import time import numpy as np import matplotlib.pyplot as plt from itertools import permutations import math import openjij as oj # ==================== 可調整參數區 ==================== # 問題規模設定 CITIES = 30 # 城市總數（含 depot=0），建議範圍: 8-30 RANDOM = False # True: 每次隨機矩陣；False: 固定 seed，每次執行都一樣 RANDOM_SEED = 42 # 當 RANDOM=False 時使用的固定 seed COORD_RANGE = (0.0, 10.0) # 城市座標範圍 # 演算法執行設定 CLASSIC = False # 是否執行經典暴力解（全域最佳）【警告：CITIES>10 會非常慢】 NUM_RUNS = 10 # SA / SQA 執行次數（建議 10-100） # QUBO 參數 PENALTY = 20.0 # 約束懲罰權重（一般約束） BIG_PENALTY = 9999.0 # 硬約束懲罰權重（起點約束） NUM_READS = 30 # 每次 QUBO 取樣的讀取次數（建議 10-100） # TSP 求解參數 EXACT_LIMIT = 8 # 暴力求解的城市數上限（超過則用貪婪法） # 魯棒優化參數 (H-infinity Robust QUBO) USE_ROBUST = False # True or False 是否使用魯棒QUBO（考慮干擾/故障風險） GAMMA = 0.5 # H-infinity 控制器參數（越小越保守，建議 0.3-1.0） SIGMA = 1.0 # 干擾強度參數 ALPHA = 10.0 # 風險權重係數（越大越重視安全性） # ===================================================== def generate_distance_matrix(num_cities, random=True, seed=None, coord_range=None): """ 產生 num_cities x num_cities 的對稱距離矩陣。 預設 city 0 為 depot，其餘 1...(num_cities-1) 為任務點。 random=False 時使用固定 seed，確保每次結果相同。 """ if seed is None: seed = RANDOM_SEED if coord_range is None: coord_range = COORD_RANGE if not random: np.random.seed(seed) else: # 如果你希望每次執行完全獨立，可以在這裡不要設 seed # 或用 np.random.seed(None) np.random.seed(None) low, high = coord_range # 這裡把所有城市都放在同一個 2D 平面上隨機產生座標 # 也可以改成固定 depot=(0,0)，其餘隨機，看你喜歡： coords = np.random.uniform(low, high, size=(num_cities, 2)) # 計算歐氏距離矩陣 D = np.zeros((num_cities, num_cities), dtype=float) for i in range(num_cities): for j in range(i + 1, num_cities): dist = np.linalg.norm(coords[i] - coords[j]) D[i, j] = dist D[j, i] = dist # 將距離四捨五入到小數點後兩位，易讀一點 D = np.round(D, 2) return D, coords def generate_disturbance_matrix(num_cities, seed=None): """產生對稱的干擾/故障機率矩陣 F (0~1)""" if seed is None: seed = RANDOM_SEED np.random.seed(seed) F = np.random.rand(num_cities, num_cities) # 對稱化 (假設 A到B 和 B到A 的風險一樣) F = (F + F.T) / 2 # 將對角線設為 0 (自己到自己沒有風險) np.fill_diagonal(F, 0.0) return F # ============================ # 1. KDE 函數 # ============================ def kde_1d(samples, num_points=200): if len(samples) == 0: return np.array([]), np.array([]) xs = np.linspace(min(samples), max(samples), num_points) n = len(samples) if n < 2: return xs, np.zeros_like(xs) std = np.std(samples) if std == 0: std = 1.0 h = 1.06 * std * (n ** (-1/5)) ys = [] inv_sqrt_2pi = 1.0 / math.sqrt(2 * math.pi) for x in xs: s = 0.0 for xi in samples: z = (x - xi) / h s += math.exp(-0.5 * z * z) * inv_sqrt_2pi ys.append(s / (n * h)) return xs, np.array(ys) # ============================ # 2. route diversity matrix（支援可變長度路徑） # ============================ def route_diversity_matrix(routes, N): """ routes: list of routes，每條 route 是城市序列，例如 [0, 2, 5, 1, 9] 我們只用前 N 個位置來統計（超過 N 的部分忽略） """ freq = np.zeros((N, N), dtype=float) valid_routes = 0 for route in routes: if len(route) == 0: continue valid_routes += 1 for t in range(min(len(route), N)): city = route[t] if 0 <= city < N: freq[city, t] += 1 if valid_routes > 0: freq /= valid_routes return freq # ============================ # 3. MTSP 變數編碼：x[k,i,p] → index # ============================ def idx_mtsp(k, i, p, N): """ x[k,i,p] → 1D index """ return k * (N * N) + i * N + p # ============================ # 4. 建立 2-UAV M-TSP QUBO（城市數不固定） # ============================ def build_mtsp_qubo_variable(D, penalty=None, big_penalty=None): """ - 城市: 0..N-1，其中 0 為 depot - 兩台 UAV: k = 0,1 - 每台 UAV 有 N 個 slot: p = 0..N-1 - 變數: x_{k,i,p} QUBO包含： 距離成本 + 位置約束 + 城市約束 + 起點約束 """ if penalty is None: penalty = PENALTY if big_penalty is None: big_penalty = BIG_PENALTY D = np.asarray(D) N = D.shape[0] Q = {} def addQ(u, v, w): if w == 0: return if u > v: u, v = v, u Q[(u, v)] = Q.get((u, v), 0.0) + w # ---- 距離成本 ---- for k in range(2): for p in range(N): q = (p + 1) % N for i in range(N): for j in range(N): dij = D[i, j] if dij == 0: continue u = idx_mtsp(k, i, p, N) v = idx_mtsp(k, j, q, N) addQ(u, v, dij) # ---- 位置約束：每 slot 只能一個城市 ---- for k in range(2): for p in range(N): vars_pos = [idx_mtsp(k, i, p, N) for i in range(N)] for u in vars_pos: addQ(u, u, -penalty) for a in range(N): for b in range(a+1, N): addQ(vars_pos[a], vars_pos[b], 2*penalty) # ---- 城市約束：1..N-1 每城恰好一次 ---- for i in range(1, N): vars_city = [] for k in range(2): for p in range(N): vars_city.append(idx_mtsp(k, i, p, N)) for u in vars_city: addQ(u, u, -penalty) L = len(vars_city) for a in range(L): for b in range(a+1, L): addQ(vars_city[a], vars_city[b], 2*penalty) # ---- 起點約束：每台 UAV 的 p=0 必須是 city 0 ---- for k in range(2): for i in range(1, N): addQ(idx_mtsp(k, i, 0, N), idx_mtsp(k, i, 0, N), big_penalty) addQ(idx_mtsp(k, 0, 0, N), idx_mtsp(k, 0, 0, N), -big_penalty) return Q, N # ============================ # 4b. 建立包含 H_infinity 魯棒項的 QUBO # ============================ def build_robust_qubo(D, F, gamma=None, sigma=None, alpha=None, penalty=None, big_penalty=None): """ 建立包含 H_infinity 魯棒項的 QUBO D: 距離矩陣 F: 干擾/故障機率矩陣 (0~1) gamma: H_infinity 控制器參數（越小越保守） sigma: 干擾強度參數 alpha: 用來平衡 Distance 與 Risk 的權重係數 penalty: 約束懲罰權重 big_penalty: 硬約束懲罰權重 """ if gamma is None: gamma = GAMMA if sigma is None: sigma = SIGMA if alpha is None: alpha = ALPHA if penalty is None: penalty = PENALTY if big_penalty is None: big_penalty = BIG_PENALTY N = D.shape[0] Q = {} def addQ(u, v, w): if w == 0: return if u > v: u, v = v, u Q[(u, v)] = Q.get((u, v), 0.0) + w # ========================== # 1. 目標函數 (距離 + H_infinity 風險) # ========================== for k in range(2): # 2台 UAV for p in range(N): q = (p + 1) % N for i in range(N): for j in range(N): dij = D[i, j] fij = F[i, j] if dij == 0: continue # --- H_infinity Robust Cost --- # Risk = (sigma / gamma^2) * F^2 # 當 F 接近 1 且 gamma 小時，這項會很大 risk_term = (sigma / (gamma**2)) * (fij**2) # 總權重 = 距離 + alpha * 風險 # alpha 越大，越重視安全性 total_weight = dij + (alpha * risk_term) u = idx_mtsp(k, i, p, N) v = idx_mtsp(k, j, q, N) addQ(u, v, total_weight) # ========================== # 2. 約束條件 (與原本 MTSP 相同) # ========================== # (A) 位置約束：每台 UAV 在每個時間點 p 只能在一個城市 for k in range(2): for p in range(N): vars_pos = [idx_mtsp(k, i, p, N) for i in range(N)] for u in vars_pos: addQ(u, u, -penalty) for a in range(N): for b in range(a+1, N): addQ(vars_pos[a], vars_pos[b], 2*penalty) # (B) 城市約束：每個任務城市 (1..N-1) 必須被拜訪恰好一次 for i in range(1, N): vars_city = [] for k in range(2): for p in range(N): vars_city.append(idx_mtsp(k, i, p, N)) for u in vars_city: addQ(u, u, -penalty) L = len(vars_city) for a in range(L): for b in range(a+1, L): addQ(vars_city[a], vars_city[b], 2*penalty) # (C) 起點約束：所有 UAV 時間 0 都在 depot (city 0) for k in range(2): # p=0 必須是 city 0 for i in range(1, N): u = idx_mtsp(k, i, 0, N) addQ(u, u, big_penalty) # 懲罰出現在 p=0 的非 depot 點 # 鼓勵 city 0 在 p=0 u_depot = idx_mtsp(k, 0, 0, N) addQ(u_depot, u_depot, -big_penalty) return Q, N # ============================ # 5. 解碼 slot 序列（不修剪） # ============================ def decode_slots(sample, N): """ 回傳： u1_slots, u2_slots 各自長度 N，裡面是城市 index（可能重複，也可能很多 0） """ slots = [] for k in range(2): row = [] for p in range(N): chosen = 0 # 預設當作待在 depot for i in range(N): if sample.get(idx_mtsp(k, i, p, N), 0) == 1: chosen = i break row.append(chosen) slots.append(row) return slots[0], slots[1] # ============================ # 6. 根據 slots 做 repair → 產生合法 uav1 / uav2 path # ============================ def repair_routes_from_slots(u1_slots, u2_slots, N): """ 依據 slots 傾向資訊，把城市分配給兩台 UAV， 並用暴力 TSP 在各自子集合裡找最短路徑，確保： - 每個城市 1..N-1 被恰好一台 UAV 拜訪 - 兩台 UAV 路徑皆為 0 -> ... -> 0（成本計算時處理） """ # 統計每個城市在兩台 UAV slots 中出現次數 count1 = [0]*N count2 = [0]*N for c in u1_slots: if 0 <= c < N: count1[c] += 1 for c in u2_slots: if 0 <= c < N: count2[c] += 1 # 分配城市：看誰出現次數多，平手則讓城市較少的一邊拿 assign1 = [] assign2 = [] for city in range(1, N): # city 0 = depot 不分配 if count1[city] > count2[city]: assign1.append(city) elif count2[city] > count1[city]: assign2.append(city) else: # 平手 → 給目前負載較少的 UAV if len(assign1) <= len(assign2): assign1.append(city) else: assign2.append(city) return sorted(assign1), sorted(assign2) # ============================ # 7. 單 UAV 成本 & 子集合最佳排列 # ============================ def uav_cost(path, D): if not path: return 0.0 path = [c for c in path if 0 <= c < len(D)] if len(path) == 0: return 0.0 cost = D[0, path[0]] for i in range(len(path)-1): cost += D[path[i], path[i+1]] cost += D[path[-1], 0] return float(cost) def uav_disturbance_energy(path, F, gamma=None, sigma=None): """ 計算單一 UAV 路徑的擾動能量 path: UAV 的路徑 (list of city indices) F: 干擾矩陣 公式: Risk = (sigma / gamma^2) * sum(F[i,j]^2 for all edges) """ if gamma is None: gamma = GAMMA if sigma is None: sigma = SIGMA if not path or len(path) == 0: return 0.0 path = [c for c in path if 0 <= c < len(F)] if len(path) == 0: return 0.0 risk = 0.0 # depot (0) -> first city risk += (sigma / (gamma**2)) * (F[0, path[0]]**2) # city to city for i in range(len(path)-1): risk += (sigma / (gamma**2)) * (F[path[i], path[i+1]]**2) # last city -> depot (0) risk += (sigma / (gamma**2)) * (F[path[-1], 0]**2) return float(risk) def best_order_for_cities(cities, D, exact_limit=None): """ cities: list of city index (1..N-1) exact_limit: 小於等於這個長度才用暴力，全排列；太多就改用近鄰貪婪 """ if exact_limit is None: exact_limit = EXACT_LIMIT cities = list(cities) if len(cities) <= 1: return cities, uav_cost(cities, D) # 小問題可以繼續用暴力（例如 <= 8） if len(cities) <= exact_limit: best_perm = None best_cost = float('inf') for perm in permutations(cities): c = uav_cost(list(perm), D) if c < best_cost: best_cost = c best_perm = list(perm) return best_perm, best_cost # 太多城市 → 改用最近鄰貪婪法 remaining = set(cities) path = [] current = 0 # 從 depot 出發 while remaining: # 找離 current 最近的城市 next_city = min(remaining, key=lambda c: D[current, c]) path.append(next_city) remaining.remove(next_city) current = next_city return path, uav_cost(path, D) # ============================ # 8. 利用 QUBO 取樣 + repair 得到合法解 # ============================ def sample_and_repair(sampler, Q, N, D, F=None, run_num=None, method_name=""): """ 一次取樣 + repair，即可保證得到合法 2-UAV M-TSP 解。 目標：minimize max(UAV1_cost, UAV2_cost)（minMax / makespan） F: 干擾矩陣（可選） """ result = sampler.sample_qubo(Q, num_reads=NUM_READS) sample = result.first.sample # 1) 先解出 slots u1_slots, u2_slots = decode_slots(sample, N) # 2) 依 slots 傾向分配城市給兩台 UAV assign1, assign2 = repair_routes_from_slots(u1_slots, u2_slots, N) # 3) 各自子集合內找最短路徑（仍是對各自子集合做最短路徑） u1_path, c1 = best_order_for_cities(assign1, D) u2_path, c2 = best_order_for_cities(assign2, D) # 🔁 這裡把原本的「總成本 = c1 + c2」改成「max(c1, c2)」 makespan = max(c1, c2) # 計算擾動能量（如果有干擾矩陣） disturbance_energy = 0.0 if F is not None: risk1 = uav_disturbance_energy(u1_path, F) risk2 = uav_disturbance_energy(u2_path, F) disturbance_energy = risk1 + risk2 # 總擾動能量 return u1_path, u2_path, c1, c2, makespan, disturbance_energy # ============================ # 9. Classic 2-UAV MTSP 暴力搜尋（全域最佳） # ============================ def classic_mtsp_two_uav_bruteforce(D): """ 2-UAV M-TSP 的經典暴力解： 目標改為 minimize max(cost(UAV1), cost(UAV2)) = 最短完成時間 (minMax) """ N = D.shape[0] cities = list(range(1, N)) best_makespan = float('inf') best_sum_cost = float('inf') best_u1, best_u2 = None, None best_route = None def cost_of(path): return uav_cost(path, D) # 計算總排列數 from math import factorial total_perms = factorial(len(cities)) total_combos = total_perms * len(cities) # 每個排列有 len+1 種切分 print(f"📊 暴力搜尋: {total_perms} 種排列 × {len(cities)+1} 種切分 = {total_combos:,} 種組合") count = 0 last_print_time = time.time() print_interval = 0.5 # 每 0.5 秒更新一次進度 for perm in permutations(cities): for cut in range(len(perm) + 1): count += 1 # 定期顯示進度 current_time = time.time() if current_time - last_print_time >= print_interval: progress = (count / total_combos) * 100 print(f"\r 進度: {count:,}/{total_combos:,} ({progress:.1f}%)", end="", flush=True) last_print_time = current_time u1 = list(perm[:cut]) u2 = list(perm[cut:]) c1 = cost_of(u1) c2 = cost_of(u2) makespan = max(c1, c2) total_sum = c1 + c2 if (makespan < best_makespan) or \ (math.isclose(makespan, best_makespan) and total_sum < best_sum_cost): best_makespan = makespan best_sum_cost = total_sum best_u1 = u1 best_u2 = u2 best_route = [0] + list(perm) print(f"\r 進度: {total_combos:,}/{total_combos:,} (100.0%) ✓") return best_u1, best_u2, best_makespan, best_route # ============================ # 10. 共用：計算兩 UAV 總成本 # ============================ def compute_two_uav_cost(uav1_path, uav2_path, D): c1 = uav_cost(uav1_path, D) c2 = uav_cost(uav2_path, D) return c1 + c2, c1, c2 # ============================ # 11. SA & SQA：每 run 使用 sample_and_repair # ============================ def run_mtsp_sa_sqa(Q, N, D, F=None, NUM_RUNS=10): """ 使用 SA / SQA 解 QUBO，每次取一組解並經過 repair。 評估指標使用 makespan = max(UAV1_cost, UAV2_cost)（minMax）。 F: 干擾矩陣（可選） """ sa_makespans = [] sa_routes = [] sa_u1_list = [] sa_u2_list = [] sa_uav_costs = [] sa_disturbances = [] # 擾動能量 sqa_makespans = [] sqa_routes = [] sqa_u1_list = [] sqa_u2_list = [] sqa_uav_costs = [] sqa_disturbances = [] # 擾動能量 sa = oj.SASampler() sqa = oj.SQASampler() # ========== SA 計時開始 ========== print("\n🔥 Running SA (with repair, always feasible, minMax objective)...") print(f"📊 總共 {NUM_RUNS} 次運行") sa_start_time = time.time() for r in range(NUM_RUNS): u1, u2, c1, c2, makespan, dist_energy = sample_and_repair(sa, Q, N, D, F, run_num=r+1, method_name="SA") full_route = [0] + u1 + u2 if F is not None: print(f" 結果: UAV1={u1}, UAV2={u2}, " f"UAV1_cost={c1:.2f}, UAV2_cost={c2:.2f}, " f"Makespan={makespan:.2f}, Disturbance={dist_energy:.4f}") else: print(f" 結果: UAV1={u1}, UAV2={u2}, " f"UAV1_cost={c1:.2f}, UAV2_cost={c2:.2f}, " f"Makespan={makespan:.2f}") sa_makespans.append(makespan) sa_routes.append(full_route) sa_u1_list.append(u1) sa_u2_list.append(u2) sa_uav_costs.append((c1, c2)) sa_disturbances.append(dist_energy) sa_elapsed = time.time() - sa_start_time print(f"⏱️ SA Total Time: {sa_elapsed:.3f} seconds ({sa_elapsed/NUM_RUNS:.3f} sec/run)") # ========== SQA 計時開始 ========== print("\n🔥 Running SQA (with repair, always feasible, minMax objective)...") print(f"📊 總共 {NUM_RUNS} 次運行") sqa_start_time = time.time() for r in range(NUM_RUNS): u1, u2, c1, c2, makespan, dist_energy = sample_and_repair(sqa, Q, N, D, F, run_num=r+1, method_name="SQA") full_route = [0] + u1 + u2 if F is not None: print(f" 結果: UAV1={u1}, UAV2={u2}, " f"UAV1_cost={c1:.2f}, UAV2_cost={c2:.2f}, " f"Makespan={makespan:.2f}, Disturbance={dist_energy:.4f}") else: print(f" 結果: UAV1={u1}, UAV2={u2}, " f"UAV1_cost={c1:.2f}, UAV2_cost={c2:.2f}, " f"Makespan={makespan:.2f}") sqa_makespans.append(makespan) sqa_routes.append(full_route) sqa_u1_list.append(u1) sqa_u2_list.append(u2) sqa_uav_costs.append((c1, c2)) sqa_disturbances.append(dist_energy) sqa_elapsed = time.time() - sqa_start_time print(f"⏱️ SQA Total Time: {sqa_elapsed:.3f} seconds ({sqa_elapsed/NUM_RUNS:.3f} sec/run)") sa_results = (sa_makespans, sa_routes, sa_u1_list, sa_u2_list, sa_uav_costs, sa_disturbances) sqa_results = (sqa_makespans, sqa_routes, sqa_u1_list, sqa_u2_list, sqa_uav_costs, sqa_disturbances) return sa_results, sqa_results, sa_elapsed, sqa_elapsed # ============================ # 12. 綜合分析圖表（你指定的版本） # ============================ def create_comprehensive_charts(sa_results, sqa_results, classic_results, D, N): """創建綜合分析圖表（目標：minMax makespan）""" fig = plt.figure(figsize=(24, 12)) # 解包結果（第一個 list 現在代表 makespan，最後一個是擾動能量） sa_costs, sa_routes, sa_uav1, sa_uav2, sa_uav_costs, sa_disturbances = sa_results sqa_costs, sqa_routes, sqa_uav1, sqa_uav2, sqa_uav_costs, sqa_disturbances = sqa_results classic_uav1, classic_uav2, classic_cost, classic_route = classic_results # --------------------------------------------------------- # 1. MTSP 完成時間 (makespan) 分布比較 (左上) # --------------------------------------------------------- ax1 = plt.subplot(2, 4, 1) bins = range(int(min(sa_costs + sqa_costs)) - 1, int(max(sa_costs + sqa_costs)) + 2) ax1.hist(sa_costs, bins=bins, alpha=0.6, label="SA Makespan", density=True, color='lightblue') ax1.hist(sqa_costs, bins=bins, alpha=0.6, label="SQA Makespan", density=True, color='lightcoral') # 添加KDE if len(sa_costs) > 1: xs_sa, ys_sa = kde_1d(sa_costs) ax1.plot(xs_sa, ys_sa, label="SA KDE", color='blue', linewidth=2) if len(sqa_costs) > 1: xs_sqa, ys_sqa = kde_1d(sqa_costs) ax1.plot(xs_sqa, ys_sqa, label="SQA KDE", color='red', linewidth=2) ax1.axvline(x=classic_cost, color='green', linestyle='--', label=f'Classic minMax: {classic_cost:.2f}', linewidth=2) ax1.set_title("System Makespan Distribution (max route length)") ax1.set_xlabel("Makespan (max cost of UAV1, UAV2)") ax1.set_ylabel("Density") ax1.legend() ax1.grid(True, alpha=0.3) # --------------------------------------------------------- # 2. 單一 UAV 成本分布比較 (右上) # --------------------------------------------------------- ax2 = plt.subplot(2, 4, 2) sa_single_costs = [c for costs in sa_uav_costs for c in costs] sqa_single_costs = [c for costs in sqa_uav_costs for c in costs] c1_classic = uav_cost(classic_uav1, D) c2_classic = uav_cost(classic_uav2, D) all_single = sa_single_costs + sqa_single_costs uav_bins = range(int(min(all_single)) - 1, int(max(all_single)) + 2) ax2.hist(sa_single_costs, bins=uav_bins, alpha=0.6, label="SA Single UAV", density=True, color='skyblue') ax2.hist(sqa_single_costs, bins=uav_bins, alpha=0.6, label="SQA Single UAV", density=True, color='salmon') ax2.axvline(x=c1_classic, color='darkgreen', linestyle=':', label='Classic UAV1') ax2.axvline(x=c2_classic, color='limegreen', linestyle=':', label='Classic UAV2') ax2.set_title("Route Length Distribution per UAV") ax2.set_xlabel("Cost per UAV") ax2.set_ylabel("Density") ax2.legend() ax2.grid(True, alpha=0.3) # --------------------------------------------------------- # 3. 箱型圖比較 (中上)：系統 makespan vs 單機成本 # --------------------------------------------------------- ax3 = plt.subplot(2, 3, 3) box_data = [sa_costs, sqa_costs, sa_single_costs, sqa_single_costs] bp = ax3.boxplot( box_data, labels=["SA\nMakespan", "SQA\nMakespan", "SA\nSingle", "SQA\nSingle"], patch_artist=True, showmeans=True ) colors = ['lightblue', 'lightcoral', 'skyblue', 'salmon'] for patch, color in zip(bp['boxes'], colors): patch.set_facecolor(color) ax3.set_title("Makespan vs Individual UAV Cost") ax3.set_ylabel("Cost") ax3.grid(True, alpha=0.3) # --------------------------------------------------------- # 4. 總能量分布比較 (Total Energy - Distance Cost) # --------------------------------------------------------- ax4 = plt.subplot(2, 4, 4) # 繪製總能量直方圖 all_energies = sa_costs + sqa_costs bins_energy = range(int(min(all_energies)) - 1, int(max(all_energies)) + 2) ax4.hist(sa_costs, bins=bins_energy, alpha=0.6, label="SA Total Energy", density=True, color='skyblue') ax4.hist(sqa_costs, bins=bins_energy, alpha=0.6, label="SQA Total Energy", density=True, color='salmon') # 添加 KDE if len(sa_costs) > 1: xs_sa, ys_sa = kde_1d(sa_costs) ax4.plot(xs_sa, ys_sa, color='blue', linewidth=2, alpha=0.8) if len(sqa_costs) > 1: xs_sqa, ys_sqa = kde_1d(sqa_costs) ax4.plot(xs_sqa, ys_sqa, color='red', linewidth=2, alpha=0.8) ax4.set_xlabel("Total Energy (Distance Cost)") ax4.set_ylabel("Density") ax4.set_title(f"Total Energy Distribution\nSA: {np.mean(sa_costs):.2f}±{np.std(sa_costs):.2f} | SQA: {np.mean(sqa_costs):.2f}±{np.std(sqa_costs):.2f}") ax4.legend() ax4.grid(alpha=0.3) # --------------------------------------------------------- # 5. SA 路徑多樣性分析 # --------------------------------------------------------- ax5 = plt.subplot(2, 4, 5) sa_mat = route_diversity_matrix(sa_routes, N) im1 = ax5.imshow(sa_mat, aspect='auto', origin='lower', cmap='viridis') ax5.set_title("SA Route Diversity") ax5.set_xlabel("Position") ax5.set_ylabel("City") plt.colorbar(im1, ax=ax5, shrink=0.8) # --------------------------------------------------------- # 6. SQA 路徑多樣性分析 # --------------------------------------------------------- ax6 = plt.subplot(2, 4, 6) sqa_mat = route_diversity_matrix(sqa_routes, N) im2 = ax6.imshow(sqa_mat, aspect='auto', origin='lower', cmap='viridis') ax6.set_title("SQA Route Diversity") ax6.set_xlabel("Position") ax6.set_ylabel("City") plt.colorbar(im2, ax=ax6, shrink=0.8) # --------------------------------------------------------- # 7. 擾動能量分布比較 (Disturbance Energy Distribution) # --------------------------------------------------------- ax7 = plt.subplot(2, 4, 7) # 繪製擾動能量直方圖 all_disturbances = sa_disturbances + sqa_disturbances if len(all_disturbances) > 0 and max(all_disturbances) > 0: bins_disturb = np.linspace(min(all_disturbances), max(all_disturbances), 20) ax7.hist(sa_disturbances, bins=bins_disturb, alpha=0.6, label="SA Disturbance", density=True, color='lightgreen') ax7.hist(sqa_disturbances, bins=bins_disturb, alpha=0.6, label="SQA Disturbance", density=True, color='lightpink') # 添加 KDE if len(sa_disturbances) > 1 and np.std(sa_disturbances) > 0: xs_sa, ys_sa = kde_1d(sa_disturbances) ax7.plot(xs_sa, ys_sa, color='green', linewidth=2, alpha=0.8) if len(sqa_disturbances) > 1 and np.std(sqa_disturbances) > 0: xs_sqa, ys_sqa = kde_1d(sqa_disturbances) ax7.plot(xs_sqa, ys_sqa, color='purple', linewidth=2, alpha=0.8) ax7.set_title(f"Disturbance Energy Distribution\\nSA: {np.mean(sa_disturbances):.4f}±{np.std(sa_disturbances):.4f} | SQA: {np.mean(sqa_disturbances):.4f}±{np.std(sqa_disturbances):.4f}") else: ax7.text(0.5, 0.5, "No disturbance data\\n(USE_ROBUST=False)", ha='center', va='center', transform=ax7.transAxes, fontsize=12) ax7.set_title("Disturbance Energy Distribution") ax7.set_xlabel("Disturbance Energy") ax7.set_ylabel("Density") ax7.legend() ax7.grid(alpha=0.3) # --------------------------------------------------------- # 8. 最佳路徑可視化 (Best Route Visualization) # --------------------------------------------------------- ax8 = plt.subplot(2, 4, 8) best_sa_idx = sa_costs.index(min(sa_costs)) best_sqa_idx = sqa_costs.index(min(sqa_costs)) best_sa_u1 = sa_uav1[best_sa_idx] best_sa_u2 = sa_uav2[best_sa_idx] best_sqa_u1 = sqa_uav1[best_sqa_idx] best_sqa_u2 = sqa_uav2[best_sqa_idx] if min(sa_costs) <= min(sqa_costs): u1 = best_sa_u1 u2 = best_sa_u2 route_name = "SA" route_cost = min(sa_costs) else: u1 = best_sqa_u1 u2 = best_sqa_u2 route_name = "SQA" route_cost = min(sqa_costs) angles = np.linspace(0, 2*np.pi, N, endpoint=False) x_pos = np.cos(angles) y_pos = np.sin(angles) ax8.scatter(x_pos, y_pos, s=200, c='red', zorder=5) for i, (x, y) in enumerate(zip(x_pos, y_pos)): ax8.annotate(str(i), (x, y), ha='center', va='center', fontsize=10, fontweight='bold', color='white', zorder=6) if len(u1) > 0: pts = [0] + u1 + [0] xs = [x_pos[c] for c in pts] ys = [y_pos[c] for c in pts] ax8.plot(xs, ys, '-o', color='blue', linewidth=2, alpha=0.8, label=f'UAV1 ({len(u1)})') if len(u2) > 0: pts = [0] + u2 + [0] xs = [x_pos[c] for c in pts] ys = [y_pos[c] for c in pts] ax8.plot(xs, ys, '-o', color='orange', linewidth=2, alpha=0.8, label=f'UAV2 ({len(u2)})') ax8.set_title(f"Best {route_name} MTSP Solution (minMax) Makespan: {route_cost:.2f}") ax8.set_xlim(-1.3, 1.3) ax8.set_ylim(-1.3, 1.3) ax8.set_aspect('equal') ax8.axis('off') ax8.legend(loc='upper right') plt.tight_layout() plt.savefig("mtsp_two_uav_comprehensive_analysis.png", dpi=300, bbox_inches='tight') print(f"\n📊 綜合分析圖表已保存: mtsp_two_uav_comprehensive_analysis.png") plt.show() # ============================ # 13. main：整合執行 # ============================ if __name__ == "__main__": # 距離矩陣：10 城市 # 讓原本程式沿用 N、D 命名 N = CITIES D, city_coords = generate_distance_matrix(CITIES, random=RANDOM) print(f"產生 {CITIES} 個城市的距離矩陣，RANDOM={RANDOM}") print("城市座標 (含 depot=0)：") for idx, (x, y) in enumerate(city_coords): print(f"City {idx}: ({x:.2f}, {y:.2f})") ''' D = np.array([ [0.00, 3.16, 4.47, 7.81, 8.54, 7.28, 6.08, 8.60, 5.83, 9.85], [3.16, 0.00, 3.16, 5.00, 7.00, 4.12, 5.39, 6.32, 2.83, 8.06], [4.47, 3.16, 0.00, 4.12, 4.12, 5.39, 2.24, 4.24, 3.16, 5.39], [7.81, 5.00, 4.12, 0.00, 4.24, 3.16, 5.10, 2.24, 2.24, 4.47], [8.54, 7.00, 4.12, 4.24, 0.00, 7.21, 2.83, 2.24, 5.39, 1.41], [7.28, 4.12, 5.39, 3.16, 7.21, 0.00, 7.21, 5.39, 2.24, 7.62], [6.08, 5.39, 2.24, 5.10, 2.83, 7.21, 0.00, 4.12, 5.00, 4.24], [8.60, 6.32, 4.24, 2.24, 2.24, 5.39, 4.12, 0.00, 4.00, 2.24], [5.83, 2.83, 3.16, 2.24, 5.39, 2.24, 5.00, 4.00, 0.00, 6.08], [9.85, 8.06, 5.39, 4.47, 1.41, 7.62, 4.24, 2.24, 6.08, 0.00], ]) D = np.array([ [0. , 7.56, 2.09, 6.49, 7.75, 4.1, 1.24, 7.15, 2.81, 4.79], [7.56, 0., 9.02, 5.63, 2.44, 6.15, 8.37, 2.37, 8.94, 7.51], [2.09, 9.02, 0., 8.57, 8.71, 6.19, 0.85, 8.97, 4.27, 6.78], [6.49, 5.63, 8.57, 0., 7.7, 2.48, 7.72, 3.39, 5.82, 2.9 ], [7.75, 2.44, 8.71, 7.7, 0., 7.6, 8.23, 4.71, 9.76, 9.05], [4.1, 6.15, 6.19, 2.48, 7.6, 0., 5.34, 4.52, 3.45, 1.45], [1.24, 8.37, 0.85, 7.72, 8.23, 5.34, 0., 8.2, 3.64, 5.98], [7.15, 2.37, 8.97, 3.39, 4.71, 4.52, 8.2, 0., 7.78, 5.7 ], [2.81, 8.94, 4.27, 5.82, 9.76, 3.45, 3.64, 7.78, 0., 3.17], [4.79, 7.51, 6.78, 2.9, 9.05, 1.45, 5.98, 5.7, 3.17, 0. ] ]) ''' N = D.shape[0] print("🚀 2-UAV M-TSP (Quantum + Repair vs Classic) 開始運行...\n") print(f"Distance Matrix ({N}x{N}):") print(D) # 建立 QUBO (根據 USE_ROBUST 決定使用哪種) F = None # 初始化干擾矩陣 if USE_ROBUST: print("\n🛡️ 使用魯棒 QUBO (H-infinity Robust)") print(f" Gamma={GAMMA}, Sigma={SIGMA}, Alpha={ALPHA}") F = generate_disturbance_matrix(N) print(f"\n干擾矩陣 F ({N}x{N}):") print(F) Q, _ = build_robust_qubo(D, F) else: print("\n📊 使用標準 QUBO (不考慮風險)") F = generate_disturbance_matrix(N) # 即使不用魯棒QUBO，也生成F用於統計 Q, _ = build_mtsp_qubo_variable(D) # SA / SQA，每 run 一定是合法解 sa_results, sqa_results, sa_time, sqa_time = run_mtsp_sa_sqa(Q, N, D, F, NUM_RUNS) # ========== Classic 計時 ========== if CLASSIC == True: print("\n🎯 Running Classic 2-UAV MTSP (Bruteforce ALL solutions)...") classic_start_time = time.time() classic_uav1, classic_uav2, classic_total_cost, classic_route = classic_mtsp_two_uav_bruteforce(D) classic_elapsed = time.time() - classic_start_time print(f"Classic UAV1={classic_uav1}, UAV2={classic_uav2}, Cost={classic_total_cost}") print(f"Classic merged route (0 + perm): {classic_route}") print(f"⏱️ Classic Total Time: {classic_elapsed:.3f} seconds") else: classic_total_cost = float('inf') classic_elapsed = 0.0 classic_uav1, classic_uav2, classic_route = [], [], [] # Summary sa_costs, _, _, _, _, sa_disturbances = sa_results sqa_costs, _, _, _, _, sqa_disturbances = sqa_results print("\n📊 Result Summary:") print(f"SA best minMax (makespan) = {min(sa_costs):.2f}, mean = {np.mean(sa_costs):.2f}") print(f"SQA best minMax (makespan) = {min(sqa_costs):.2f}, mean = {np.mean(sqa_costs):.2f}") print(f"Classic global minMax optimum = {classic_total_cost:.2f}") # 擾動能量統計 if F is not None: print("\n⚡ Disturbance Energy Summary:") print(f"SA min = {min(sa_disturbances):.4f}, max = {max(sa_disturbances):.4f}, mean = {np.mean(sa_disturbances):.4f}") print(f"SQA min = {min(sqa_disturbances):.4f}, max = {max(sqa_disturbances):.4f}, mean = {np.mean(sqa_disturbances):.4f}") # ========== 時間比較摘要 ========== print("\n⏱️ Execution Time Comparison:") print(f" SA : {sa_time:.3f} sec (avg {sa_time/NUM_RUNS:.3f} sec/run)") print(f" SQA : {sqa_time:.3f} sec (avg {sqa_time/NUM_RUNS:.3f} sec/run)") print(f" Classic: {classic_elapsed:.3f} sec") print(f" SA speedup vs Classic: {classic_elapsed/sa_time:.2f}x") print(f" SQA speedup vs Classic: {classic_elapsed/sqa_time:.2f}x") # 畫圖 classic_results = (classic_uav1, classic_uav2, classic_total_cost, classic_route) print("\n🎨 Creating comprehensive analysis charts...") create_comprehensive_charts(sa_results, sqa_results, classic_results, D, N) print("\n🏁 Done.")