Add more problems from More Garbow Hillstrom.
Also try solving the unconstrained problems from
three different starting points.
Change-Id: I8343a4dd979a3e8733981819915d25d6e9fcf993
diff --git a/examples/more_garbow_hillstrom.cc b/examples/more_garbow_hillstrom.cc
index 471eed4..f064488 100644
--- a/examples/more_garbow_hillstrom.cc
+++ b/examples/more_garbow_hillstrom.cc
@@ -28,7 +28,7 @@
//
// Author: sameeragarwal@google.com (Sameer Agarwal)
//
-// Bounds constrained test problems from the paper
+// Test problems from the paper
//
// Testing Unconstrained Optimization Software
// Jorge J. More, Burton S. Garbow and Kenneth E. Hillstrom
@@ -48,15 +48,19 @@
// http://www.mat.univie.ac.at/~neum/glopt/bounds.html
//
// A problem is considered solved if of the log relative error of its
-// objective function is at least 5.
+// objective function is at least 4.
#include <cmath>
#include <iostream> // NOLINT
+#include <sstream> // NOLINT
+#include <string>
#include "ceres/ceres.h"
#include "gflags/gflags.h"
#include "glog/logging.h"
+DEFINE_string(problem, "all", "Which problem to solve");
+
namespace ceres {
namespace examples {
@@ -160,8 +164,8 @@
const T x2 = x[1];
for (int i = 1; i <= 10; ++i) {
residual[i - 1] = T(2.0) + T(2.0 * i) -
- exp(T(static_cast<double>(i)) * x1) -
- exp(T(static_cast<double>(i) * x2));
+ (exp(T(static_cast<double>(i)) * x1) +
+ exp(T(static_cast<double>(i) * x2)));
}
END_MGH_PROBLEM;
@@ -178,7 +182,6 @@
const T x2 = x[1];
const T x3 = x[2];
const T theta = T(0.5 / M_PI) * atan(x2 / x1) + (x1 > 0.0 ? T(0.0) : T(0.5));
-
residual[0] = T(10.0) * (x3 - T(10.0) * theta);
residual[1] = T(10.0) * (sqrt(x1 * x1 + x2 * x2) - T(1.0));
residual[2] = x3;
@@ -204,7 +207,7 @@
const T u = T(static_cast<double>(i));
const T v = T(static_cast<double>(16 - i));
const T w = T(static_cast<double>(std::min(i, 16 - i)));
- residual[i - 1] = T(y[i - 1]) - x1 + u / (v * x2 + w * x3);
+ residual[i - 1] = T(y[i - 1]) - (x1 + u / (v * x2 + w * x3));
}
END_MGH_PROBLEM;
@@ -249,35 +252,270 @@
8261, 7030, 6005, 5147, 4427, 3820, 3307, 2872};
for (int i = 0; i < 16; ++i) {
- T t = T(45 + 5.0 * (i + 1));
- residual[i] = x1 * exp(x2 / (t + x3)) - y[i];
+ const T ti = T(45 + 5.0 * (i + 1));
+ const T yi = T(y[i]);
+ residual[i] = x1 * exp(x2 / (ti + x3)) - yi;
}
END_MGH_PROBLEM
-
const double TestProblem10::initial_x[] = {0.02, 4000, 250};
-const double TestProblem10::lower_bounds[] ={
+const double TestProblem10::lower_bounds[] = {
-kDoubleMax, -kDoubleMax, -kDoubleMax};
-const double TestProblem10::upper_bounds[] ={
+const double TestProblem10::upper_bounds[] = {
kDoubleMax, kDoubleMax, kDoubleMax};
const double TestProblem10::constrained_optimal_cost =
std::numeric_limits<double>::quiet_NaN();
const double TestProblem10::unconstrained_optimal_cost = 87.9458;
+// Gulf research and development function
+BEGIN_MGH_PROBLEM(TestProblem11, 3, 100)
+ const T x1 = x[0];
+ const T x2 = x[1];
+ const T x3 = x[2];
+ for (int i = 1; i <= 100; ++i) {
+ const double ti = static_cast<double>(i) / 100.0;
+ const double yi = 25.0 + pow(-50.0 * log(ti), 2.0 / 3.0);
+ residual[i - 1] = exp(-pow(abs(T(yi * 100.0 * i) * x2), x3) / x1) - T(ti);
+ }
+END_MGH_PROBLEM
+
+const double TestProblem11::initial_x[] = {5.0, 2.5, 0.15};
+const double TestProblem11::lower_bounds[] = {1e-16, 0.0, 0.0};
+const double TestProblem11::upper_bounds[] = {10.0, 10.0, 10.0};
+const double TestProblem11::constrained_optimal_cost = 0.58281431e-4;
+const double TestProblem11::unconstrained_optimal_cost = 0.0;
+
+// Box three-dimensional function.
+BEGIN_MGH_PROBLEM(TestProblem12, 3, 3)
+ const T x1 = x[0];
+ const T x2 = x[1];
+ const T x3 = x[2];
+
+ const T t1 = T(0.1);
+ const T t2 = T(0.2);
+ const T t3 = T(0.3);
+
+ residual[0] = exp(-t1 * x1) - exp(-t1 * x2) - x3 * (exp(-t1) - exp(-T(10.0) * t1));
+ residual[1] = exp(-t2 * x1) - exp(-t2 * x2) - x3 * (exp(-t2) - exp(-T(10.0) * t2));
+ residual[2] = exp(-t3 * x1) - exp(-t3 * x2) - x3 * (exp(-t3) - exp(-T(10.0) * t3));
+END_MGH_PROBLEM
+
+const double TestProblem12::initial_x[] = {0.0, 10.0, 20.0};
+const double TestProblem12::lower_bounds[] = {0.0, 5.0, 0.0};
+const double TestProblem12::upper_bounds[] = {2.0, 9.5, 20.0};
+const double TestProblem12::constrained_optimal_cost = 0.30998153e-5;
+const double TestProblem12::unconstrained_optimal_cost = 0.0;
+
+// Powell Singular function.
+BEGIN_MGH_PROBLEM(TestProblem13, 4, 4)
+ const T x1 = x[0];
+ const T x2 = x[1];
+ const T x3 = x[2];
+ const T x4 = x[3];
+
+ residual[0] = x1 + T(10.0) * x2;
+ residual[1] = T(sqrt(5.0)) * (x3 - x4);
+ residual[2] = (x2 - T(2.0) * x3) * (x2 - T(2.0) * x3);
+ residual[3] = sqrt(10.0) * (x1 - x4) * (x1 - x4);
+END_MGH_PROBLEM
+
+const double TestProblem13::initial_x[] = {3.0, -1.0, 0.0, 1.0};
+const double TestProblem13::lower_bounds[] = {
+ -kDoubleMax, -kDoubleMax, -kDoubleMax};
+const double TestProblem13::upper_bounds[] = {
+ kDoubleMax, kDoubleMax, kDoubleMax};
+const double TestProblem13::constrained_optimal_cost =
+ std::numeric_limits<double>::quiet_NaN();
+const double TestProblem13::unconstrained_optimal_cost = 0.0;
+
+// Wood function.
+BEGIN_MGH_PROBLEM(TestProblem14, 4, 6)
+ const T x1 = x[0];
+ const T x2 = x[1];
+ const T x3 = x[2];
+ const T x4 = x[3];
+
+ residual[0] = T(10.0) * (x2 - x1 * x1);
+ residual[1] = T(1.0) - x1;
+ residual[2] = T(sqrt(90.0)) * (x4 - x3 * x3);
+ residual[3] = T(1.0) - x3;
+ residual[4] = T(sqrt(10.0)) * (x2 + x4 - T(2.0));
+ residual[5] = T(1.0/sqrt(10.0)) * (x2 - x4);
+END_MGH_PROBLEM;
+
+const double TestProblem14::initial_x[] = {-3.0, -1.0, -3.0, -1.0};
+const double TestProblem14::lower_bounds[] = {-100.0, -100.0, -100.0, -100.0};
+const double TestProblem14::upper_bounds[] = {0.0, 10.0, 100.0, 100.0};
+const double TestProblem14::constrained_optimal_cost = 0.15567008e1;
+const double TestProblem14::unconstrained_optimal_cost = 0.0;
+
+// Kowalik and Osborne function.
+BEGIN_MGH_PROBLEM(TestProblem15, 4, 11)
+ const T x1 = x[0];
+ const T x2 = x[1];
+ const T x3 = x[2];
+ const T x4 = x[3];
+
+ const double y[] = {0.1957, 0.1947, 0.1735, 0.1600, 0.0844, 0.0627,
+ 0.0456, 0.0342, 0.0323, 0.0235, 0.0246};
+ const double u[] = {4.0, 2.0, 1.0, 0.5, 0.25, 0.167, 0.125, 0.1,
+ 0.0833, 0.0714, 0.0625};
+
+ for (int i = 0; i < 11; ++i) {
+ const T yi = T(y[i]);
+ const T ui = T(u[i]);
+ residual[i] = yi - x1 * (ui * ui + ui * x2) / (ui * ui + ui * x3 + x4);
+ }
+END_MGH_PROBLEM;
+
+const double TestProblem15::initial_x[] = {0.25, 0.39, 0.415, 0.39};
+const double TestProblem15::lower_bounds[] = {
+ -kDoubleMax, -kDoubleMax, -kDoubleMax, -kDoubleMax};
+const double TestProblem15::upper_bounds[] = {
+ kDoubleMax, kDoubleMax, kDoubleMax, kDoubleMax};
+const double TestProblem15::constrained_optimal_cost =
+ std::numeric_limits<double>::quiet_NaN();
+const double TestProblem15::unconstrained_optimal_cost = 3.07505e-4;
+
+// Brown and Dennis function.
+BEGIN_MGH_PROBLEM(TestProblem16, 4, 20)
+ const T x1 = x[0];
+ const T x2 = x[1];
+ const T x3 = x[2];
+ const T x4 = x[3];
+
+ for (int i = 0; i < 20; ++i) {
+ const T ti = T(static_cast<double>(i + 1) / 5.0);
+ residual[i] = (x1 + ti * x2 - exp(ti)) * (x1 + ti * x2 - exp(ti)) +
+ (x3 + x4 * sin(ti) - cos(ti)) * (x3 + x4 * sin(ti) - cos(ti));
+ }
+END_MGH_PROBLEM;
+
+const double TestProblem16::initial_x[] = {25.0, 5.0, -5.0, -1.0};
+const double TestProblem16::lower_bounds[] = {-10.0, 0.0, -100.0, -20.0};
+const double TestProblem16::upper_bounds[] = {100.0, 15.0, 0.0, 0.2};
+const double TestProblem16::constrained_optimal_cost = 0.88860479e5;
+const double TestProblem16::unconstrained_optimal_cost = 85822.2;
+
+// Osborne 1 function.
+BEGIN_MGH_PROBLEM(TestProblem17, 5, 33)
+ const T x1 = x[0];
+ const T x2 = x[1];
+ const T x3 = x[2];
+ const T x4 = x[3];
+ const T x5 = x[4];
+
+ const double y[] = {0.844, 0.908, 0.932, 0.936, 0.925, 0.908, 0.881, 0.850, 0.818,
+ 0.784, 0.751, 0.718, 0.685, 0.658, 0.628, 0.603, 0.580, 0.558,
+ 0.538, 0.522, 0.506, 0.490, 0.478, 0.467, 0.457, 0.448, 0.438,
+ 0.431, 0.424, 0.420, 0.414, 0.411, 0.406};
+
+ for (int i = 0; i < 33; ++i) {
+ const T yi = T(y[i]);
+ const T ti = T(10.0 * i);
+ residual[i] = yi - (x1 + x2 * exp(-ti * x4) + x3 * exp(-ti * x5));
+ }
+END_MGH_PROBLEM;
+
+const double TestProblem17::initial_x[] = {0.5, 1.5, -1.0, 0.01, 0.02};
+const double TestProblem17::lower_bounds[] = {
+ -kDoubleMax, -kDoubleMax, -kDoubleMax, -kDoubleMax};
+const double TestProblem17::upper_bounds[] = {
+ kDoubleMax, kDoubleMax, kDoubleMax, kDoubleMax};
+const double TestProblem17::constrained_optimal_cost =
+ std::numeric_limits<double>::quiet_NaN();
+const double TestProblem17::unconstrained_optimal_cost = 5.46489e-5;
+
+// Biggs EXP6 function.
+BEGIN_MGH_PROBLEM(TestProblem18, 6, 13)
+ const T x1 = x[0];
+ const T x2 = x[1];
+ const T x3 = x[2];
+ const T x4 = x[3];
+ const T x5 = x[4];
+ const T x6 = x[5];
+
+ for (int i = 0; i < 13; ++i) {
+ const double ti = 0.1 * (i + 1.0);
+ const double yi = exp(-ti) - 5.0 * exp(-10.0 * ti) + 3.0 * exp(-4.0 * ti);
+ const T si = T(ti);
+ residual[i] =x3 * exp(-si * x1) - x4 * exp(-si * x2) + x6 * exp(-si * x5) - T(yi);
+ }
+END_MGH_PROBLEM
+
+const double TestProblem18::initial_x[] = {1.0, 2.0, 1.0, 1.0, 1.0, 1.0};
+const double TestProblem18::lower_bounds[] = {0.0, 0.0, 0.0, 1.0, 0.0, 0.0};
+const double TestProblem18::upper_bounds[] = {2.0, 8.0, 1.0, 7.0, 5.0, 5.0};
+const double TestProblem18::constrained_optimal_cost = 0.53209865e-3;
+const double TestProblem18::unconstrained_optimal_cost = 0.0;
+
+// Osborne 2 function.
+BEGIN_MGH_PROBLEM(TestProblem19, 11, 65)
+ const T x1 = x[0];
+ const T x2 = x[1];
+ const T x3 = x[2];
+ const T x4 = x[3];
+ const T x5 = x[4];
+ const T x6 = x[5];
+ const T x7 = x[6];
+ const T x8 = x[7];
+ const T x9 = x[8];
+ const T x10 = x[9];
+ const T x11 = x[10];
+
+ const double y[] = {1.366, 1.191, 1.112, 1.013, 0.991,
+ 0.885, 0.831, 0.847, 0.786, 0.725,
+ 0.746, 0.679, 0.608, 0.655, 0.616,
+ 0.606, 0.602, 0.626, 0.651, 0.724,
+ 0.649, 0.649, 0.694, 0.644, 0.624,
+ 0.661, 0.612, 0.558, 0.533, 0.495,
+ 0.500, 0.423, 0.395, 0.375, 0.372,
+ 0.391, 0.396, 0.405, 0.428, 0.429,
+ 0.523, 0.562, 0.607, 0.653, 0.672,
+ 0.708, 0.633, 0.668, 0.645, 0.632,
+ 0.591, 0.559, 0.597, 0.625, 0.739,
+ 0.710, 0.729, 0.720, 0.636, 0.581,
+ 0.428, 0.292, 0.162, 0.098, 0.054};
+
+ for (int i = 0; i < 65; ++i) {
+ const T ti = T(static_cast<double>(i) / 10.0);
+ residual[i] = T(y[i]) - (x1 * exp(-(ti * x5)) +
+ x2 * exp(-(ti - x9) * (ti - x9) * x6) +
+ x3 * exp(-(ti - x10) * (ti - x10) * x7) +
+ x4 * exp(-(ti - x11) * (ti - x11) * x8));
+ }
+END_MGH_PROBLEM;
+
+const double TestProblem19::initial_x[] = {1.3, 0.65, 0.65, 0.7, 0.6,
+ 3.0, 5.0, 7.0, 2.0, 4.5, 5.5};
+const double TestProblem19::lower_bounds[] = {
+ -kDoubleMax, -kDoubleMax, -kDoubleMax, -kDoubleMax};
+const double TestProblem19::upper_bounds[] = {
+ kDoubleMax, kDoubleMax, kDoubleMax, kDoubleMax};
+const double TestProblem19::constrained_optimal_cost =
+ std::numeric_limits<double>::quiet_NaN();
+const double TestProblem19::unconstrained_optimal_cost = 4.01377e-2;
+
+
#undef BEGIN_MGH_PROBLEM
#undef END_MGH_PROBLEM
-template<typename TestProblem> string ConstrainedSolve() {
+template<typename TestProblem> bool Solve(bool is_constrained, int trial) {
double x[TestProblem::kNumParameters];
- std::copy(TestProblem::initial_x,
- TestProblem::initial_x + TestProblem::kNumParameters,
- x);
+ for (int i = 0; i < TestProblem::kNumParameters; ++i) {
+ x[i] = pow(10, trial) * TestProblem::initial_x[i];
+ }
Problem problem;
problem.AddResidualBlock(TestProblem::Create(), NULL, x);
- for (int i = 0; i < TestProblem::kNumParameters; ++i) {
- problem.SetParameterLowerBound(x, i, TestProblem::lower_bounds[i]);
- problem.SetParameterUpperBound(x, i, TestProblem::upper_bounds[i]);
+ double optimal_cost = TestProblem::unconstrained_optimal_cost;
+
+ if (is_constrained) {
+ for (int i = 0; i < TestProblem::kNumParameters; ++i) {
+ problem.SetParameterLowerBound(x, i, TestProblem::lower_bounds[i]);
+ problem.SetParameterUpperBound(x, i, TestProblem::upper_bounds[i]);
+ }
+ optimal_cost = TestProblem::constrained_optimal_cost;
}
Solver::Options options;
@@ -289,48 +527,18 @@
Solver::Summary summary;
Solve(options, &problem, &summary);
- const double kMinLogRelativeError = 5.0;
+ const double kMinLogRelativeError = 4.0;
const double log_relative_error = -std::log10(
- std::abs(2.0 * summary.final_cost -
- TestProblem::constrained_optimal_cost) /
- (TestProblem::constrained_optimal_cost > 0.0
- ? TestProblem::constrained_optimal_cost
- : 1.0));
+ std::abs(2.0 * summary.final_cost - optimal_cost) /
+ (optimal_cost > 0.0 ? optimal_cost : 1.0));
- return (log_relative_error >= kMinLogRelativeError
- ? "Success\n"
- : "Failure\n");
-}
-
-template<typename TestProblem> string UnconstrainedSolve() {
- double x[TestProblem::kNumParameters];
- std::copy(TestProblem::initial_x,
- TestProblem::initial_x + TestProblem::kNumParameters,
- x);
-
- Problem problem;
- problem.AddResidualBlock(TestProblem::Create(), NULL, x);
-
- Solver::Options options;
- options.parameter_tolerance = 1e-18;
- options.function_tolerance = 0.0;
- options.gradient_tolerance = 1e-18;
- options.max_num_iterations = 1000;
- options.linear_solver_type = DENSE_QR;
- Solver::Summary summary;
- Solve(options, &problem, &summary);
-
- const double kMinLogRelativeError = 5.0;
- const double log_relative_error = -std::log10(
- std::abs(2.0 * summary.final_cost -
- TestProblem::unconstrained_optimal_cost) /
- (TestProblem::unconstrained_optimal_cost > 0.0
- ? TestProblem::unconstrained_optimal_cost
- : 1.0));
-
- return (log_relative_error >= kMinLogRelativeError
- ? "Success\n"
- : "Failure\n");
+ const bool success = log_relative_error >= kMinLogRelativeError;
+ LOG(INFO) << "Expected : " << optimal_cost
+ << " actual: " << 2.0 * summary.final_cost
+ << " " << success
+ << " in " << summary.total_time_in_seconds
+ << " seconds";
+ return success;
}
} // namespace examples
@@ -340,18 +548,39 @@
CERES_GFLAGS_NAMESPACE::ParseCommandLineFlags(&argc, &argv, true);
google::InitGoogleLogging(argv[0]);
- using ceres::examples::UnconstrainedSolve;
- using ceres::examples::ConstrainedSolve;
+ using ceres::examples::Solve;
+
+ int unconstrained_problems = 0;
+ int unconstrained_successes = 0;
+ int constrained_problems = 0;
+ int constrained_successes = 0;
+ std::stringstream ss;
#define UNCONSTRAINED_SOLVE(n) \
- std::cout << "Problem " << n << " : " \
- << UnconstrainedSolve<ceres::examples::TestProblem##n>();
+ ss << "Unconstrained Problem" << n << " : "; \
+ if (FLAGS_problem == #n || FLAGS_problem == "all") { \
+ unconstrained_problems += 3; \
+ if (Solve<ceres::examples::TestProblem##n>(false, 0)) { \
+ unconstrained_successes += 1; \
+ ss << "Yes "; \
+ } else { \
+ ss << "No "; \
+ } \
+ if (Solve<ceres::examples::TestProblem##n>(false, 1)) { \
+ unconstrained_successes += 1; \
+ ss << "Yes "; \
+ } else { \
+ ss << "No "; \
+ } \
+ if (Solve<ceres::examples::TestProblem##n>(false, 2)) { \
+ unconstrained_successes += 1; \
+ ss << "Yes "; \
+ } else { \
+ ss << "No "; \
+ } \
+ } \
+ ss << std::endl;
-#define CONSTRAINED_SOLVE(n) \
- std::cout << "Problem " << n << " : " \
- << ConstrainedSolve<ceres::examples::TestProblem##n>();
-
- std::cout << "Unconstrained problems\n";
UNCONSTRAINED_SOLVE(1);
UNCONSTRAINED_SOLVE(2);
UNCONSTRAINED_SOLVE(3);
@@ -362,13 +591,49 @@
UNCONSTRAINED_SOLVE(8);
UNCONSTRAINED_SOLVE(9);
UNCONSTRAINED_SOLVE(10);
+ UNCONSTRAINED_SOLVE(11);
+ UNCONSTRAINED_SOLVE(12);
+ UNCONSTRAINED_SOLVE(13);
+ UNCONSTRAINED_SOLVE(14);
+ UNCONSTRAINED_SOLVE(15);
+ UNCONSTRAINED_SOLVE(16);
+ UNCONSTRAINED_SOLVE(17);
+ UNCONSTRAINED_SOLVE(18);
+ UNCONSTRAINED_SOLVE(19);
- std::cout << "\nConstrained problems\n";
+ ss << "Unconstrained : "
+ << unconstrained_successes
+ << "/"
+ << unconstrained_problems << std::endl;
+
+#define CONSTRAINED_SOLVE(n) \
+ ss << "Constrained Problem " << n << " : "; \
+ if (FLAGS_problem == #n || FLAGS_problem == "all") { \
+ constrained_problems += 1; \
+ if (Solve<ceres::examples::TestProblem##n>(true, 0)) { \
+ constrained_successes += 1; \
+ ss << "Yes "; \
+ } else { \
+ ss << "No "; \
+ } \
+ } \
+ ss << std::endl;
+
CONSTRAINED_SOLVE(3);
CONSTRAINED_SOLVE(4);
CONSTRAINED_SOLVE(5);
CONSTRAINED_SOLVE(7);
CONSTRAINED_SOLVE(9);
+ CONSTRAINED_SOLVE(11);
+ CONSTRAINED_SOLVE(12);
+ CONSTRAINED_SOLVE(14);
+ CONSTRAINED_SOLVE(16);
+ CONSTRAINED_SOLVE(18);
+ ss << "Constrained : "
+ << constrained_successes
+ << "/"
+ << constrained_problems << std::endl;
+ std::cout << ss.str();
return 0;
}
