优化cpmpy中累计约束的性能：解决与ortools集成时的效率瓶颈

import cpmpy as cp
import logging
from typing import List

class CumulativeTestModel:
    def __init__(self, task_duration: int, nb_tasks: int, end_date: int):
        self.model: cp.Model = cp.Model()

        # 定义变量
        # objective: 目标变量，表示所需的机器数量，范围从0到任务总数
        self.objective: cp.IntVar = cp.intvar(0, nb_tasks)
        # starts: 每个任务的开始时间变量
        starts: List[cp.IntVar] = [cp.intvar(0, end_date) for _ in range(nb_tasks)]
        # durations: 每个任务的持续时间（此处所有任务持续时间相同）
        durations: List[int] = [task_duration] * nb_tasks
        # ends: 每个任务的结束时间变量
        ends: List[cp.IntVar] = [cp.intvar(0, end_date) for _ in range(nb_tasks)]
        # demands: 每个任务的资源需求（此处每个任务占用1个机器）
        demands: List[int] = [1] * nb_tasks

        # 添加累计约束到模型中
        # 确保在任何时间点，所有正在运行任务的总需求（demands）不超过容量（objective）
        self.model += cp.Cumulative(
            start=starts,
            duration=durations,
            end=ends,
            demand=demands,
            capacity=self.objective,
        )

        # 最小化目标变量，即寻找最少的机器数量
        self.model.minimize(self.objective)
        logging.info(f"Model created with {nb_tasks} tasks.")

    def run(self):
        # 使用ortools作为求解器
        solver = cp.model.SolverLookup.get("ortools", self.model)
        has_solution = solver.solve()

        if not has_solution:
            logging.info("No solution found.")
        else:
            logging.info(f"Solution found: {solver.status()} ({(solver.solution_time):.3f} seconds) -> {self.objective.value()}")

if __name__ == "__main__":
    logging.basicConfig(level=logging.INFO)
    print("[ortools]")
    CumulativeTestModel(task_duration=10, nb_tasks=3, end_date=15).run()
    CumulativeTestModel(task_duration=10, nb_tasks=5, end_date=25).run()
    CumulativeTestModel(task_duration=10, nb_tasks=7, end_date=35).run()
    CumulativeTestModel(task_duration=10, nb_tasks=9, end_date=45).run()
    CumulativeTestModel(task_duration=10, nb_tasks=11, end_date=55).run()
    # CumulativeTestModel(task_duration=10, nb_tasks=13, end_date=65).run() # 此任务数量下可能长时间无解

    print("\n[minizinc:chuffed]")
    # 也可以测试其他MiniZinc求解器，例如Chuffed
    # 注意：需要安装minizinc-python并配置Chuffed求解器
    # solver_chuffed = cp.model.SolverLookup.get("minizinc:chuffed", CumulativeTestModel(10, 11, 55).model)
    # solver_chuffed.solve()

Model created with 3 tasks.
Solution found: ExitStatus.OPTIMAL (0.009 seconds) -> 3
Model created with 11 tasks.
Solution found: ExitStatus.OPTIMAL (0.002 seconds) -> 3
Model created with 13 tasks.
Solution found: ExitStatus.OPTIMAL (0.001 seconds) -> 3
Model created with 21 tasks.
Solution found: ExitStatus.OPTIMAL (0.001 seconds) -> 3