c34026b101
note: done using ```sh git grep -l "2010-2024 Google" | xargs sed -i 's/2010-2024 Google/2010-2025 Google/' ```
89 lines
3.3 KiB
C++
89 lines
3.3 KiB
C++
// Copyright 2010-2025 Google LLC
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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// Simple SOCP problem showing that minimizing the perimeter of a rectangle
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// with fixed area results in equal width and height.
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#include <cmath>
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#include <iostream>
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#include <limits>
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#include <ostream>
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#include "absl/flags/flag.h"
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#include "absl/status/status.h"
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#include "ortools/base/init_google.h"
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#include "ortools/base/logging.h"
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#include "ortools/base/status_macros.h"
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#include "ortools/math_opt/cpp/math_opt.h"
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ABSL_FLAG(double, area, 9, "Area lower bound.");
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namespace {
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namespace math_opt = ::operations_research::math_opt;
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constexpr double kInf = std::numeric_limits<double>::infinity();
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// We want to minimize the width plus height of a rectangle with area A.
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//
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// First we can relax to the area being at least A:
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// min width + height
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// s.t. width*height >= A (Area)
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// width in [0.0, infinity)
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// height in [0.0, infinity)
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//
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// Next we need to reformulate the area constraint as a second order cone
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// constraint:
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// min width + height
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// s.t. ||((width - height)/2, sqrt(A))||_2 <= (width + height)/2 (Area-SOCP)
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// width in [0.0, infinity)
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// height in [0.0, infinity)
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//
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// To see how these two problems are equivalent, first note that by squaring
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// both sides of constraint (Area-SOCP) we can see that it is equivalent to:
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// (width - height)^2/4 + A <= (width + height)^2/4
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// because width + height >= 0. Expanding the two squares and reordering shows
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// the equivalence to constraint (Area).
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absl::Status Main(const double target_area) {
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math_opt::Model model;
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const math_opt::Variable width =
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model.AddContinuousVariable(0.0, kInf, "width");
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const math_opt::Variable height =
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model.AddContinuousVariable(0.0, kInf, "height");
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model.AddSecondOrderConeConstraint(
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{(width - height) / 2, std::sqrt(target_area)}, (width + height) / 2);
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model.Minimize(width + height);
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ASSIGN_OR_RETURN(const math_opt::SolveResult result,
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Solve(model, math_opt::SolverType::kEcos));
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RETURN_IF_ERROR(result.termination.EnsureIsOptimalOrFeasible());
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std::cout << "Target area: " << target_area << std::endl;
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std::cout << "Area: "
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<< result.variable_values().at(width) *
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result.variable_values().at(height)
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<< std::endl;
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std::cout << "Perimeter = " << result.objective_value() << std::endl;
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std::cout << "Width: " << result.variable_values().at(width) << std::endl;
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std::cout << "Height: " << result.variable_values().at(height) << std::endl;
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return absl::OkStatus();
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}
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} // namespace
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int main(int argc, char** argv) {
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InitGoogle(argv[0], &argc, &argv, true);
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const absl::Status status = Main(absl::GetFlag(FLAGS_area));
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if (!status.ok()) {
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LOG(QFATAL) << status;
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}
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return 0;
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}
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