m[i][j];
//only use positive constants or it seems to explode
if(constant >= 0) {
row[0] = -1;
row[1] = 1;
row[2] = -m[i][j];
add_constraintex(lp, 3, row, colno, GE, constant);
} else {
row[0] = 1;
row[1] = -1;
row[2] = m[i][j];
add_constraintex(lp, 3, row, colno, LE, -constant);
}
}
}
//constraints 7, 8, and 9
for(int i = 0; i < points.size(); i++) {
if(points[i]->type == 1) {
//dropoff point
//make sure to add an extra 1 because we're not including current location
colno[0] = ncol + 1 + i + 1;
colno[1] = ncol + 1 + pairIndex[i] + 1;
row[0] = 1;
row[1] = -1;
//constraints on L_i (= B_i - B_pickup[i])
//7. L_i >= time(pickup[i], i)
add_constraintex(lp, 2, row, colno, GE, costMatrix[pairIndex[i] + 1][i]);
//8. L_i <= remaining service constraint
add_constraintex(lp, 2, row, colno, LE, points[i]->remaining);
} else if(points[i]->type == 0 || points[i]->type == 2) {
//pickup or stand-alone dropoff point
colno[0] = ncol + 1 + i + 1;
row[0] = 1;
//9. B_i <= remaining pickup constraint
add_constraintex(lp, 1, row, colno, LE, points[i]->remaining);
}
}
//10. this used to enforce that all varibles be
// non-negative, but it seems to be working now
// (lpsolve makes variables non-negative unless
// explicitly stated in a constraint)
for(int i = ncol; i < ncol_total; i++) {
colno[0] = i + 1;
row[0] = 1;
//add_constraintex(lp, 1, row, colno, GE, 0);
}
//disable rowmode because we're done building model
set_add_rowmode(lp, FALSE);
//objective function: minimize sum( time(i, j) * x_ij )
//we maximize the negative though
// (we could change to set_minim(lp), but it's the same thing)
for(int i = 0; i < points.size() + 1; i++) {
for(int j = 0; j < points.size(); j++) {
colno[i * points.size() + j] = i * points.size() + j + 1;;
row[i * points.size() + j] = -costMatrix[i][j];
}
}
set_obj_fnex(lp, ncol, row, colno);
set_maxim(lp); //maximize the objective function
struct timeval solveStartTime;
struct timeval solveEndTime;
gettimeofday(&solveStartTime, NULL);
int ret = solve(lp);
gettimeofday(&solveEndTime, NULL);
long tS = solveStartTime.tv_sec*1000000 + (solveStartTime.tv_usec);
long tE = solveEndTime.tv_sec*1000000 + (solveEndTime.tv_usec);
long solveTime = tE - tS;
if(iteration == 0 && ret != TIMEOUT) {
lpTotalTime += solveTime;
if(solveTime > lpMaxTime) lpMaxTime = solveTime;
lpNum++;
cout << "lptimestatus: " << lpTotalTime / lpNum << " " << lpMaxTime << " " << lpNum << " " << solveTime << endl;
}
//if we didn't get the optimal solution, don't continue
if(ret != OPTIMAL) {
delete colno;
delete row;
delete_lp(lp);
bestList.clear();
if(ret == TIMEOUT) {
//if we timed out, then we need to try again
cout << "timed out on iteration " << iteration << ", advancing..." << endl;
continue;
} else {
return bestList;
}
}
get_variables(lp, row); //store variables in our row array
//extract the ordering of the points from the x_ij in the row
//at the same time, we calculate the route's distance
int previous = 0;
minTour = 0;
for(int i = 0; i < points.size(); i++) {
for(int j = 0; j < points.size(); j++) {
if(row[previous * points.size() + j] == 1) {
minTour += costMatrix[previous][j];
bestList.push_back(points[j]);
previous = j + 1;
break;
}
}
}
delete colno;
delete row;
delete_lp(lp);
//sometimes errors occur, probably because M was
// too large and double-precision isn't accurate
// enough
//in these cases, since they're rare enough, we
// assume that the model was infeasible
if(bestList.size() != points.size()) {
bestList.clear();
minTour = numeric_limits<double>::max();
return bestList;
}
return bestList;
}
}
//Execute function
int LPSolveClass::Execute()
{
/*
std::cout << "---------------------------------\n";
std::cout << "objective function\n";
for (unsigned int i = 0; i < coefficients.size(); i++)
std::cout << coefficients[i] << "\t";
std::cout << "\nConstant Value = " << obj_const << std::endl;
std::cout << "---------------------------------\n";
std::cout << "Equality Constraints\n";
for (unsigned int i = 0; i < A_equ.size(); i++){
//std::cout << "Row index = " << i << "\t\t";
for (unsigned int j = 0; j < A_equ[i].size(); j++)
std::cout << A_equ[i][j] << "\t";
std::cout << "\n";
}
std::cout << "b\n";
for (unsigned int i = 0; i < b_equ.size(); i++)
std::cout << b_equ[i] << "\t";
std::cout << "\n";
std::cout << "---------------------------------\n";
std::cout << "InEquality Constraints\n";
for (unsigned int i = 0; i < A_inequ.size(); i++){
//std::cout << "Row index = " << i << "\t\t";
for (unsigned int j = 0; j < A_inequ[i].size(); j++)
std::cout << A_inequ[i][j] << "\t";
std::cout << "\n";
}
std::cout << "b\n";
for (unsigned int i = 0; i < b_inequ.size(); i++)
std::cout << b_inequ[i] << "\t";
std::cout << "\n";
*/
lprec *lp;
int Ncol = coefficients.size(), *colno = NULL, j, ret = 0;
REAL *row = NULL;
/* We will build the model row by row
So we start with creating a model with 0 rows and n columns */
lp = make_lp(0, Ncol);
if (lp == NULL)
ret = 1;/* couldn't construct a new model... */
if (ret == 0){
//let us name our variables
std::string s = "x";
for (int i = 0; i < Ncol; i++){
std::stringstream out;
out << i;
s = s + out.str();
char *cpy = new char[s.size()+1] ;
strcpy(cpy, s.c_str());
set_col_name(lp, i+1, cpy);
}
/* create space large enough for one row */
colno = (int *) malloc(Ncol * sizeof(*colno));
row = (REAL *) malloc(Ncol * sizeof(*row));
if ((colno == NULL) || (row == NULL))
ret = 2;
}
set_add_rowmode(lp, TRUE);
//add the equation constraints
if (ret == 0){
/* makes building the model faster if it is done rows by row */
if (A_equ.size() > 0){
for (unsigned int i = 0; i < A_equ.size(); i++){//loop over the rows of equality constraints
for (unsigned int j = 0; j < A_equ[i].size(); j++){//loop over the columns of equality constraints
colno[j] = j+1;//add the j-th column to lpsolve
row[j] = A_equ[i][j];
}
/* add the row to lpsolve */
if(!add_constraintex(lp, A_equ[i].size(), row, colno, EQ, b_equ[i]))
ret = 2;
}
}
}
//add the inequality constraints
if (ret == 0){
/* makes building the model faster if it is done rows by row */
if (A_inequ.size() > 0){
for (unsigned int i = 0; i < A_inequ.size(); i++){//loop over the rows of inequality constraints
for (unsigned int j = 0; j < A_inequ[i].size(); j++){//loop over the columns of inequality constraints
colno[j] = j+1;//add the j-th column to lpsolve
row[j] = A_inequ[i][j];
}
/* add the row to lpsolve */
if(!add_constraintex(lp, A_inequ[i].size(), row, colno, LE, b_inequ[i]))
ret = 3;
}
}
}
//add the const constraint
if (ret == 0){
if (b_const.size()>0){
for (unsigned int i = 0; i < b_const.size(); i++){
if (b_const[i] > 0){
for (unsigned int j = 0; j < b_const.size(); j++){
if (i == j){
colno[j] = j+1;//add the j-th column to lpsolve
row[j] = 1.0;
}
else{
colno[j] = j+1;//add the j-th column to lpsolve
row[j] = 0.0;
}
}
if(!add_constraintex(lp, b_const.size(), row, colno, EQ, b_const[i]))
ret = 4;
}
}
}
}
//set the variables to be integer
if (ret == 0){
for (int i = 0; i < Ncol; i++)
set_int(lp, i+1, TRUE);
}
/* rowmode should be turned off again when done building the model */
set_add_rowmode(lp, FALSE);
//add the objective function
if (ret == 0){
//set the objective function
for (unsigned int i = 0; i < coefficients.size(); i++){
colno[i] = i+1;
row[i] = coefficients[i];
}
//set the objective in lpsolve
if(!set_obj_fnex(lp, coefficients.size(), row, colno))
ret = 4;
}
//set the objective to minimize
if (ret == 0){
set_minim(lp);
/* just out of curioucity, now show the model in lp format on screen */
/* this only works if this is a console application. If not, use write_lp and a filename */
write_LP(lp, stdout);
/* I only want to see important messages on screen while solving */
set_verbose(lp, IMPORTANT);
/* Now let lpsolve calculate a solution */
ret = solve(lp);
if(ret == OPTIMAL)
ret = 0;
else
ret = 5;
}
//get some results
if (ret == 0){
/* a solution is calculated, now lets get some results */
/* objective value */
std::cout << "Objective value: " << get_objective(lp) << std::endl;
/* variable values */
get_variables(lp, row);
/* variable values */
variables.resize(Ncol);
for(j = 0; j < Ncol; j++)
variables[j] = row[j];
/* we are done now */
}
else{
std::cout << "The optimal value can't be solved for linear programming, please check the constraints!!\n";
exit(1);
}
std::cout << "print the result\t # of line segments is \n";
for (int i = 0; i < Ncol; i++)
std::cout << "index = " << i << "\t# = " << variables[i] << std::endl;
/* free allocated memory */
if(row != NULL)
free(row);
if(colno != NULL)
free(colno);
/* clean up such that all used memory by lpsolve is freed */
if (lp != NULL)
delete_lp(lp);
return ret;
}
int CLPLpsolve::addConstraints(
int rcnt,
const double* rhs,
const char* sense,
const double* rngval,
char** rowname,
int numcoefs,
const int* rowlist,
const int* collist,
const double* vallist
)
{
/*
int rcnt, //number of constraints
const double* rhs, //constraints's bounds
const char* sense, //constraints'sense
const double* rngval,
char** rowname, //constraints's names
int numcoefs, //nonzeros variables number
const int* rowlist, //y index of coeffs
const int* collist, //x index of coeffs
const double* vallist //coeffs's table
*/
int rowindex = -1, nbVals, constraintCounter = 0;
int *beglist = new int[rcnt];
int * cols = new int[numcoefs];
double *newRhs = new double[rcnt];
char * newSense = new char[rcnt];
char ** newRowname = new char*[rcnt];
for (int i = 0; i < numcoefs; ++i) {
int newrowindex = rowlist[i];
if (newrowindex == rowindex)
continue;
rowindex = newrowindex;
beglist[constraintCounter] = i;
newRhs[constraintCounter] = rhs[rowindex];
newSense[constraintCounter] = sense[rowindex];
newRowname[constraintCounter] = rowname[rowindex];
++constraintCounter;
}
for(int i = 0; i < constraintCounter; ++i)
{
if(i < constraintCounter - 1)
nbVals = beglist[i+1] - beglist[i];
else
nbVals = numcoefs - beglist[i];
if(nbVals <= 0)
continue;
for (int j = beglist[i]; j < beglist[i] + nbVals; ++j) {
cols[j - beglist[i]] = collist[j] + 1;
}
//m_status = set_rowex(m_env, i + 1, numcoefs, const_cast<double *>(vallist), cols);
char senseV;
switch (newSense[i]) {
case 'L' :
senseV = LE;
break;
case 'G' :
senseV = GE;
break;
case 'E' :
senseV = EQ;
break;
}
m_status = add_constraintex(m_env, nbVals, &(const_cast<double*>(vallist)[beglist[i]]), cols, senseV ,newRhs[i]);
//m_status = set_rh_range(m_env, i + 1, rngval[i];
m_status = set_row_name(m_env, i + 1, newRowname[i]);
}
delete [] beglist;
delete [] cols;
delete [] newRhs;
delete [] newSense;
delete [] newRowname;
return getStatus();
}
double solve_constraints(int this_task)
{
lprec *lp;
int numVar = 0, *var = NULL, ret = 0, i, j, k, var_count;
double *coeff = NULL, lhs,rhs, obj;
char col_name[10];
/* Creating a model */
for(i = 1;i < this_task; i++)
numVar+=i;
lp = make_lp(0, numVar);
if(lp == NULL)
ret = 1; /* Couldn't construct a new model */
if(ret == 0) {
var_count = 1;
for(i = 1 ; i < this_task; i++){
for(j = i+1 ; j <= this_task; j++)
{
sprintf(col_name, "%dNNP%d_%d", this_task, i, j);
set_col_name(lp, var_count, col_name);
var_count++;
}
}
/* create space large enough for one row(i.e. equation) */
var = (int *) malloc(numVar * sizeof(*var));
coeff = (double *) malloc(numVar * sizeof(*coeff));
if((var == NULL) || (coeff == NULL))
ret = 2;
}
/* add the equations to lpsolve */
if(ret == 0) {
set_add_rowmode(lp, TRUE);
/* --------------------adding EQN-D-------------------- */
for(j = 2;j <= this_task;j++){
var_count = 0;
for(i = 1; i < j; i++){
sprintf(col_name,"%dNNP%d_%d",this_task, i, j);
var[var_count] = get_nameindex(lp, col_name, FALSE);
coeff[var_count] = 1;
var_count++;
}
lhs= 0;
for(i = 1; i < j; i++)
lhs+= nnp_min[i][j];
lhs*= floor(R[this_task]/task[j].p);
rhs = 0;
for(i = 1; i < j; i++)
rhs += nnp_max[i][j];
rhs *= ceil(R[this_task]/task[j].p);
if(!add_constraintex(lp, var_count, coeff, var, GE, lhs))
ret = 3;
if(!add_constraintex(lp, var_count, coeff, var, LE, rhs))
ret = 3;
}
}
if(ret == 0) {
/* --------------------adding EQN-E-------------------- */
for(k = 2;k <= this_task;k++)
{
var_count = 0;
for(j = 2; j <= k; j++){
for(i = 1; i < j; i++){
sprintf(col_name,"%dNNP%d_%d",this_task, i, j);
var[var_count] = get_nameindex(lp, col_name, FALSE);
coeff[var_count] = 1;
var_count++;
}
}
rhs = 0;
for(i = 1; i < k; i++)
rhs += ceil(R[this_task]/task[i].p);
if(!add_constraintex(lp, var_count, coeff, var, LE,rhs))
ret = 3;
}
}
if(ret == 0) {
/* ------------------adding EQN-G & H------------------ */
for(j = 2; j <= this_task ; j++){
for(i = 1; i < j; i++){
lhs= floor(R[this_task]/task[j].p) * nnp_min[i][j];
sprintf(col_name,"%dNNP%d_%d",this_task, i, j);
var[0] = get_nameindex(lp, col_name, FALSE);
coeff[0] = 1;
if(!add_constraintex(lp, 1, coeff, var, GE, lhs))
ret = 3;
rhs = min(ceil(R[this_task]/task[i].p), ceil(R[this_task]/task[j].p) * ceil(R[j]/task[i].p), ceil(R[this_task]/task[j].p) * nnp_max[i][j]);
if(!add_constraintex(lp, 1, coeff, var, LE,rhs))
ret = 3;
}
}
}
if(ret == 0) {
/* --------------------adding EQN-I-------------------- */
for(i = 1; i < this_task; i++){
var_count = 0;
for(j = i+1; j <= this_task; j++){
sprintf(col_name,"%dNNP%d_%d",this_task, i, j);
var[var_count] = get_nameindex(lp, col_name, FALSE);
coeff[var_count] = 1;
var_count++;
}
rhs = ceil(R[this_task]/task[i].p);
if(!add_constraintex(lp, var_count, coeff, var, LE,rhs))
ret = 3;
}
}
set_add_rowmode(lp, FALSE);
if(ret == 0) {
/* -----------------set the objective----------------- */
var_count = 0;
for(i = 1 ; i < this_task; i++){
for(j = i+1 ; j<= this_task; j++){
sprintf(col_name,"%dNNP%d_%d",this_task, i, j);
var[var_count] = get_nameindex(lp, col_name, FALSE);
coeff[var_count] = get_f(this_task, i, j);
var_count++;
}
}
if(!set_obj_fnex(lp, var_count, coeff, var))
ret = 4;
set_maxim(lp);
write_LP(lp, stdout);
set_verbose(lp, IMPORTANT);
ret = solve(lp);
if(ret == OPTIMAL)
ret = 0;
else
ret = 5;
}
if(ret == 0) {
obj = get_objective(lp);
/* Displaying calculated values */
/* variable values */
printf("\nVariable values:\n");
get_variables(lp, coeff);
printf("\n");
for(j = 0; j < numVar; j++)
printf("%s: %f\n", get_col_name(lp, j + 1), coeff[j]);
/* objective value */
printf("\nObjective value: %f\n\n", obj);
}
printf("LP ERROR = %d\n\n", ret);
/* free allocated memory */
if(coeff != NULL)
free(coeff);
if(var != NULL)
free(var);
if(lp != NULL)
delete_lp(lp);
return ret == 0 ? obj : 0;
}
int calculate (IN int nCols /* variables in the model */,
IN int nRows,
IN double** rows,
IN double* rights,
IN double* objectives,
OUT int* answer,
IN int verbose)
{
lprec *lp;
int result = 0;
char *str = NULL;
int *colno = NULL;
double *row = NULL;
/* We will build the model row by row
* So we start with creating a model
* with 0 rows and 2 columns
*/
if ( !(lp = make_lp (0, nCols)) )
{
/* couldn't construct a new model... */
result = 1;
goto RESULT;
}
if ( !(str = (char*) malloc ((log10 (nCols) + 10) * sizeof (*str))) )
{
result = 2;
goto RESULT;
}
/* let us name our variables. Not required,
* but can be useful for debugging
*/
for ( int i = 1; i <= nCols; ++i )
{
str[0] = 't';
_itoa (i, str + 1, 10);
set_col_name (lp, i, str);
// set_int (lp, i, TRUE);
}
/* create space large enough for one row */
colno = (int *) malloc (nCols * sizeof (*colno));
row = (double*) malloc (nCols * sizeof (*row));
if ( (colno == NULL) || (row == NULL) )
{
result = 2;
goto RESULT;
}
for ( int j = 0; j < nCols; ++j )
{ colno[j] = j + 1; /* (j + 1) column */ }
/* makes building the model faster if it is done rows by row */
set_add_rowmode (lp, TRUE);
for ( int i = 0; i < nRows; ++i )
{
// /* construct j row */
// for ( int j = 0; j < nCols; ++j )
// { row[j] = ??? ; }
/* (210 * t2 + 156 * t3 == 0.0178) */
/* (230 * t2 + 160 * t3 == 0.0176) */
/* add the row to lp_solve */
if ( !add_constraintex (lp, nCols, rows[i], colno, EQ, rights[i]) )
{
result = 3;
goto RESULT;
}
}
/* rowmode should be turned off again when done building the model */
set_add_rowmode (lp, FALSE);
// /* set the objective function */
// for ( int j = 0; j < nCols; ++j )
// { row[j] = objectives[j]; }
/* (t1 + t2 + t3 + t4) */
/* set the objective in lp_solve */
if ( !set_obj_fnex (lp, nCols, objectives, colno) )
{
result = 4;
goto RESULT;
}
/* set the object direction to maximize */
set_minim (lp);
if ( verbose )
{
/* just out of curioucity, now show the model in lp format on screen */
/* this only works if this is a console application. If not, use write_lp and a filename */
write_LP (lp, stdout);
/* write_lp(lp, "model.lp"); */
}
/* I only want to see important messages on screen while solving */
set_verbose (lp, IMPORTANT);
/* Now let lpsolve calculate a solution */
result = solve (lp);
if ( result == OPTIMAL )
{ result = 0; }
else
{
result = 5;
goto RESULT;
}
/* a solution is calculated,
* now lets get some results
*/
if ( verbose )
{
/* objective value */
printf ("Objective value: %f\n", get_objective (lp));
}
/* variable values */
get_variables (lp, row);
for ( int j = 0; j < nCols; j++ )
{
if ( verbose )
printf ("%s: %f\n", get_col_name (lp, j + 1), row[j]);
answer[j] = row[j];
}
/* we are done now */
RESULT:;
/* free allocated memory */
if ( str != NULL )free (str);
if ( row != NULL ) free (row);
if ( colno != NULL ) free (colno);
if ( lp != NULL )
{
/* clean up such that all used memory by lpsolve is freed */
delete_lp (lp);
}
return result;
}
void LoadBalancing::lp_create_model() {
int Ncol=3*num_using_nodes_+(num_using_nodes_-1)*(num_quantiles_+2);
int i,j;
int *colno=(int*)malloc((Ncol+1)*sizeof(int));
REAL *row=(REAL*)malloc((Ncol+1)*sizeof(REAL));
int *sosvars=(int*)malloc((num_quantiles_+2)*sizeof(int));
int ret;
lp = make_lp(0,Ncol);
if(lp == NULL) {
fprintf(stderr, "Unable to create new LP model\n");
// return(-1);
}
resize_lp(lp, 6*num_using_nodes_-3, Ncol);
//Set objective function
set_obj(lp,num_using_nodes_+1,1);
//Add constraints:
set_add_rowmode(lp, TRUE);
// D*x + E*ip - t <= -G
for(i=0;i<num_using_nodes_;i++){
for(j=0;j<num_using_nodes_;j++){
colno[j]=POS_Xi(j);
row[j]=lp_D[i*num_using_nodes_+j];
}
colno[j]=POS_IPi(i); //ip(i);
row[j]=Mopt_*lp_E[i];
colno[j+1]=POS_T;
row[j+1]=-1;// -t
add_constraintex(lp,j+2,row,colno,LE,-lp_G[i]);
}
//Increasing constraints, considering the overlap, (x[n]-x[n+1]<=-2*overlap_)
for(i=0;i<num_using_nodes_-2;i++){
colno[0]=POS_Xi(i);
row[0]=1;
colno[1]=POS_Xi(i+1);
row[1]=-1;
add_constraintex(lp,2,row,colno,LE,-2*overlap_);
}
colno[0]=POS_Xi(i);
row[0]=1;
colno[1]=POS_Xi(i+1);
row[1]=-1;
add_constraintex(lp,2,row,colno,LE,-overlap_);
//And the last cut must be 1: (x[num_using_nodes_]=1)
colno[0]=POS_Xi(num_using_nodes_-1);
row[0]=1;
add_constraintex(lp,1,row,colno,EQ,1);
//And now we define the number of interest points for each cut (ip1, ip2,...)
// ip1=f1
// ip2=f2-f1
// ip3=f3-f2
// ipN=1-f3
//ip1:
colno[0]=POS_IPi(0); //ip1
row[0]=-1;
colno[1]=POS_Fi(0); //f1
row[1]=1;
add_constraintex(lp,2,row,colno,EQ,0);
//ip2 to ip(N-1):
for(i=1;i<num_using_nodes_-1;i++){
colno[0]=POS_IPi(i); //ip(i)
row[0]=-1;
colno[1]=POS_Fi(i); //f(i)
row[1]=1;
colno[2]=POS_Fi(i-1); //f(i-1)
row[2]=-1;
add_constraintex(lp,3,row,colno,EQ,0);
}
//ipN:
colno[0]=POS_IPi(num_using_nodes_-1); //ipN
row[0]=1;
colno[1]=POS_Fi(num_using_nodes_-2); //f(N-1)
row[1]=1;
add_constraintex(lp,2,row,colno,EQ,1);
//SOS variables:
// d10+d11+d12+d13+...=1
for(i=0;i<num_using_nodes_-1;i++){
for(j=0;j<num_quantiles_+2;j++){
colno[j]=POS_Dij(i,j);
row[j]=1;
sosvars[j]=POS_Dij(i,j);
}
char sosName[] = "SOS"; //Gives a warning otherwise...
add_SOS(lp, sosName, 2, 1, num_quantiles_+2, sosvars, NULL);
add_constraintex(lp,num_quantiles_+2,row,colno,EQ,1);
}
//So now we define the piecewise functions f (number of interest points left of x)
for(i=0;i<num_using_nodes_-1;i++){
colno[0]=POS_Fi(i); //fi
row[0]=-1;
for(j=0;j<num_quantiles_;j++){
colno[j+1]=POS_Dij(i,j+1);
row[j+1]=(j+1.0)/num_quantiles_;
}
colno[j+1]=POS_Dij(i,j+1);
row[j+1]=1;
add_constraintex(lp,num_quantiles_+2,row,colno,EQ,0);
}
// Now x1=q1*d11 + q2*d12 + ...
for(i=0;i<num_using_nodes_-1;i++){
colno[0]=POS_Xi(i);
row[0]=-1;
for(j=0;j<num_quantiles_;j++){
colno[j+1]=POS_Dij(i,j+1);
row[j+1]=(float)IPx_quantile_aprox_.at(j)/width_;
}
colno[j+1]=POS_Dij(i,j+1);
row[j+1]=1;
add_constraintex(lp,num_quantiles_+2,row,colno,EQ,0);
}
set_add_rowmode(lp, FALSE);
free(colno);
free(row);
free(sosvars);
is_lpmodel_created_=true;
}
int demo()
{
lprec *lp;
int Ncol, *colno = NULL, j, ret = 0;
REAL *row = NULL;
/* We will build the model row by row
So we start with creating a model with 0 rows and 2 columns */
Ncol = 2; /* there are two variables in the model */
lp = make_lp(0, Ncol);
if(lp == NULL)
ret = 1; /* couldn't construct a new model... */
if(ret == 0) {
/* let us name our variables. Not required, but can be useful for debugging */
set_col_name(lp, 1, "x");
set_col_name(lp, 2, "y");
/* create space large enough for one row */
colno = (int *) malloc(Ncol * sizeof(*colno));
row = (REAL *) malloc(Ncol * sizeof(*row));
if((colno == NULL) || (row == NULL))
ret = 2;
}
if(ret == 0) {
set_add_rowmode(lp, TRUE); /* makes building the model faster if it is done rows by row */
/* construct first row (120 x + 210 y <= 15000) */
j = 0;
colno[j] = 1; /* first column */
row[j++] = 120;
colno[j] = 2; /* second column */
row[j++] = 210;
/* add the row to lpsolve */
if(!add_constraintex(lp, j, row, colno, LE, 15000))
ret = 3;
}
if(ret == 0) {
/* construct second row (110 x + 30 y <= 4000) */
j = 0;
colno[j] = 1; /* first column */
row[j++] = 110;
colno[j] = 2; /* second column */
row[j++] = 30;
/* add the row to lpsolve */
if(!add_constraintex(lp, j, row, colno, LE, 4000))
ret = 3;
}
if(ret == 0) {
/* construct third row (x + y <= 75) */
j = 0;
colno[j] = 1; /* first column */
row[j++] = 1;
colno[j] = 2; /* second column */
row[j++] = 1;
/* add the row to lpsolve */
if(!add_constraintex(lp, j, row, colno, LE, 75))
ret = 3;
}
if(ret == 0) {
set_add_rowmode(lp, FALSE); /* rowmode should be turned off again when done building the model */
/* set the objective function (143 x + 60 y) */
j = 0;
colno[j] = 1; /* first column */
row[j++] = 143;
colno[j] = 2; /* second column */
row[j++] = 60;
/* set the objective in lpsolve */
if(!set_obj_fnex(lp, j, row, colno))
ret = 4;
}
if(ret == 0) {
/* set the object direction to maximize */
set_maxim(lp);
/* just out of curioucity, now show the model in lp format on screen */
/* this only works if this is a console application. If not, use write_lp and a filename */
write_LP(lp, stdout);
/* write_lp(lp, "model.lp"); */
/* I only want to see important messages on screen while solving */
set_verbose(lp, IMPORTANT);
/* Now let lpsolve calculate a solution */
ret = solve(lp);
if(ret == OPTIMAL)
ret = 0;
else
ret = 5;
}
if(ret == 0) {
/* a solution is calculated, now lets get some results */
/* objective value */
printf("Objective value: %f\n", get_objective(lp));
/* variable values */
get_variables(lp, row);
for(j = 0; j < Ncol; j++)
printf("%s: %f\n", get_col_name(lp, j + 1), row[j]);
/* we are done now */
}
/* free allocated memory */
if(row != NULL)
free(row);
if(colno != NULL)
free(colno);
if(lp != NULL) {
/* clean up such that all used memory by lpsolve is freed */
delete_lp(lp);
}
return(ret);
}