401 lines
15 KiB
Python
401 lines
15 KiB
Python
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"""
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Task 3 - Step 7: 敏感性分析
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============================
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分析以下参数对模型输出的影响：
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1. 合并比例 r_merge: [1/3, 1/2, 2/3]
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2. 距离阈值 l_max: [30, 40, 50, 60, 70]
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3. 容量上限 μ_sum_max: [400, 425, 450, 475, 500]
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4. CV阈值: [0.3, 0.4, 0.5, 0.6]
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输出: 07_sensitivity.xlsx (各参数对E1', E2', F1', R1的影响)
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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 scipy import stats
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import warnings
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warnings.filterwarnings('ignore')
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# ============================================
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# 基础参数和函数
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# ============================================
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Q = 400
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QUALITY_THRESHOLD = 250
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SHORTFALL_THRESHOLD = 0.8
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def quality_factor(mu_total):
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return min(1.0, QUALITY_THRESHOLD / mu_total) if mu_total > 0 else 1.0
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def expected_service(q, mu, sigma):
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if sigma == 0:
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return min(mu, q)
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z = (q - mu) / sigma
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return mu * stats.norm.cdf(z) - sigma * stats.norm.pdf(z) + q * (1 - stats.norm.cdf(z))
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def gini_coefficient(values):
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values = np.array(values)
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values = values[~np.isnan(values)]
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if len(values) == 0:
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return 0
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values = np.sort(values)
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n = len(values)
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cumsum = np.cumsum(values)
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return (2 * np.sum((np.arange(1, n + 1) * values)) - (n + 1) * cumsum[-1]) / (n * cumsum[-1]) if cumsum[-1] > 0 else 0
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def shortfall_probability(q, mu, sigma, threshold=0.8):
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if sigma == 0:
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return 0 if q >= mu * threshold else 1
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critical_demand = q / threshold
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return 1 - stats.norm.cdf((critical_demand - mu) / sigma)
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def optimal_allocation(mu_i, sigma_i, mu_j, sigma_j, Q=400):
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if sigma_i + sigma_j == 0:
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return mu_i
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return (sigma_j * mu_i + sigma_i * (Q - mu_j)) / (sigma_i + sigma_j)
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def calc_distance(lat1, lon1, lat2, lon2):
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lat_avg = (lat1 + lat2) / 2
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lat_avg_rad = np.radians(lat_avg)
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delta_lat = lat1 - lat2
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delta_lon = lon1 - lon2
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return 69.0 * np.sqrt(delta_lat**2 + (np.cos(lat_avg_rad) * delta_lon)**2)
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# ============================================
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# 完整流水线函数
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# ============================================
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def run_pipeline(sites_df, l_max=50, mu_sum_max=450, cv_max=0.5, merge_ratio=0.5):
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"""
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运行完整的Task 3流水线，返回评估指标
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"""
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sites = sites_df.copy()
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sites['cv'] = sites['sigma'] / sites['mu']
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n = len(sites)
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# Step 1: 计算距离矩阵
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distance_matrix = np.zeros((n, n))
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for i in range(n):
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for j in range(n):
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if i != j:
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distance_matrix[i, j] = calc_distance(
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sites.iloc[i]['lat'], sites.iloc[i]['lon'],
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sites.iloc[j]['lat'], sites.iloc[j]['lon']
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)
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# Step 2: 配对筛选
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candidates = []
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for i in range(n):
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for j in range(i + 1, n):
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site_i = sites.iloc[i]
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site_j = sites.iloc[j]
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dist = distance_matrix[i, j]
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if dist > l_max:
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continue
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mu_sum = site_i['mu'] + site_j['mu']
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if mu_sum > mu_sum_max:
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continue
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if site_i['cv'] > cv_max or site_j['cv'] > cv_max:
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continue
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sigma_sq_sum = site_i['sigma']**2 + site_j['sigma']**2
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value = (1.0 * mu_sum / Q - 0.3 * dist / l_max - 0.5 * sigma_sq_sum / mu_sum**2)
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candidates.append({
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'idx_i': i, 'idx_j': j,
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'site_i_id': site_i['site_id'], 'site_j_id': site_j['site_id'],
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'distance': dist,
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'mu_i': site_i['mu'], 'mu_j': site_j['mu'],
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'sigma_i': site_i['sigma'], 'sigma_j': site_j['sigma'],
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'k_i': site_i['k'], 'k_j': site_j['k'],
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'mu_tilde_i': site_i['mu_tilde'], 'mu_tilde_j': site_j['mu_tilde'],
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'value': value
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})
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if len(candidates) == 0:
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# 无可行配对，返回Task 1的指标
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E1 = (sites['k'] * sites['mu']).sum()
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E2 = sum(sites['k'] * sites['mu'].apply(quality_factor) * sites['mu'])
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rates = [row['k'] * row['mu'] / row['mu_tilde'] for _, row in sites.iterrows()]
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F1 = gini_coefficient(rates)
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F2 = min(rates)
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return {
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'num_pairs': 0, 'num_dual_visits': 0,
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'E1': E1, 'E2': E2, 'F1': F1, 'F2': F2, 'R1': 0, 'RS': 0
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}
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# 贪心配对选择
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df_cand = pd.DataFrame(candidates).sort_values('value', ascending=False)
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selected = []
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used = set()
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for _, row in df_cand.iterrows():
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if row['idx_i'] not in used and row['idx_j'] not in used:
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selected.append(row.to_dict())
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used.add(row['idx_i'])
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used.add(row['idx_j'])
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# Step 3: 计算最优分配
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for pair in selected:
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q_star = optimal_allocation(pair['mu_i'], pair['sigma_i'],
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pair['mu_j'], pair['sigma_j'], Q)
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pair['q_final'] = q_star
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pair['E_Si'] = expected_service(q_star, pair['mu_i'], pair['sigma_i'])
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pair['E_Sj'] = expected_service(Q - q_star, pair['mu_j'], pair['sigma_j'])
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pair['E_total'] = pair['E_Si'] + pair['E_Sj']
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# Step 4: 重分配访问次数
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sites['k_single'] = sites['k'].copy()
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sites['k_dual'] = 0
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pair_k = {}
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for pair in selected:
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k_i, k_j = pair['k_i'], pair['k_j']
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k_ij = int(min(k_i, k_j) * merge_ratio)
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if k_ij >= min(k_i, k_j):
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k_ij = min(k_i, k_j) - 1
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if k_ij < 1:
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k_ij = 0
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idx_i, idx_j = pair['idx_i'], pair['idx_j']
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sites.loc[idx_i, 'k_single'] = k_i - k_ij
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sites.loc[idx_i, 'k_dual'] = k_ij
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sites.loc[idx_j, 'k_single'] = k_j - k_ij
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sites.loc[idx_j, 'k_dual'] = k_ij
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pair_k[(pair['site_i_id'], pair['site_j_id'])] = k_ij
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# 计算释放槽位并重分配
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total_single = sites['k_single'].sum()
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total_dual = sum(pair_k.values())
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delta_N = 730 - (total_single + total_dual)
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if delta_N > 0:
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total_demand = sites['mu_tilde'].sum()
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sites['k_extra'] = (delta_N * sites['mu_tilde'] / total_demand).apply(np.floor).astype(int)
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remainder = delta_N - sites['k_extra'].sum()
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if remainder > 0:
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fractional = delta_N * sites['mu_tilde'] / total_demand - sites['k_extra']
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top_idx = fractional.nlargest(int(remainder)).index
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sites.loc[top_idx, 'k_extra'] += 1
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sites['k_single_final'] = sites['k_single'] + sites['k_extra']
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else:
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sites['k_single_final'] = sites['k_single']
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# Step 5: 计算指标
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# E1'
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E1 = (sites['k_single_final'] * sites['mu']).sum()
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for pair in selected:
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k_ij = pair_k.get((pair['site_i_id'], pair['site_j_id']), 0)
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E1 += k_ij * pair['E_total']
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# E2'
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E2 = sum(sites['k_single_final'] * sites['mu'].apply(quality_factor) * sites['mu'])
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for pair in selected:
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k_ij = pair_k.get((pair['site_i_id'], pair['site_j_id']), 0)
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mu_sum = pair['mu_i'] + pair['mu_j']
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q_factor = quality_factor(mu_sum)
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E2 += k_ij * q_factor * pair['E_total']
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# 满足率
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site_satisfaction = {}
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for idx, row in sites.iterrows():
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r = row['k_single_final'] * row['mu'] / row['mu_tilde'] if row['mu_tilde'] > 0 else 0
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site_satisfaction[row['site_id']] = r
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for pair in selected:
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k_ij = pair_k.get((pair['site_i_id'], pair['site_j_id']), 0)
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r_i = k_ij * pair['E_Si'] / pair['mu_tilde_i'] if pair['mu_tilde_i'] > 0 else 0
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r_j = k_ij * pair['E_Sj'] / pair['mu_tilde_j'] if pair['mu_tilde_j'] > 0 else 0
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site_satisfaction[pair['site_i_id']] += r_i
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site_satisfaction[pair['site_j_id']] += r_j
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rates = list(site_satisfaction.values())
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F1 = gini_coefficient(rates)
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F2 = min(rates) if rates else 0
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# R1: 缺口风险
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shortfall_probs = []
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for pair in selected:
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q = pair['q_final']
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p_i = shortfall_probability(q, pair['mu_i'], pair['sigma_i'])
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p_j = shortfall_probability(Q - q, pair['mu_j'], pair['sigma_j'])
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shortfall_probs.append(1 - (1 - p_i) * (1 - p_j))
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R1 = np.mean(shortfall_probs) if shortfall_probs else 0
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# RS: 资源节省率
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RS = total_dual / 730
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return {
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'num_pairs': len(selected),
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'num_dual_visits': total_dual,
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'E1': E1, 'E2': E2, 'F1': F1, 'F2': F2, 'R1': R1, 'RS': RS
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}
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# ============================================
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# 主程序
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# ============================================
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print("=" * 60)
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print("Task 3 - Step 7: 敏感性分析")
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print("=" * 60)
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# 读取基础数据
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sites_df = pd.read_excel('../task1/03_allocate.xlsx')
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print(f"\n读取站点数据: {len(sites_df)} 个站点")
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# 基准参数
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BASE_L_MAX = 50
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BASE_MU_SUM_MAX = 450
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BASE_CV_MAX = 0.5
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BASE_MERGE_RATIO = 0.5
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# 计算基准结果
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print(f"\n计算基准结果...")
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base_result = run_pipeline(sites_df, BASE_L_MAX, BASE_MU_SUM_MAX, BASE_CV_MAX, BASE_MERGE_RATIO)
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print(f"基准: E1={base_result['E1']:.0f}, E2={base_result['E2']:.0f}, F1={base_result['F1']:.4f}, R1={base_result['R1']:.4f}")
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# ============================================
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# 敏感性分析
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# ============================================
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all_results = []
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# 1. 合并比例敏感性
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print(f"\n" + "-" * 40)
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print("1. 合并比例敏感性 (merge_ratio)")
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print("-" * 40)
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merge_ratios = [1/3, 0.5, 2/3]
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for mr in merge_ratios:
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result = run_pipeline(sites_df, BASE_L_MAX, BASE_MU_SUM_MAX, BASE_CV_MAX, mr)
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result['param'] = 'merge_ratio'
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result['param_value'] = mr
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all_results.append(result)
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print(f" merge_ratio={mr:.3f}: pairs={result['num_pairs']}, dual={result['num_dual_visits']}, "
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f"E1={result['E1']:.0f}, E2={result['E2']:.0f}, F1={result['F1']:.4f}, R1={result['R1']:.4f}")
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# 2. 距离阈值敏感性
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print(f"\n" + "-" * 40)
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print("2. 距离阈值敏感性 (l_max)")
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print("-" * 40)
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l_max_values = [30, 40, 50, 60, 70]
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for lm in l_max_values:
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result = run_pipeline(sites_df, lm, BASE_MU_SUM_MAX, BASE_CV_MAX, BASE_MERGE_RATIO)
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result['param'] = 'l_max'
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result['param_value'] = lm
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all_results.append(result)
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print(f" l_max={lm}: pairs={result['num_pairs']}, dual={result['num_dual_visits']}, "
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f"E1={result['E1']:.0f}, E2={result['E2']:.0f}, F1={result['F1']:.4f}, R1={result['R1']:.4f}")
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# 3. 容量上限敏感性
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print(f"\n" + "-" * 40)
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print("3. 容量上限敏感性 (mu_sum_max)")
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print("-" * 40)
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mu_sum_values = [400, 425, 450, 475, 500]
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for ms in mu_sum_values:
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result = run_pipeline(sites_df, BASE_L_MAX, ms, BASE_CV_MAX, BASE_MERGE_RATIO)
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result['param'] = 'mu_sum_max'
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result['param_value'] = ms
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all_results.append(result)
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print(f" mu_sum_max={ms}: pairs={result['num_pairs']}, dual={result['num_dual_visits']}, "
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f"E1={result['E1']:.0f}, E2={result['E2']:.0f}, F1={result['F1']:.4f}, R1={result['R1']:.4f}")
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# 4. CV阈值敏感性
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print(f"\n" + "-" * 40)
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print("4. CV阈值敏感性 (cv_max)")
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print("-" * 40)
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cv_max_values = [0.3, 0.4, 0.5, 0.6]
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for cv in cv_max_values:
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result = run_pipeline(sites_df, BASE_L_MAX, BASE_MU_SUM_MAX, cv, BASE_MERGE_RATIO)
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result['param'] = 'cv_max'
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result['param_value'] = cv
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all_results.append(result)
|
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|
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print(f" cv_max={cv}: pairs={result['num_pairs']}, dual={result['num_dual_visits']}, "
|
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|
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f"E1={result['E1']:.0f}, E2={result['E2']:.0f}, F1={result['F1']:.4f}, R1={result['R1']:.4f}")
|
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|
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|
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|
|
# ============================================
|
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|
|
# 汇总分析
|
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|
|
# ============================================
|
|||
|
|
df_results = pd.DataFrame(all_results)
|
|||
|
|
|
|||
|
|
print(f"\n" + "=" * 60)
|
|||
|
|
print("敏感性分析汇总")
|
|||
|
|
print("=" * 60)
|
|||
|
|
|
|||
|
|
# 计算各参数的影响范围
|
|||
|
|
for param in ['merge_ratio', 'l_max', 'mu_sum_max', 'cv_max']:
|
|||
|
|
subset = df_results[df_results['param'] == param]
|
|||
|
|
print(f"\n{param}:")
|
|||
|
|
print(f" E1 变化范围: [{subset['E1'].min():.0f}, {subset['E1'].max():.0f}], "
|
|||
|
|
f"变化幅度: {(subset['E1'].max() - subset['E1'].min()) / base_result['E1'] * 100:.2f}%")
|
|||
|
|
print(f" E2 变化范围: [{subset['E2'].min():.0f}, {subset['E2'].max():.0f}], "
|
|||
|
|
f"变化幅度: {(subset['E2'].max() - subset['E2'].min()) / base_result['E2'] * 100:.2f}%")
|
|||
|
|
print(f" F1 变化范围: [{subset['F1'].min():.4f}, {subset['F1'].max():.4f}]")
|
|||
|
|
print(f" R1 变化范围: [{subset['R1'].min():.4f}, {subset['R1'].max():.4f}]")
|
|||
|
|
|
|||
|
|
# ============================================
|
|||
|
|
# 保存结果
|
|||
|
|
# ============================================
|
|||
|
|
OUTPUT_FILE = '07_sensitivity.xlsx'
|
|||
|
|
|
|||
|
|
with pd.ExcelWriter(OUTPUT_FILE, engine='openpyxl') as writer:
|
|||
|
|
# Sheet 1: 所有结果
|
|||
|
|
df_results.to_excel(writer, sheet_name='all_results', index=False)
|
|||
|
|
|
|||
|
|
# Sheet 2: 合并比例敏感性
|
|||
|
|
df_merge = df_results[df_results['param'] == 'merge_ratio'].copy()
|
|||
|
|
df_merge.to_excel(writer, sheet_name='merge_ratio', index=False)
|
|||
|
|
|
|||
|
|
# Sheet 3: 距离阈值敏感性
|
|||
|
|
df_lmax = df_results[df_results['param'] == 'l_max'].copy()
|
|||
|
|
df_lmax.to_excel(writer, sheet_name='l_max', index=False)
|
|||
|
|
|
|||
|
|
# Sheet 4: 容量上限敏感性
|
|||
|
|
df_musum = df_results[df_results['param'] == 'mu_sum_max'].copy()
|
|||
|
|
df_musum.to_excel(writer, sheet_name='mu_sum_max', index=False)
|
|||
|
|
|
|||
|
|
# Sheet 5: CV阈值敏感性
|
|||
|
|
df_cv = df_results[df_results['param'] == 'cv_max'].copy()
|
|||
|
|
df_cv.to_excel(writer, sheet_name='cv_max', index=False)
|
|||
|
|
|
|||
|
|
# Sheet 6: 基准结果
|
|||
|
|
base_df = pd.DataFrame([{
|
|||
|
|
'param': 'baseline',
|
|||
|
|
'l_max': BASE_L_MAX,
|
|||
|
|
'mu_sum_max': BASE_MU_SUM_MAX,
|
|||
|
|
'cv_max': BASE_CV_MAX,
|
|||
|
|
'merge_ratio': BASE_MERGE_RATIO,
|
|||
|
|
**base_result
|
|||
|
|
}])
|
|||
|
|
base_df.to_excel(writer, sheet_name='baseline', index=False)
|
|||
|
|
|
|||
|
|
# Sheet 7: 汇总统计
|
|||
|
|
summary_rows = []
|
|||
|
|
for param in ['merge_ratio', 'l_max', 'mu_sum_max', 'cv_max']:
|
|||
|
|
subset = df_results[df_results['param'] == param]
|
|||
|
|
summary_rows.append({
|
|||
|
|
'param': param,
|
|||
|
|
'E1_min': subset['E1'].min(),
|
|||
|
|
'E1_max': subset['E1'].max(),
|
|||
|
|
'E1_range_pct': (subset['E1'].max() - subset['E1'].min()) / base_result['E1'] * 100,
|
|||
|
|
'E2_min': subset['E2'].min(),
|
|||
|
|
'E2_max': subset['E2'].max(),
|
|||
|
|
'E2_range_pct': (subset['E2'].max() - subset['E2'].min()) / base_result['E2'] * 100,
|
|||
|
|
'F1_min': subset['F1'].min(),
|
|||
|
|
'F1_max': subset['F1'].max(),
|
|||
|
|
'R1_min': subset['R1'].min(),
|
|||
|
|
'R1_max': subset['R1'].max()
|
|||
|
|
})
|
|||
|
|
df_summary = pd.DataFrame(summary_rows)
|
|||
|
|
df_summary.to_excel(writer, sheet_name='summary', index=False)
|
|||
|
|
|
|||
|
|
print(f"\n结果已保存至: {OUTPUT_FILE}")
|
|||
|
|
print(" - Sheet 'all_results': 所有结果")
|
|||
|
|
print(" - Sheet 'merge_ratio': 合并比例敏感性")
|
|||
|
|
print(" - Sheet 'l_max': 距离阈值敏感性")
|
|||
|
|
print(" - Sheet 'mu_sum_max': 容量上限敏感性")
|
|||
|
|
print(" - Sheet 'cv_max': CV阈值敏感性")
|
|||
|
|
print(" - Sheet 'baseline': 基准结果")
|
|||
|
|
print(" - Sheet 'summary': 汇总统计")
|
|||
|
|
print("\n" + "=" * 60)
|