bool IASolverRelaxed::solve()
{
// solve the nlp to get a non-integral solution, which we hope is close to a good integer solution
// adapted from HS071 ipopt example
// p_norm set in constructor. 3 seems to work well, comes close to lex-max-min
// smaller p has the effect of valuing the fidelity of shorter curves over longer curves more
// larger p approaches min max
IANlp *myianlp = new IANlp(iaData, iaSolution, silent);
Ipopt::SmartPtr<TNLP> mynlp = myianlp; // Ipopt requires the use of smartptrs!
Ipopt::SmartPtr<Ipopt::IpoptApplication> app = IpoptApplicationFactory();
app->Options()->SetNumericValue("tol", 1e-7); // 2 seems close enough, could do less, say .1
app->Options()->SetStringValue("mu_strategy", "adaptive");
// print level 0 to 12, most. Ipopt Default is 5
int print_level = (silent) ? 0 : 1; // 1, 5
// int print_level = 5;
app->Options()->SetIntegerValue("print_level", print_level);
// uncomment next line to write the solution to an output file
// app->Options()->SetStringValue("output_file", "IA.out");
// The following overwrites the default name (ipopt.opt) of the options file
// app->Options()->SetStringValue("option_file_name", "IA.opt");
// Intialize the IpoptApplication and process the options
Ipopt::ApplicationReturnStatus status;
status = app->Initialize();
if (status != Ipopt::Solve_Succeeded) {
if (!silent)
printf("\n\n*** Error during ipopt initialization!\n");
return (int) status;
}
// Ask Ipopt to solve the problem
status = app->OptimizeTNLP(mynlp); // the inherited IANlp
// todo: also check for a valid solution even if ! Solve_Succeeded, such as a sub-optimal time-out
bool is_solved = (status == Ipopt::Solve_Succeeded);
bool is_satisfied = is_solved && equal_constraints( false, debugging );
// don't check even-ness, as those are like the integrality constraints and are not solved here
if (!silent)
{
if (is_solved) {
printf("\n\n*** The relaxed problem solved!");
if (!is_satisfied)
printf(" But equality-constraints were VIOLATED!");
printf("\n");
}
else {
printf("\n\n*** The relaxed problem FAILED!\n");
}
}
return is_satisfied;
}
IpoptSolution CppADSolver::solve(OptProblemData &data){
size_t n = opt_prob->num_of_variables();
size_t m = opt_prob->num_of_constraints();
// create the Ipopt interface
cppad_ipopt_solution solution;
CppADOptProblemData cppad_data(data);
Ipopt::SmartPtr<Ipopt::TNLP> cppad_nlp = new cppad_ipopt_nlp(
n, m, cppad_data.x_i, cppad_data.x_l, cppad_data.x_u, cppad_data.g_l, cppad_data.g_u, &(*fg_info_ptr), &solution
);
// Create an instance of the IpoptApplication
Ipopt::SmartPtr<Ipopt::IpoptApplication> app = new IpoptApplication();
// turn off any printing
app->Options()->SetIntegerValue("print_level", 4);
app->Options()->SetStringValue("sb", "yes");
// maximum number of iterations
app->Options()->SetIntegerValue("max_iter", 5000);
// approximate accuracy in first order necessary conditions;
// see Mathematical Programming, Volume 106, Number 1,
// Pages 25-57, Equation (6)
app->Options()->SetNumericValue("tol", 1e-9);
// derivative testing
// app->Options()->
// SetStringValue("derivative_test", "second-order");
// app->Options()-> SetNumericValue(
// "point_perturbation_radius", 0.
// );
// Initialize the IpoptApplication and process the options
Ipopt::ApplicationReturnStatus status = app->Initialize();
assert(status == Ipopt::Solve_Succeeded);
// Run the IpoptApplication
status = app->OptimizeTNLP(cppad_nlp);
return IpoptSolution(solution);
}
bool retape_k1_l1(void)
{ bool ok = true;
size_t j;
// number of independent variables (domain dimension for f and g)
size_t n = 2;
// number of constraints (range dimension for g)
size_t m = 1;
// initial value of the independent variables
NumberVector x_i(n);
x_i[0] = 2.0;
x_i[1] = 2.0;
// lower and upper limits for x
NumberVector x_l(n);
NumberVector x_u(n);
for(j = 0; j < n; j++)
{ x_l[j] = -10.;
x_u[j] = +10.;
}
// lower and upper limits for g
NumberVector g_l(m);
NumberVector g_u(m);
g_l[0] = -1.;
g_u[0] = 1.0e19;
// object in derived class
FG_retape fg_retape;
cppad_ipopt_fg_info *fg_info = &fg_retape;
// create the Ipopt interface
cppad_ipopt_solution solution;
Ipopt::SmartPtr<Ipopt::TNLP> cppad_nlp = new cppad_ipopt_nlp(
n, m, x_i, x_l, x_u, g_l, g_u, fg_info, &solution
);
// Create an instance of the IpoptApplication
using Ipopt::IpoptApplication;
Ipopt::SmartPtr<IpoptApplication> app = new IpoptApplication();
// turn off any printing
app->Options()->SetIntegerValue("print_level", 0);
app->Options()->SetStringValue("sb", "yes");
// maximum number of iterations
app->Options()->SetIntegerValue("max_iter", 10);
// approximate accuracy in first order necessary conditions;
// see Mathematical Programming, Volume 106, Number 1,
// Pages 25-57, Equation (6)
app->Options()->SetNumericValue("tol", 1e-9);
// derivative testing
app->Options()->
SetStringValue("derivative_test", "second-order");
// Initialize the IpoptApplication and process the options
Ipopt::ApplicationReturnStatus status = app->Initialize();
ok &= status == Ipopt::Solve_Succeeded;
// Run the IpoptApplication
status = app->OptimizeTNLP(cppad_nlp);
ok &= status == Ipopt::Solve_Succeeded;
/*
Check some of the solution values
*/
ok &= solution.status == cppad_ipopt_solution::success;
//
double check_x[] = { -1., 0. };
double rel_tol = 1e-6; // relative tolerance
double abs_tol = 1e-6; // absolute tolerance
for(j = 0; j < n; j++)
{ ok &= CppAD::NearEqual(
check_x[j], solution.x[j], rel_tol, abs_tol
);
}
return ok;
}
bool multiple_solution(void)
{
bool ok = true;
// number of independent variables (domain dimension for f and g)
size_t n = 2;
// number of constraints (range dimension for g)
size_t m = 2;
// initial value of the independent variables
NumberVector x_i(n);
NumberVector x_l(n);
NumberVector x_u(n);
size_t i = 0;
for(i = 0; i < n; i++)
{ x_i[i] = 0.;
x_l[i] = -1.0;
x_u[i] = +1.0;
}
// lower and upper limits for g
NumberVector g_l(m);
NumberVector g_u(m);
g_l[0] = -1; g_u[0] = 0.;
g_l[1] = 0.; g_u[1] = 1.;
// object for evaluating function
bool retape = false;
FG_J_changes my_fg_info(retape);
cppad_ipopt_fg_info *fg_info = &my_fg_info;
cppad_ipopt_solution solution;
Ipopt::SmartPtr<Ipopt::TNLP> cppad_nlp = new cppad_ipopt_nlp(
n, m, x_i, x_l, x_u, g_l, g_u, fg_info, &solution
);
// Create an instance of the IpoptApplication
using Ipopt::IpoptApplication;
Ipopt::SmartPtr<IpoptApplication> app = new IpoptApplication();
// turn off any printing
app->Options()->SetIntegerValue("print_level", 0);
app->Options()->SetStringValue("sb", "yes");
// approximate accuracy in first order necessary conditions;
// see Mathematical Programming, Volume 106, Number 1,
// Pages 25-57, Equation (6)
app->Options()->SetNumericValue("tol", 1e-9);
app->Options()-> SetStringValue("derivative_test", "second-order");
// Initialize the IpoptApplication and process the options
Ipopt::ApplicationReturnStatus status = app->Initialize();
ok &= status == Ipopt::Solve_Succeeded;
// Run the IpoptApplication
status = app->OptimizeTNLP(cppad_nlp);
ok &= status == Ipopt::Solve_Succeeded;
/*
Check solution status
*/
ok &= solution.status == cppad_ipopt_solution::success;
ok &= CppAD::NearEqual(solution.x[1], 0., 1e-6, 1e-6);
return ok;
}
bool k_gt_one(void)
{ bool ok = true;
size_t j;
// number of independent variables (domain dimension for f and g)
size_t n = 4;
// number of constraints (range dimension for g)
size_t m = 2;
// initial value of the independent variables
NumberVector x_i(n);
x_i[0] = 1.0;
x_i[1] = 5.0;
x_i[2] = 5.0;
x_i[3] = 1.0;
// lower and upper limits for x
NumberVector x_l(n);
NumberVector x_u(n);
for(j = 0; j < n; j++)
{ x_l[j] = 1.0;
x_u[j] = 5.0;
}
// lower and upper limits for g
NumberVector g_l(m);
NumberVector g_u(m);
g_l[0] = 25.0; g_u[0] = 1.0e19;
g_l[1] = 40.0; g_u[1] = 40.0;
// known solution to check against
double check_x[] = { 1.000000, 4.743000, 3.82115, 1.379408 };
size_t icase;
for(icase = 0; icase <= 1; icase++)
{ // Should cppad_ipopt_nlp retape the operation sequence for
// every new x. Can test both true and false cases because
// the operation sequence does not depend on x (for this case).
bool retape = bool(icase);
// check case where upper and lower limits are equal
if( icase == 1 )
{ x_l[2] = check_x[2];
x_u[2] = check_x[2];
}
// object in derived class
FG_K_gt_one my_fg_info(retape);
cppad_ipopt_fg_info *fg_info = &my_fg_info;
// create the Ipopt interface
cppad_ipopt_solution solution;
Ipopt::SmartPtr<Ipopt::TNLP> cppad_nlp = new cppad_ipopt_nlp(
n, m, x_i, x_l, x_u, g_l, g_u, fg_info, &solution
);
// Create an instance of the IpoptApplication
using Ipopt::IpoptApplication;
Ipopt::SmartPtr<IpoptApplication> app = new IpoptApplication();
// turn off any printing
app->Options()->SetIntegerValue("print_level", 0);
// maximum number of iterations
app->Options()->SetIntegerValue("max_iter", 10);
// approximate accuracy in first order necessary conditions;
// see Mathematical Programming, Volume 106, Number 1,
// Pages 25-57, Equation (6)
app->Options()->SetNumericValue("tol", 1e-9);
// derivative testing
app->Options()->
SetStringValue("derivative_test", "second-order");
// Initialize the IpoptApplication and process the options
Ipopt::ApplicationReturnStatus status = app->Initialize();
ok &= status == Ipopt::Solve_Succeeded;
// Run the IpoptApplication
status = app->OptimizeTNLP(cppad_nlp);
ok &= status == Ipopt::Solve_Succeeded;
/*
Check some of the solution values
*/
ok &= solution.status == cppad_ipopt_solution::success;
//
double check_z_l[] = { 1.087871, 0., 0., 0. };
double check_z_u[] = { 0., 0., 0., 0. };
double rel_tol = 1e-6; // relative tolerance
double abs_tol = 1e-6; // absolute tolerance
for(j = 0; j < n; j++)
{ ok &= CppAD::NearEqual(
check_x[j], solution.x[j], rel_tol, abs_tol
);
ok &= CppAD::NearEqual(
check_z_l[j], solution.z_l[j], rel_tol, abs_tol
);
ok &= CppAD::NearEqual(
check_z_u[j], solution.z_u[j], rel_tol, abs_tol
);
}
}
return ok;
}
void solve(
const std::string& options ,
const Dvector& xi ,
const Dvector& xl ,
const Dvector& xu ,
const Dvector& gl ,
const Dvector& gu ,
FG_eval& fg_eval ,
ipopt::solve_result<Dvector>& solution )
{ bool ok = true;
typedef typename FG_eval::ADvector ADvector;
CPPAD_ASSERT_KNOWN(
xi.size() == xl.size() && xi.size() == xu.size() ,
"ipopt::solve: size of xi, xl, and xu are not all equal."
);
CPPAD_ASSERT_KNOWN(
gl.size() == gu.size() ,
"ipopt::solve: size of gl and gu are not equal."
);
size_t nx = xi.size();
size_t ng = gl.size();
// Create an IpoptApplication
using Ipopt::IpoptApplication;
Ipopt::SmartPtr<IpoptApplication> app = new IpoptApplication();
// process the options argument
size_t begin_1, end_1, begin_2, end_2, begin_3, end_3;
begin_1 = 0;
bool retape = false;
bool sparse_forward = false;
bool sparse_reverse = false;
while( begin_1 < options.size() )
{ // split this line into tokens
while( options[begin_1] == ' ')
begin_1++;
end_1 = options.find_first_of(" \n", begin_1);
begin_2 = end_1;
while( options[begin_2] == ' ')
begin_2++;
end_2 = options.find_first_of(" \n", begin_2);
begin_3 = end_2;
while( options[begin_3] == ' ')
begin_3++;
end_3 = options.find_first_of(" \n", begin_3);
// check for errors
CPPAD_ASSERT_KNOWN(
(end_1 != std::string::npos) &
(end_2 != std::string::npos) &
(end_3 != std::string::npos) ,
"ipopt::solve: missing '\\n' at end of an option line"
);
CPPAD_ASSERT_KNOWN(
(end_1 > begin_1) & (end_2 > begin_2) ,
"ipopt::solve: an option line does not have two tokens"
);
// get first two tokens
std::string tok_1 = options.substr(begin_1, end_1 - begin_1);
std::string tok_2 = options.substr(begin_2, end_2 - begin_2);
// get third token
std::string tok_3;
bool three_tok = false;
three_tok |= tok_1 == "Sparse";
three_tok |= tok_1 == "String";
three_tok |= tok_1 == "Numeric";
three_tok |= tok_1 == "Integer";
if( three_tok )
{ CPPAD_ASSERT_KNOWN(
(end_3 > begin_3) ,
"ipopt::solve: a Sparse, String, Numeric, or Integer\n"
"option line does not have three tokens."
);
tok_3 = options.substr(begin_3, end_3 - begin_3);
}
// switch on option type
if( tok_1 == "Retape" )
{ CPPAD_ASSERT_KNOWN(
(tok_2 == "true") | (tok_2 == "false") ,
"ipopt::solve: Retape value is not true or false"
);
retape = (tok_2 == "true");
}
else if( tok_1 == "Sparse" )
{ CPPAD_ASSERT_KNOWN(
(tok_2 == "true") | (tok_2 == "false") ,
"ipopt::solve: Sparse value is not true or false"
);
CPPAD_ASSERT_KNOWN(
(tok_3 == "forward") | (tok_3 == "reverse") ,
"ipopt::solve: Sparse direction is not forward or reverse"
);
if( tok_2 == "false" )
{ sparse_forward = false;
sparse_reverse = false;
}
else
{ sparse_forward = tok_3 == "forward";
sparse_reverse = tok_3 == "reverse";
}
}
else if ( tok_1 == "String" )
app->Options()->SetStringValue(tok_2.c_str(), tok_3.c_str());
else if ( tok_1 == "Numeric" )
{ Ipopt::Number value = std::atof( tok_3.c_str() );
app->Options()->SetNumericValue(tok_2.c_str(), value);
}
else if ( tok_1 == "Integer" )
{ Ipopt::Index value = std::atoi( tok_3.c_str() );
app->Options()->SetIntegerValue(tok_2.c_str(), value);
}
else CPPAD_ASSERT_KNOWN(
false,
"ipopt::solve: First token is not one of\n"
"Retape, Sparse, String, Numeric, Integer"
);
begin_1 = end_3;
while( options[begin_1] == ' ')
begin_1++;
if( options[begin_1] != '\n' ) CPPAD_ASSERT_KNOWN(
false,
"ipopt::solve: either more than three tokens "
"or no '\\n' at end of a line"
);
begin_1++;
}
CPPAD_ASSERT_KNOWN(
! ( retape & (sparse_forward | sparse_reverse) ) ,
"ipopt::solve: retape and sparse both true is not supported."
);
// Initialize the IpoptApplication and process the options
Ipopt::ApplicationReturnStatus status = app->Initialize();
ok &= status == Ipopt::Solve_Succeeded;
if( ! ok )
{ solution.status = solve_result<Dvector>::unknown;
return;
}
// Create an interface from Ipopt to this specific problem.
// Note the assumption here that ADvector is same as cppd_ipopt::ADvector
size_t nf = 1;
Ipopt::SmartPtr<Ipopt::TNLP> cppad_nlp =
new CppAD::ipopt::solve_callback<Dvector, ADvector, FG_eval>(
nf,
nx,
ng,
xi,
xl,
xu,
gl,
gu,
fg_eval,
retape,
sparse_forward,
sparse_reverse,
solution
);
// Run the IpoptApplication
app->OptimizeTNLP(cppad_nlp);
return;
}
bool IASolverInt::solve_round()
{
// set up and call the separate IARoundingNlp, which has a linear objective to get a natural integer solution
// the intuition is this will solve integrality for most variables all at once
if (debugging)
{
printf("IASolverInt::solve_bend_workhorse() - ");
}
// solver setup
Ipopt::SmartPtr<Ipopt::IpoptApplication> app = IpoptApplicationFactory();
// convergence parameters
// see $IPOPTDIR/Ipopt/src/Interfaces/IpIpoptApplication.cpp
// our real criteria are: all integer, constraints satisfied. How to test the "all_integer" part?
app->Options()->SetNumericValue("tol", 1e-6); //"converged" if NLP error<this, default is 1e-7. Obj are scaled to be >1, so e-2 is plenty // was 1e-2
app->Options()->SetNumericValue("max_cpu_time", sqrt( iaData->num_variables() ) ); // max time allowed in seconds
app->Options()->SetIntegerValue("max_iter", 3 * iaData->num_variables() ); // max number of iterations
// app->Options()->SetNumericValue("primal_inf_tol", 1e-2 );
app->Options()->SetNumericValue("dual_inf_tol", 1e-6 ); // how close to infeasibility? // was 1e-2
app->Options()->SetNumericValue("constr_viol_tol", 1e-6 ); // by how much can constraints be violated?
app->Options()->SetNumericValue("compl_inf_tol", 1e-6 ); // max norm of complementary condition // was 1e-2
// second criteria convergence parameters: quit if within this tol for many iterations
// was app->Options()->SetIntegerValue("acceptable_iter", 4 + sqrt( iaData->num_variables() ) ); //as "tol"
app->Options()->SetNumericValue("acceptable_tol", 1e-6 ); //as "tol" was 1e-1
app->Options()->SetStringValue("mu_strategy", "adaptive");
// print level 0 to 12, Ipopt default is 5
const int print_level = (silent) ? 0 : 1;
app->Options()->SetIntegerValue("print_level", print_level);
// uncomment next line to write the solution to an output file
// app->Options()->SetStringValue("output_file", "IA.out");
// The following overwrites the default name (ipopt.opt) of the options file
// app->Options()->SetStringValue("option_file_name", "IA.opt");
// Intialize the IpoptApplication and process the options
Ipopt::ApplicationReturnStatus status;
status = app->Initialize();
if (status != Ipopt::Solve_Succeeded) {
if (!silent)
printf("\n\n*** Error during initialization!\n");
return (int) status;
}
Ipopt::TNLP *tnlp = NULL;
IARoundingNlp *myianlp = new IARoundingNlp(iaData, ipData, iaSolution, silent);
if (debugging)
{
printf("ROUNDING problem formulation\n");
printf("Attempting to find a naturally-integer solution by linearizing the objective function.\n");
printf("Variables are constrained within [floor,ceil] of relaxed solution.\n");
}
// problem setup
// a couple of different models, simplest to more complex
// IARoundingFarNlp *myianlp = new IARoundingFarNlp(iaData, ipData, this);
// IARoundingFar3StepNlp *myianlp = new IARoundingFar3StepNlp(iaData, ipData, this); // haven't tested this. It compiles and runs but perhaps isn't correct
// IAIntWaveNlp *myianlp = new IAIntWaveNlp(iaData, ipData, this); // haven't tested this. It compiles and runs but perhaps isn't correct
tnlp = myianlp;
Ipopt::SmartPtr<Ipopt::TNLP> mynlp = tnlp; // Ipopt requires the use of smartptrs!
bool try_again = true;
int iter = 0;
do {
printf("%d rounding iteration\n", iter );
// Ask Ipopt to solve the problem
status = app->OptimizeTNLP(mynlp); // the inherited IANlp
if (!silent)
{
if (status == Ipopt::Solve_Succeeded) {
printf("\n\n*** The problem solved!\n");
}
else {
printf("\n\n*** The problem FAILED!\n");
}
}
// The problem should have been feasible, but it is possible that it had no integer solution.
// figure out which variables are still integer
// check solution for integrality and constraint satified
if (debugging)
{
printf("\nChecking Natural (non-rounded) solution.\n");
bool integer_sat = solution_is_integer(true);
bool even_sat = even_constraints( false, true);
bool equal_sat = equal_constraints( false, true );
printf("Natural solution summary, %s, equal-constraints %s, even-constraints %s.\n",
integer_sat ? "integer" : "NON-INTEGER",
equal_sat ? "satisfied" : "VIOLATED",
even_sat ? "satisfied" : "VIOLATED" );
if (!integer_sat)
printf("investigate this\n");
}
IASolution nlp_solution;
nlp_solution.x_solution = ia_solution()->x_solution; // vector copy
IASolverToolInt sti( ia_data(), &nlp_solution );
sti.round_solution();
if (debugging)
printf("Checking rounded solution, ignoring even constraints.\n");
if (sti.equal_constraints(false, debugging))
{
// also even constraints
if (debugging)
printf("Rounding worked.\n");
// rounding was a valid integer solution
ia_solution()->x_solution.swap( nlp_solution.x_solution );
// ia_solution()->obj_value is no longer accurate, as it was for the non-rounded solution
return true;
}
// find out which vars were not integer,
// try rounding their weights and resolving
// bool int_sat = solution_is_integer();
++iter;
try_again = iter < 4 + sqrt(iaData->num_variables());
if (try_again)
{
if (debugging)
printf("rounding failed, randomizing weights\n");
myianlp->randomize_weights_of_non_int(); // try again? debug
}
else if (debugging)
printf("giving up on rounding to non-integer solution\n");
// try_again = false; // debug
} while (try_again);
// todo: update partially-integer solution, perhaps using ipData - figure out how we're going to use it, first, for what structure makes sense.
// As the SmartPtrs go out of scope, the reference count
// will be decremented and the objects will automatically
// be deleted.
return status == Ipopt::Solve_Succeeded;
}