304 lines
9.8 KiB
Python
304 lines
9.8 KiB
Python
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"""
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Step 05: 日历排程 - 贪心装箱算法
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输入: 03_allocate.xlsx
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输出: 05_schedule.xlsx
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功能:
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1. 将年度频次 k_i 转化为具体日期
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2. 保证每天恰好2个站点
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3. 优化访问间隔的均匀性
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4. 输出完整的365天日历
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约束:
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- 每天恰好2个站点
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- 每站点出现次数 = k_i
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- 同一站点相邻访问间隔尽量均匀
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"""
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import pandas as pd
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import numpy as np
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from pathlib import Path
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from collections import defaultdict
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import random
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# 路径配置
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INPUT_PATH = Path(__file__).parent / "03_allocate.xlsx"
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OUTPUT_PATH = Path(__file__).parent / "05_schedule.xlsx"
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# 排程参数
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T = 365 # 全年天数
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CAPACITY = 2 # 每天站点数
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RANDOM_SEED = 42 # 随机种子 (用于局部优化)
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def generate_ideal_dates(k: int, T: int = 365) -> list:
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"""
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生成站点的理想访问日期
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将 k 次访问均匀分布在 [1, T] 内
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t_j = round((j + 0.5) * T / k), j = 0, 1, ..., k-1
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"""
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dates = []
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for j in range(k):
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ideal_day = round((j + 0.5) * T / k)
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ideal_day = max(1, min(T, ideal_day))
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dates.append(ideal_day)
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return dates
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def greedy_schedule(site_visits: dict, T: int = 365, capacity: int = 2) -> dict:
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"""
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贪心装箱算法
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Args:
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site_visits: {site_id: k} 各站点的年度访问次数
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T: 全年天数
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capacity: 每天站点容量
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Returns:
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calendar: {day: [site_id, ...]} 日历排程
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"""
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# 生成所有访问事件: (理想日期, 站点ID)
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events = []
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for site_id, k in site_visits.items():
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ideal_dates = generate_ideal_dates(k, T)
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for ideal_day in ideal_dates:
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events.append((ideal_day, site_id))
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# 按理想日期排序
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events.sort(key=lambda x: (x[0], x[1]))
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# 初始化日历
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calendar = {day: [] for day in range(1, T + 1)}
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# 贪心分配
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for ideal_day, site_id in events:
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assigned = False
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# 从理想日期向两侧搜索可用槽位
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for offset in range(T):
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for day in [ideal_day + offset, ideal_day - offset]:
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if 1 <= day <= T:
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# 检查容量和重复
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if len(calendar[day]) < capacity and site_id not in calendar[day]:
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calendar[day].append(site_id)
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assigned = True
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break
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if assigned:
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break
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if not assigned:
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print(f"警告: 无法分配站点 {site_id} (理想日期 {ideal_day})")
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return calendar
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def compute_gap_stats(calendar: dict, site_id: int) -> dict:
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"""计算单个站点的访问间隔统计"""
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days = sorted([day for day, sites in calendar.items() if site_id in sites])
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if len(days) < 2:
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return {
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'n_visits': len(days),
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'gaps': [],
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'gap_mean': None,
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'gap_std': None,
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'gap_min': None,
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'gap_max': None,
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'gap_cv': None
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}
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gaps = [days[i + 1] - days[i] for i in range(len(days) - 1)]
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return {
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'n_visits': len(days),
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'gaps': gaps,
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'gap_mean': np.mean(gaps),
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'gap_std': np.std(gaps),
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'gap_min': min(gaps),
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'gap_max': max(gaps),
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'gap_cv': np.std(gaps) / np.mean(gaps) if np.mean(gaps) > 0 else 0
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}
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def local_optimization(calendar: dict, site_ids: list, max_iter: int = 5000, seed: int = 42) -> dict:
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"""
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局部搜索优化间隔均匀性
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通过随机交换两天的站点，若改善总间隔方差则接受
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"""
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random.seed(seed)
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calendar = {day: list(sites) for day, sites in calendar.items()} # 深拷贝
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def total_gap_variance():
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"""计算所有站点间隔方差之和"""
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total_var = 0
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for site_id in site_ids:
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stats = compute_gap_stats(calendar, site_id)
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if stats['gap_std'] is not None:
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total_var += stats['gap_std'] ** 2
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return total_var
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current_var = total_gap_variance()
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improved = 0
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for iteration in range(max_iter):
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# 随机选两天
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t1, t2 = random.sample(range(1, 366), 2)
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if len(calendar[t1]) == 2 and len(calendar[t2]) == 2:
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# 随机选择交换位置
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pos1, pos2 = random.randint(0, 1), random.randint(0, 1)
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s1, s2 = calendar[t1][pos1], calendar[t2][pos2]
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# 检查交换可行性 (不能产生重复)
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if s1 != s2:
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other1 = calendar[t1][1 - pos1]
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other2 = calendar[t2][1 - pos2]
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if s2 != other1 and s1 != other2:
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# 尝试交换
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calendar[t1][pos1], calendar[t2][pos2] = s2, s1
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new_var = total_gap_variance()
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if new_var < current_var:
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current_var = new_var
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improved += 1
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else:
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# 撤销
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calendar[t1][pos1], calendar[t2][pos2] = s1, s2
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return calendar, improved
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def main():
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print("=" * 60)
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print("Step 05: 日历排程 - 贪心装箱算法")
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print("=" * 60)
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# 1. 读取分配结果
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print(f"\n[1] 读取输入: {INPUT_PATH}")
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df = pd.read_excel(INPUT_PATH)
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print(f" 读取 {len(df)} 条记录")
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# 构建 site_visits 字典
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site_visits = dict(zip(df['site_id'], df['k']))
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total_visits = sum(site_visits.values())
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print(f" 总访问次数: {total_visits}")
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print(f" 期望日历天数: {total_visits // CAPACITY} 天")
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# 2. 执行贪心排程
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print(f"\n[2] 执行贪心装箱排程...")
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calendar = greedy_schedule(site_visits, T, CAPACITY)
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# 验证
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total_assigned = sum(len(sites) for sites in calendar.values())
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print(f" 已分配访问事件: {total_assigned} / {total_visits}")
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empty_days = sum(1 for sites in calendar.values() if len(sites) == 0)
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partial_days = sum(1 for sites in calendar.values() if len(sites) == 1)
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full_days = sum(1 for sites in calendar.values() if len(sites) == 2)
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print(f" 日历统计: {full_days} 满载 + {partial_days} 部分 + {empty_days} 空闲")
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# 3. 局部优化
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print(f"\n[3] 局部优化 (改善间隔均匀性)...")
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site_ids = list(site_visits.keys())
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calendar_opt, n_improved = local_optimization(calendar, site_ids, max_iter=5000, seed=RANDOM_SEED)
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print(f" 优化迭代: 5000 次")
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print(f" 接受的改进: {n_improved} 次")
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# 4. 间隔统计
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print(f"\n[4] 访问间隔统计")
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gap_stats_list = []
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for site_id in site_ids:
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stats = compute_gap_stats(calendar_opt, site_id)
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stats['site_id'] = site_id
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gap_stats_list.append(stats)
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df_gaps = pd.DataFrame(gap_stats_list)
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df_gaps = df_gaps.merge(df[['site_id', 'site_name', 'k']], on='site_id')
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# 全局统计
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valid_gaps = df_gaps[df_gaps['gap_mean'].notna()]
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print(f" 平均间隔均值: {valid_gaps['gap_mean'].mean():.2f} 天")
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print(f" 平均间隔标准差: {valid_gaps['gap_std'].mean():.2f} 天")
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print(f" 最大单次间隔: {valid_gaps['gap_max'].max():.0f} 天")
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print(f" 平均间隔CV: {valid_gaps['gap_cv'].mean():.4f}")
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# 5. 生成日历输出
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print(f"\n[5] 生成日历输出...")
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# 日历表: date, site_1, site_2
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calendar_rows = []
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for day in range(1, T + 1):
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sites = calendar_opt.get(day, [])
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site_1 = sites[0] if len(sites) > 0 else None
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site_2 = sites[1] if len(sites) > 1 else None
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calendar_rows.append({
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'day': day,
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'site_1_id': site_1,
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'site_2_id': site_2
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})
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df_calendar = pd.DataFrame(calendar_rows)
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# 添加站点名称
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site_name_map = dict(zip(df['site_id'], df['site_name']))
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df_calendar['site_1_name'] = df_calendar['site_1_id'].map(site_name_map)
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df_calendar['site_2_name'] = df_calendar['site_2_id'].map(site_name_map)
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# 6. 站点日期列表
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site_dates = []
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for site_id in site_ids:
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days = sorted([day for day, sites in calendar_opt.items() if site_id in sites])
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site_dates.append({
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'site_id': site_id,
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'site_name': site_name_map[site_id],
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'k': len(days),
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'dates': ','.join(map(str, days))
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})
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df_site_dates = pd.DataFrame(site_dates)
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# 7. 保存输出
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print(f"\n[6] 保存输出: {OUTPUT_PATH}")
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with pd.ExcelWriter(OUTPUT_PATH, engine='openpyxl') as writer:
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# Sheet 1: 日历 (365天)
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df_calendar.to_excel(writer, sheet_name='calendar', index=False)
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# Sheet 2: 站点日期列表
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df_site_dates.to_excel(writer, sheet_name='site_dates', index=False)
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# Sheet 3: 间隔统计
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df_gaps_out = df_gaps[['site_id', 'site_name', 'k', 'n_visits', 'gap_mean', 'gap_std', 'gap_min', 'gap_max', 'gap_cv']]
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df_gaps_out.to_excel(writer, sheet_name='gap_statistics', index=False)
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# Sheet 4: 排程参数
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params = pd.DataFrame([
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{'parameter': 'T (days)', 'value': T},
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{'parameter': 'CAPACITY (sites/day)', 'value': CAPACITY},
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{'parameter': 'total_visits', 'value': total_visits},
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{'parameter': 'optimization_iterations', 'value': 5000},
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{'parameter': 'improvements_accepted', 'value': n_improved},
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])
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params.to_excel(writer, sheet_name='parameters', index=False)
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print(f" 已保存4个工作表: calendar, site_dates, gap_statistics, parameters")
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# 8. 输出预览
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print(f"\n[7] 日历预览 (前10天):")
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print(df_calendar.head(10).to_string(index=False))
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print(f"\n 间隔最大的5个站点:")
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top5_gap = df_gaps.nlargest(5, 'gap_max')[['site_id', 'site_name', 'k', 'gap_mean', 'gap_max', 'gap_cv']]
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print(top5_gap.to_string(index=False))
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print("\n" + "=" * 60)
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print("Step 05 完成")
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print("=" * 60)
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return df_calendar, df_gaps
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if __name__ == "__main__":
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main()
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