原 CP 求解器

本部分介绍了原始约束编程求解器，它已被高级的 CP-SAT 求解器取代。

注意 ：我们强烈建议使用 CP-SAT 求解器，而不是原始的 CP 求解器。

以下部分介绍了如何求解 CP-SAT 部分中所述的示例，这次使用原始 CP 求解器。如果您坚持要使用原始 CP 求解器，可以浏览 API 参考文档。请注意，原始 CP 求解器是路由库的基础，自定义路由模型可能需要其 API。

导入库

以下代码会导入所需的库。

Python

from ortools.constraint_solver import pywrapcp

C++

#include <ostream>
#include <string>

#include "ortools/constraint_solver/constraint_solver.h"

Java

import com.google.ortools.Loader;
import com.google.ortools.constraintsolver.DecisionBuilder;
import com.google.ortools.constraintsolver.IntVar;
import com.google.ortools.constraintsolver.Solver;
import java.util.logging.Logger;

C#

using System;
using Google.OrTools.ConstraintSolver;

声明求解器

以下代码会声明求解器。

Python

solver = pywrapcp.Solver("CPSimple")

C++

Solver solver("CpSimple");

Java

Solver solver = new Solver("CpSimple");

C#

Solver solver = new Solver("CpSimple");

创建变量

以下代码用于创建该问题的变量。

该求解器会创建 x、y 和 z 三个变量，每个变量可以取值 0、1 或 2。

Python

num_vals = 3
x = solver.IntVar(0, num_vals - 1, "x")
y = solver.IntVar(0, num_vals - 1, "y")
z = solver.IntVar(0, num_vals - 1, "z")

C++

const int64_t num_vals = 3;
IntVar* const x = solver.MakeIntVar(0, num_vals - 1, "x");
IntVar* const y = solver.MakeIntVar(0, num_vals - 1, "y");
IntVar* const z = solver.MakeIntVar(0, num_vals - 1, "z");

Java

final long numVals = 3;
final IntVar x = solver.makeIntVar(0, numVals - 1, "x");
final IntVar y = solver.makeIntVar(0, numVals - 1, "y");
final IntVar z = solver.makeIntVar(0, numVals - 1, "z");

C#

const long numVals = 3;
IntVar x = solver.MakeIntVar(0, numVals - 1, "x");
IntVar y = solver.MakeIntVar(0, numVals - 1, "y");
IntVar z = solver.MakeIntVar(0, numVals - 1, "z");

创建限制条件

以下代码会创建约束条件 x ≠ y。

Python

solver.Add(x != y)
print("Number of constraints: ", solver.Constraints())

C++

solver.AddConstraint(solver.MakeAllDifferent({x, y}));
LOG(INFO) << "Number of constraints: "
          << std::to_string(solver.constraints());

Java

solver.addConstraint(solver.makeAllDifferent(new IntVar[] {x, y}));
logger.info("Number of constraints: " + solver.constraints());

C#

solver.Add(solver.MakeAllDifferent(new IntVar[] { x, y }));
Console.WriteLine($"Number of constraints: {solver.Constraints()}");

调用求解器

以下代码调用求解器。

决策构建器是原始 CP 求解器的主要输入。它包含以下内容：

• vars - 包含问题变量的数组。
• 一条规则，用于选择要向哪个变量赋值。
• 一条规则，用于选择要分配给该变量的下一个值。

如需了解详情，请参阅决策构建器。

Python

decision_builder = solver.Phase(
    [x, y, z], solver.CHOOSE_FIRST_UNBOUND, solver.ASSIGN_MIN_VALUE
)

C++

DecisionBuilder* const db = solver.MakePhase(
    {x, y, z}, Solver::CHOOSE_FIRST_UNBOUND, Solver::ASSIGN_MIN_VALUE);

Java

final DecisionBuilder db = solver.makePhase(
    new IntVar[] {x, y, z}, Solver.CHOOSE_FIRST_UNBOUND, Solver.ASSIGN_MIN_VALUE);

C#

DecisionBuilder db =
    solver.MakePhase(new IntVar[] { x, y, z }, Solver.CHOOSE_FIRST_UNBOUND, Solver.ASSIGN_MIN_VALUE);

输出解决方案

解决方案打印机的代码会在求解器找到后显示每个解决方案，详见下一部分。

由于我们的问题有多种解决方案，因此可以使用 while solver.NextSolution() 循环遍历这些解决方案。（请注意，这与 CP-SAT 求解器的解决方案打印机的运作方式不同）。

Python

count = 0
solver.NewSearch(decision_builder)
while solver.NextSolution():
    count += 1
    solution = f"Solution {count}:\n"
    for var in [x, y, z]:
        solution += f" {var.Name()} = {var.Value()}"
    print(solution)
solver.EndSearch()
print(f"Number of solutions found: {count}")

C++

int count = 0;
solver.NewSearch(db);
while (solver.NextSolution()) {
  ++count;
  LOG(INFO) << "Solution " << count << ":" << std::endl
            << " x=" << x->Value() << " y=" << y->Value()
            << " z=" << z->Value();
}
solver.EndSearch();
LOG(INFO) << "Number of solutions found: " << solver.solutions();

Java

int count = 0;
solver.newSearch(db);
while (solver.nextSolution()) {
  ++count;
  logger.info(
      String.format("Solution: %d\n x=%d y=%d z=%d", count, x.value(), y.value(), z.value()));
}
solver.endSearch();
logger.info("Number of solutions found: " + solver.solutions());

C#

int count = 0;
solver.NewSearch(db);
while (solver.NextSolution())
{
    ++count;
    Console.WriteLine($"Solution: {count}\n x={x.Value()} y={y.Value()} z={z.Value()}");
}
solver.EndSearch();
Console.WriteLine($"Number of solutions found: {solver.Solutions()}");

求解器返回的结果

以下是求解器找到的 18 个解：

Number of constraints:  1
Solution 1:
 x = 0 y = 1 z = 0
Solution 2:
 x = 0 y = 1 z = 1
Solution 3:
 x = 0 y = 1 z = 2
Solution 4:
 x = 0 y = 2 z = 0
Solution 5:
 x = 0 y = 2 z = 1
Solution 6:
 x = 0 y = 2 z = 2
Solution 7:
 x = 1 y = 0 z = 0
Solution 8:
 x = 1 y = 0 z = 1
Solution 9:
 x = 1 y = 0 z = 2
Solution 10:
 x = 1 y = 2 z = 0
Solution 11:
 x = 1 y = 2 z = 1
Solution 12:
 x = 1 y = 2 z = 2
Solution 13:
 x = 2 y = 0 z = 0
Solution 14:
 x = 2 y = 0 z = 1
Solution 15:
 x = 2 y = 0 z = 2
Solution 16:
 x = 2 y = 1 z = 0
Solution 17:
 x = 2 y = 1 z = 1
Solution 18:
 x = 2 y = 1 z = 2
Number of solutions found:  18
Advanced usage:
Problem solved in  2 ms
Memory usage:  13918208 bytes

完整程序

以下是使用原始 CP 求解器的示例的完整程序。

Python

"""Simple Constraint optimization example."""

from ortools.constraint_solver import pywrapcp


def main():
    """Entry point of the program."""
    # Instantiate the solver.
    solver = pywrapcp.Solver("CPSimple")

    # Create the variables.
    num_vals = 3
    x = solver.IntVar(0, num_vals - 1, "x")
    y = solver.IntVar(0, num_vals - 1, "y")
    z = solver.IntVar(0, num_vals - 1, "z")

    # Constraint 0: x != y.
    solver.Add(x != y)
    print("Number of constraints: ", solver.Constraints())

    # Solve the problem.
    decision_builder = solver.Phase(
        [x, y, z], solver.CHOOSE_FIRST_UNBOUND, solver.ASSIGN_MIN_VALUE
    )

    # Print solution on console.
    count = 0
    solver.NewSearch(decision_builder)
    while solver.NextSolution():
        count += 1
        solution = f"Solution {count}:\n"
        for var in [x, y, z]:
            solution += f" {var.Name()} = {var.Value()}"
        print(solution)
    solver.EndSearch()
    print(f"Number of solutions found: {count}")

    print("Advanced usage:")
    print(f"Problem solved in {solver.WallTime()}ms")
    print(f"Memory usage: {pywrapcp.Solver.MemoryUsage()}bytes")


if __name__ == "__main__":
    main()

C++

#include <ostream>
#include <string>

#include "ortools/constraint_solver/constraint_solver.h"

namespace operations_research {

void SimpleCpProgram() {
  // Instantiate the solver.
  Solver solver("CpSimple");

  // Create the variables.
  const int64_t num_vals = 3;
  IntVar* const x = solver.MakeIntVar(0, num_vals - 1, "x");
  IntVar* const y = solver.MakeIntVar(0, num_vals - 1, "y");
  IntVar* const z = solver.MakeIntVar(0, num_vals - 1, "z");

  // Constraint 0: x != y..
  solver.AddConstraint(solver.MakeAllDifferent({x, y}));
  LOG(INFO) << "Number of constraints: "
            << std::to_string(solver.constraints());

  // Solve the problem.
  DecisionBuilder* const db = solver.MakePhase(
      {x, y, z}, Solver::CHOOSE_FIRST_UNBOUND, Solver::ASSIGN_MIN_VALUE);

  // Print solution on console.
  int count = 0;
  solver.NewSearch(db);
  while (solver.NextSolution()) {
    ++count;
    LOG(INFO) << "Solution " << count << ":" << std::endl
              << " x=" << x->Value() << " y=" << y->Value()
              << " z=" << z->Value();
  }
  solver.EndSearch();
  LOG(INFO) << "Number of solutions found: " << solver.solutions();

  LOG(INFO) << "Advanced usage:" << std::endl
            << "Problem solved in " << std::to_string(solver.wall_time())
            << "ms" << std::endl
            << "Memory usage: " << std::to_string(Solver::MemoryUsage())
            << "bytes";
}

}  // namespace operations_research

int main(int /*argc*/, char* /*argv*/[]) {
  operations_research::SimpleCpProgram();
  return EXIT_SUCCESS;
}

Java

package com.google.ortools.constraintsolver.samples;
import com.google.ortools.Loader;
import com.google.ortools.constraintsolver.DecisionBuilder;
import com.google.ortools.constraintsolver.IntVar;
import com.google.ortools.constraintsolver.Solver;
import java.util.logging.Logger;

/** Simple CP Program.*/
public class SimpleCpProgram {
  private SimpleCpProgram() {}

  private static final Logger logger = Logger.getLogger(SimpleCpProgram.class.getName());

  public static void main(String[] args) throws Exception {
    Loader.loadNativeLibraries();
    // Instantiate the solver.
    Solver solver = new Solver("CpSimple");

    // Create the variables.
    final long numVals = 3;
    final IntVar x = solver.makeIntVar(0, numVals - 1, "x");
    final IntVar y = solver.makeIntVar(0, numVals - 1, "y");
    final IntVar z = solver.makeIntVar(0, numVals - 1, "z");

    // Constraint 0: x != y..
    solver.addConstraint(solver.makeAllDifferent(new IntVar[] {x, y}));
    logger.info("Number of constraints: " + solver.constraints());

    // Solve the problem.
    final DecisionBuilder db = solver.makePhase(
        new IntVar[] {x, y, z}, Solver.CHOOSE_FIRST_UNBOUND, Solver.ASSIGN_MIN_VALUE);

    // Print solution on console.
    int count = 0;
    solver.newSearch(db);
    while (solver.nextSolution()) {
      ++count;
      logger.info(
          String.format("Solution: %d\n x=%d y=%d z=%d", count, x.value(), y.value(), z.value()));
    }
    solver.endSearch();
    logger.info("Number of solutions found: " + solver.solutions());

    logger.info(String.format("Advanced usage:\nProblem solved in %d ms\nMemory usage: %d bytes",
        solver.wallTime(), Solver.memoryUsage()));
  }
}

C#

using System;
using Google.OrTools.ConstraintSolver;

/// <summary>
///   This is a simple CP program.
/// </summary>
public class SimpleCpProgram
{
    public static void Main(String[] args)
    {
        // Instantiate the solver.
        Solver solver = new Solver("CpSimple");

        // Create the variables.
        const long numVals = 3;
        IntVar x = solver.MakeIntVar(0, numVals - 1, "x");
        IntVar y = solver.MakeIntVar(0, numVals - 1, "y");
        IntVar z = solver.MakeIntVar(0, numVals - 1, "z");

        // Constraint 0: x != y..
        solver.Add(solver.MakeAllDifferent(new IntVar[] { x, y }));
        Console.WriteLine($"Number of constraints: {solver.Constraints()}");

        // Solve the problem.
        DecisionBuilder db =
            solver.MakePhase(new IntVar[] { x, y, z }, Solver.CHOOSE_FIRST_UNBOUND, Solver.ASSIGN_MIN_VALUE);

        // Print solution on console.
        int count = 0;
        solver.NewSearch(db);
        while (solver.NextSolution())
        {
            ++count;
            Console.WriteLine($"Solution: {count}\n x={x.Value()} y={y.Value()} z={z.Value()}");
        }
        solver.EndSearch();
        Console.WriteLine($"Number of solutions found: {solver.Solutions()}");

        Console.WriteLine("Advanced usage:");
        Console.WriteLine($"Problem solved in {solver.WallTime()}ms");
        Console.WriteLine($"Memory usage: {Solver.MemoryUsage()}bytes");
    }
}

决策者

原始 CP 求解器的主要输入是决策构建器，它包含问题的变量并设置求解器的选项。

上一部分中的代码示例使用 Phase 方法（对应于 C++ 方法 MakePhase）创建决策构建器。

“阶段”一词指的是搜索的一个阶段。在这个简单示例中，只有一个阶段，但对于更复杂的问题，决策制定工具可以有多个阶段，以便求解器从一个阶段到下一个阶段采用不同的搜索策略。

Phase 方法有三个输入参数：

• vars - 包含问题变量的数组，在本例中为 [x, y, z]。
• IntVarStrategy - 用于选择下一个未绑定变量来赋值的规则。此处的代码使用了默认的 CHOOSE_FIRST_UNBOUND，这意味着在每一步，求解器都会按照第一个未绑定变量在传递给 Phase 方法的变量数组中出现的顺序选择第一个未绑定变量。
• IntValueStrategy - 用于选择要为变量分配的下一个值的规则。 此处的代码使用默认 ASSIGN_MIN_VALUE，它会选择尚未为变量尝试过的最小值。这将按递增顺序分配值。另一个选项是 ASSIGN_MAX_VALUE，在这种情况下，求解器将按降序分配值。