diff --git a/.gitignore b/.gitignore index 0d7149b..50a5148 100644 --- a/.gitignore +++ b/.gitignore @@ -1,3 +1,4 @@ +__pycache__/ latex-template/ .DS_Store ~$*.* diff --git a/kmin_effectiveness.png b/kmin_effectiveness.png index da6da19..e960552 100644 Binary files a/kmin_effectiveness.png and b/kmin_effectiveness.png differ diff --git a/kmin_effectiveness.py b/kmin_effectiveness.py index ec49942..038d42c 100644 --- a/kmin_effectiveness.py +++ b/kmin_effectiveness.py @@ -1,10 +1,13 @@ """ K_min-有效性分析 k_min为实数：如2.7表示70%站点最低2次，30%站点最低3次 + +有效性计算支持引入需求标准差（正态分布），并通过 Monte Carlo 多次模拟求均值。 """ import numpy as np import pandas as pd +import math try: import matplotlib @@ -21,8 +24,82 @@ except ModuleNotFoundError: # 参数 C_OPT = 250 N_TOTAL = 722 -ALPHA = 0.4 +ALPHA = 0.5 BETA = 0.2 +N_SIMS = 2000 +RANDOM_SEED = 42 + + +def gini_coefficient(values): + """ + 计算基尼系数（0=完全均等，1=完全不均等） + 约定：values 非负；若总和为0，则返回0。 + """ + x = np.asarray(values, dtype=float) + x = x[np.isfinite(x)] + if x.size == 0: + return 0.0 + x = np.clip(x, 0, None) + total = x.sum() + if total <= 0: + return 0.0 + + x_sorted = np.sort(x) + n = x_sorted.size + idx = np.arange(1, n + 1, dtype=float) + return float((2.0 * (idx * x_sorted).sum()) / (n * total) - (n + 1.0) / n) + + +def _norm_pdf(z): + return np.exp(-0.5 * z * z) / np.sqrt(2.0 * np.pi) + + +def _norm_cdf(z): + z = np.asarray(z, dtype=float) + erf_vec = np.vectorize(math.erf, otypes=[float]) + return 0.5 * (1.0 + erf_vec(z / np.sqrt(2.0))) + + +def expected_clipped_normal(mu, sigma, lower=0.0, upper=1.0): + """ + X ~ Normal(mu, sigma^2). 返回 E[clip(X, lower, upper)]. + - 支持 lower=0 用于避免负需求 + - sigma<=0 时退化为 clip(mu, lower, upper) + """ + mu = np.asarray(mu, dtype=float) + sigma = np.asarray(sigma, dtype=float) + lower = float(lower) + upper = float(upper) + + if lower > upper: + raise ValueError("lower must be <= upper") + + out = np.empty_like(mu, dtype=float) + mask = sigma > 0 + out[~mask] = np.clip(mu[~mask], lower, upper) + + if np.any(mask): + m = mu[mask] + s = sigma[mask] + + z_u = (upper - m) / s + z_l = (lower - m) / s + + Phi_u = _norm_cdf(z_u) + Phi_l = _norm_cdf(z_l) + phi_u = _norm_pdf(z_u) + phi_l = _norm_pdf(z_l) + + # E[X 1_{X<=a}] = mu*Phi(z) - sigma*phi(z), z=(a-mu)/sigma + ex_le_u = m * Phi_u - s * phi_u + ex_le_l = m * Phi_l - s * phi_l + + p_le_l = Phi_l + p_gt_u = 1.0 - Phi_u + + out[mask] = lower * p_le_l + (ex_le_u - ex_le_l) + upper * p_gt_u + + return out def load_data(): @@ -76,67 +153,148 @@ def allocate_visits(df, k_min_real, n_total, c_opt): return df -def calc_effectiveness(df, c_opt=C_OPT, alpha=ALPHA, beta=BETA): - """计算有效性指标""" +def calc_effectiveness( + df, + c_opt=C_OPT, + alpha=ALPHA, + beta=BETA, + method="mc", + n_sims=N_SIMS, + seed=RANDOM_SEED, +): + """计算有效性指标（method='mc' 多次模拟取均值；method='analytic' 用闭式期望）""" d = df['Average Demand per Visit'].values + d_std = df.get('StDev(Demand per Visit)', pd.Series(0.0, index=df.index)).values + d_std = np.clip(d_std, 0, None) k = df['AllocatedVisits'].values D = df['TotalDemand'].values - # 截断：单次有效服务 = min(需求, 容量) - eff_per_visit = np.minimum(d, c_opt) - annual_eff = k * eff_per_visit + method = (method or "mc").lower() + if method not in {"mc", "analytic"}: + raise ValueError("method must be 'mc' or 'analytic'") - # 缺货率、浪费率 - unmet = np.maximum(0, D - annual_eff) / np.maximum(D, 1) - waste = np.maximum(0, k * c_opt - D) / np.maximum(k * c_opt, 1) + if method == "analytic": + # 正态分布需求：单次期望有效服务 = E[min(max(N(d, std),0), 容量)] + eff_per_visit = expected_clipped_normal(d, d_std, lower=0.0, upper=float(c_opt)) + annual_eff = k * eff_per_visit - # 有效性得分 - base = annual_eff / np.maximum(D, 1) - score = np.clip(base - alpha * unmet - beta * waste, 0, 1) + unmet = np.maximum(0, D - annual_eff) / np.maximum(D, 1) + waste = np.maximum(0, k * c_opt - annual_eff) / np.maximum(k * c_opt, 1) - n = score.size - bottom_n = max(1, int(np.ceil(n * 0.10))) - bottom10_mean = float(np.sort(score)[:bottom_n].mean()) + base = annual_eff / np.maximum(D, 1) + score = np.clip(base - alpha * unmet - beta * waste, 0, 1) - # 总服务客户数 = Σ min(供给能力, 需求) - total_served = np.minimum(k * c_opt, D).sum() - total_demand = D.sum() + n = score.size + bottom_n = max(1, int(np.ceil(n * 0.10))) + + total_served = np.minimum(annual_eff, D).sum() + total_demand = D.sum() + + return { + 'mean': float(score.mean()), + 'min': float(score.min()), + 'bottom10_mean': float(np.sort(score)[:bottom_n].mean()), + 'gini_eff': float(gini_coefficient(score)), + 'std': float(score.std()), + 'total_unmet': float((D - annual_eff).clip(min=0).sum()), + 'total_waste': float((k * c_opt - annual_eff).clip(min=0).sum()), + 'total_served': float(total_served), + 'total_demand': float(total_demand), + 'serve_ratio': float(total_served / total_demand) if total_demand > 0 else 0.0 + } + + # Monte Carlo：每次访问的需求 ~ Normal(mu, sigma)，重复 n_sims 次取均值 + n_sims = int(n_sims) + if n_sims <= 0: + raise ValueError("n_sims must be > 0") + + rng = np.random.default_rng(seed) + n_sites = len(df) + annual_eff_sims = np.zeros((n_sites, n_sims), dtype=float) + + for i in range(n_sites): + k_i = int(k[i]) + if k_i <= 0: + continue + + mu_i = float(d[i]) + sigma_i = float(d_std[i]) + if sigma_i <= 0: + demand = np.full((n_sims, k_i), mu_i, dtype=float) + else: + demand = rng.normal(mu_i, sigma_i, size=(n_sims, k_i)) + demand = np.clip(demand, 0, None) + annual_eff_sims[i, :] = np.minimum(demand, float(c_opt)).sum(axis=1) + + D2 = D.reshape(-1, 1) + cap2 = (k * c_opt).reshape(-1, 1) + + unmet = np.maximum(0, D2 - annual_eff_sims) / np.maximum(D2, 1) + waste = np.maximum(0, cap2 - annual_eff_sims) / np.maximum(cap2, 1) + base = annual_eff_sims / np.maximum(D2, 1) + score_sims = np.clip(base - alpha * unmet - beta * waste, 0, 1) + + # 每个站点的期望得分（跨模拟平均） + avg_score = score_sims.mean(axis=1) + bottom_n = max(1, int(np.ceil(n_sites * 0.10))) + + total_served_sims = np.minimum(annual_eff_sims, D2).sum(axis=0) + total_unmet_sims = np.maximum(0, D2 - annual_eff_sims).sum(axis=0) + total_waste_sims = np.maximum(0, cap2 - annual_eff_sims).sum(axis=0) + total_demand = float(D.sum()) + total_served = float(total_served_sims.mean()) return { - 'mean': score.mean(), - 'min': score.min(), - 'bottom10_mean': bottom10_mean, - 'std': score.std(), - 'total_unmet': (D - annual_eff).clip(min=0).sum(), - 'total_waste': (k * c_opt - D).clip(min=0).sum(), + 'mean': float(avg_score.mean()), + 'min': float(avg_score.min()), + 'bottom10_mean': float(np.sort(avg_score)[:bottom_n].mean()), + 'gini_eff': float(gini_coefficient(avg_score)), + 'std': float(avg_score.std()), + 'total_unmet': float(total_unmet_sims.mean()), + 'total_waste': float(total_waste_sims.mean()), 'total_served': total_served, 'total_demand': total_demand, - 'serve_ratio': total_served / total_demand + 'serve_ratio': float(total_served / total_demand) if total_demand > 0 else 0.0 } -def analyze_kmin_range(df, k_range=np.arange(1.0, 10.1, 0.1)): +def analyze_kmin_range( + df, + k_range=np.arange(1.0, 10.1, 0.1), + method="mc", + n_sims=N_SIMS, + seed=RANDOM_SEED, +): """扫描k_min范围，计算有效性""" results = [] + n_sites = len(df) + site_cols = [f"visits_{i+1:02d}" for i in range(n_sites)] for k_min in k_range: df_alloc = allocate_visits(df, k_min, N_TOTAL, C_OPT) if df_alloc is None: continue - metrics = calc_effectiveness(df_alloc) - results.append({ + metrics = calc_effectiveness(df_alloc, method=method, n_sims=n_sims, seed=seed) + row = { 'k_min': k_min, 'effectiveness': metrics['mean'], 'min_eff': metrics['min'], 'bottom10_eff': metrics['bottom10_mean'], + 'gini_eff': metrics['gini_eff'], 'std_eff': metrics['std'], 'unmet': metrics['total_unmet'], 'waste': metrics['total_waste'], 'total_served': metrics['total_served'], 'total_demand': metrics['total_demand'], 'serve_ratio': metrics['serve_ratio'] - }) + } + + # 追加每个站点在该 k_min 下的访问次数（按 df 当前排序的站点顺序） + alloc = df_alloc["AllocatedVisits"].astype(int).tolist() + row.update({col: v for col, v in zip(site_cols, alloc)}) + + results.append(row) return pd.DataFrame(results) @@ -146,18 +304,26 @@ def plot_results(results): if not _HAS_MPL: raise RuntimeError("缺少依赖: matplotlib（无法绘图）。请先安装 matplotlib 再运行绘图部分。") - fig, axes = plt.subplots(3, 2, figsize=(12, 10)) + fig, axes = plt.subplots(4, 2, figsize=(12, 13)) - # 找最优点 - best_idx = results['effectiveness'].idxmax() - best_k = results.loc[best_idx, 'k_min'] - best_eff = results.loc[best_idx, 'effectiveness'] + # 红线选点：基尼系数第一次 < 0.2 的 k_min（若不存在则回退到均值有效性最优点） + gini_candidates = results.loc[results["gini_eff"] < 0.2, "k_min"] + if len(gini_candidates) > 0: + selected_k = float(gini_candidates.iloc[0]) + selected_label = f'First Gini<0.2: k_min={selected_k:.1f}' + else: + best_idx = results['effectiveness'].idxmax() + selected_k = float(results.loc[best_idx, 'k_min']) + selected_label = f'Best mean eff: k_min={selected_k:.1f}' + + selected_idx = (results["k_min"] - selected_k).abs().idxmin() + selected_eff = float(results.loc[selected_idx, "effectiveness"]) # 1. 有效性均值 ax = axes[0, 0] ax.plot(results['k_min'], results['effectiveness'], 'b-', lw=2) - ax.axvline(best_k, color='r', ls='--', label=f'Best k_min={best_k:.1f}') - ax.scatter([best_k], [best_eff], c='r', s=100, zorder=5) + ax.axvline(selected_k, color='r', ls='--', label=selected_label) + ax.scatter([selected_k], [selected_eff], c='r', s=100, zorder=5) ax.set_xlabel('k_min') ax.set_ylabel('Mean Effectiveness') ax.set_title('Mean Effectiveness vs k_min') @@ -167,7 +333,7 @@ def plot_results(results): # 2. 最低10%有效性均值 ax = axes[0, 1] ax.plot(results['k_min'], results['bottom10_eff'], 'm-', lw=2) - ax.axvline(best_k, color='r', ls='--') + ax.axvline(selected_k, color='r', ls='--') ax.set_xlabel('k_min') ax.set_ylabel('Bottom 10% Mean Effectiveness') ax.set_title('Bottom 10% Mean Effectiveness vs k_min') @@ -177,7 +343,7 @@ def plot_results(results): ax = axes[1, 0] ax.plot(results['k_min'], results['total_served'] / 1000, 'c-', lw=2) ax.axhline(results['total_demand'].iloc[0] / 1000, color='gray', ls=':', label='Total Demand') - ax.axvline(best_k, color='r', ls='--') + ax.axvline(selected_k, color='r', ls='--') ax.set_xlabel('k_min') ax.set_ylabel('Served Families (×1000)') ax.set_title('Total Served vs k_min') @@ -187,7 +353,7 @@ def plot_results(results): # 4. 最小有效性 ax = axes[1, 1] ax.plot(results['k_min'], results['min_eff'], 'g-', lw=2) - ax.axvline(best_k, color='r', ls='--') + ax.axvline(selected_k, color='r', ls='--') ax.set_xlabel('k_min') ax.set_ylabel('Min Effectiveness') ax.set_title('Worst Site Effectiveness vs k_min') @@ -197,7 +363,7 @@ def plot_results(results): ax = axes[2, 0] ax.plot(results['k_min'], results['unmet'] / 1000, 'r-', lw=2, label='Unmet') ax.plot(results['k_min'], results['waste'] / 1000, 'b-', lw=2, label='Waste') - ax.axvline(best_k, color='gray', ls='--') + ax.axvline(selected_k, color='gray', ls='--') ax.set_xlabel('k_min') ax.set_ylabel('Families (×1000)') ax.set_title('Unmet Demand vs Wasted Capacity') @@ -207,17 +373,30 @@ def plot_results(results): # 6. 有效性标准差 ax = axes[2, 1] ax.plot(results['k_min'], results['std_eff'], color='tab:orange', lw=2) - ax.axvline(best_k, color='gray', ls='--') + ax.axvline(selected_k, color='gray', ls='--') ax.set_xlabel('k_min') ax.set_ylabel('Std Effectiveness') ax.set_title('Effectiveness Std vs k_min') ax.grid(True, alpha=0.3) + # 7. 基尼系数 + ax = axes[3, 0] + ax.plot(results['k_min'], results['gini_eff'], color='tab:purple', lw=2) + ax.axhline(0.2, color='gray', ls=':', lw=1) + ax.axvline(selected_k, color='r', ls='--') + ax.set_xlabel('k_min') + ax.set_ylabel('Gini Coefficient') + ax.set_title('Gini (Effectiveness) vs k_min') + ax.grid(True, alpha=0.3) + + # 8. 空白占位（避免最后一格空图框太挤） + axes[3, 1].axis('off') + plt.tight_layout() plt.savefig('kmin_effectiveness.png', dpi=150) plt.close(fig) - return best_k, best_eff + return selected_k, selected_eff def main(): @@ -225,10 +404,19 @@ def main(): df = load_data() print(f"站点数: {len(df)}, 总运力: {N_TOTAL}") print(f"总需求: {df['TotalDemand'].sum():,.0f} 家庭次") + site_name_col = "Site Name" if "Site Name" in df.columns else None + sites_out = pd.DataFrame( + { + "site_idx": np.arange(1, len(df) + 1, dtype=int), + "site_name": df[site_name_col].astype(str).values if site_name_col else [f"Site_{i+1:02d}" for i in range(len(df))], + "total_demand": df["TotalDemand"].values, + } + ) # 2. 扫描k_min print("\n扫描 k_min ∈ [1.0, 10.0]...") - results = analyze_kmin_range(df) + print(f"使用 Monte Carlo 平均：n_sims={N_SIMS}, seed={RANDOM_SEED}") + results = analyze_kmin_range(df, method="mc", n_sims=N_SIMS, seed=RANDOM_SEED) # 3. 绘图 best_idx = results['effectiveness'].idxmax() @@ -245,7 +433,7 @@ def main(): # 5. 生成最优方案 df_opt = allocate_visits(df, best_k, N_TOTAL, C_OPT) - metrics = calc_effectiveness(df_opt) + metrics = calc_effectiveness(df_opt, method="mc", n_sims=N_SIMS, seed=RANDOM_SEED) print(f"\n最优方案统计:") print(f" 有效性: {metrics['mean']:.4f} (min={metrics['min']:.4f})") @@ -256,7 +444,8 @@ def main(): # 6. 保存 results.to_csv('kmin_effectiveness_data.csv', index=False) - print("\n已保存: kmin_effectiveness.png, kmin_effectiveness_data.csv") + sites_out.to_csv("kmin_effectiveness_sites.csv", index=False) + print("\n已保存: kmin_effectiveness.png, kmin_effectiveness_data.csv, kmin_effectiveness_sites.csv") if __name__ == '__main__': diff --git a/kmin_effectiveness_data.csv b/kmin_effectiveness_data.csv new file mode 100644 index 0000000..6089440 --- /dev/null +++ b/kmin_effectiveness_data.csv @@ -0,0 +1,92 @@ 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College Corning Community College,1506.0 +36,MFP College TC3 -College,1569.0 +37,MFP Montour Falls-Schuyler County Human Services Complex,1643.0 +38,MFP Millport,1660.0 +39,MFP Beaver Dams,1707.0 +40,MFP Birnie Transportation Services,1707.0 +41,MFP Prattsburgh,1734.0 +42,MFP First Assembly Of God Church,1752.0 +43,MFP Canisteo,1770.0 +44,MFP Conklin- Maines Community Center,1838.0 +45,MFP Deposit,1879.0 +46,MFP Erin,1913.0 +47,MFP Lansing,1991.0 +48,MFP Salvation Army Ithaca,1993.0 +49,MFP Campbell,2022.0 +50,MFP Boys and Girls Club,2108.0 +51,MFP Woodhull,2112.0 +52,MFP Owego VFW,2115.0 +53,MFP Tuscarora,2119.0 +54,MFP Van Etten,2137.0 +55,MFP Wayland,2165.0 +56,MFP Reach for Christ Church Freeville,2200.0 +57,MFP American Legion - Binghamton,2202.0 +58,MFP Windsor,2210.0 +59,MFP Whitney Point,2228.0 +60,MFP Redeemer Lutheran Church,2306.0 +61,MFP Lindley,2329.0 +62,MFP Rehoboth Deliverance Ministry,2359.0 +63,MFP Colesville,2368.0 +64,MFP Richford,2925.0000000000005 +65,MFP 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