import numpy as np def cargo_load_planning_heuristic(weights, cargo_names, cargo_types_dict, positions, cg_impact, cg_impact_2u, cg_impact_4u, max_positions, max_iterations=1000): """ 使用两阶段启发式算法计算货物装载方案，最小化重心的变化量。 参数: weights (list): 每个货物的质量列表。 cargo_names (list): 每个货物的名称。 cargo_types_dict (dict): 货物名称和占用的货位数量。 positions (list): 可用的货位编号。 cg_impact (list): 每个位置每kg货物对重心index的影响系数。 cg_impact_2u (list): 两个位置组合的重心影响系数。 cg_impact_4u (list): 四个位置组合的重心影响系数。 max_positions (int): 总货位的数量。 max_iterations (int): 优化阶段的最大迭代次数。 返回: solution (np.array): 最优装载方案矩阵。 total_cg_change (float): 最优方案的重心变化量。 """ # 将货物类型映射为对应的占用单位数 cargo_types = [cargo_types_dict[name] for name in cargo_names] num_cargos = len(weights) # 货物数量 num_positions = len(positions) # 可用货位数量 # 初始化装载方案矩阵 solution = np.zeros((num_cargos, num_positions), dtype=int) # 标记已占用的位置 occupied = np.zeros(num_positions, dtype=int) # 按照货物类型（占用单位数降序）和重量降序排序货物 sorted_indices = sorted(range(num_cargos), key=lambda i: (-cargo_types[i], -weights[i])) # 阶段1：初始装载方案生成 for i in sorted_indices: cargo_type = cargo_types[i] feasible_positions = [] # 根据货物类型确定可行的起始位置 if cargo_type == 1: possible_starts = range(0, num_positions) elif cargo_type == 2: possible_starts = range(0, num_positions - 1, 2) elif cargo_type == 4: possible_starts = range(0, num_positions - 3, 4) else: possible_starts = [] for start in possible_starts: # 检查是否超出边界 if start + cargo_type > num_positions: continue # 检查是否与已占用位置重叠 if np.any(occupied[start:start + cargo_type]): continue # 计算重心变化量 if cargo_type == 1: cg = abs(weights[i] * cg_impact[start]) elif cargo_type == 2: cg = abs(weights[i] * cg_impact_2u[start // 2]) elif cargo_type == 4: cg = abs(weights[i] * cg_impact_4u[start // 4]) feasible_positions.append((start, cg)) # 如果有可行位置，选择使重心变化最小的位置 if feasible_positions: best_start, best_cg = min(feasible_positions, key=lambda x: x[1]) solution[i, best_start:best_start + cargo_type] = 1 occupied[best_start:best_start + cargo_type] = 1 else: # 如果没有可行位置，则尝试分配到任何未占用的位置（可能违反约束） for start in range(0, num_positions - cargo_type + 1): if np.all(occupied[start:start + cargo_type] == 0): solution[i, start:start + cargo_type] = 1 occupied[start:start + cargo_type] = 1 break # 计算初始重心变化量 total_cg_change = 0.0 for i in range(num_cargos): cargo_type = cargo_types[i] assigned_positions = np.where(solution[i] == 1)[0] if len(assigned_positions) == 0: continue if cargo_type == 1: total_cg_change += abs(weights[i] * cg_impact[assigned_positions[0]]) elif cargo_type == 2: total_cg_change += abs(weights[i] * cg_impact_2u[assigned_positions[0] // 2]) elif cargo_type == 4: total_cg_change += abs(weights[i] * cg_impact_4u[assigned_positions[0] // 4]) # 阶段2：装载方案优化 for _ in range(max_iterations): improved = False for i in range(num_cargos): cargo_type = cargo_types[i] current_positions = np.where(solution[i] == 1)[0] if len(current_positions) == 0: continue current_start = current_positions[0] # 根据货物类型确定可行的起始位置 if cargo_type == 1: possible_starts = range(0, num_positions) elif cargo_type == 2: possible_starts = range(0, num_positions - 1, 2) elif cargo_type == 4: possible_starts = range(0, num_positions - 3, 4) else: possible_starts = [] best_start = current_start best_cg = total_cg_change for start in possible_starts: if start == current_start: continue # 检查是否超出边界 if start + cargo_type > num_positions: continue # 检查是否与已占用位置重叠 if np.any(occupied[start:start + cargo_type]): continue # 计算重心变化量 if cargo_type == 1: new_cg = abs(weights[i] * cg_impact[start]) elif cargo_type == 2: new_cg = abs(weights[i] * cg_impact_2u[start // 2]) elif cargo_type == 4: new_cg = abs(weights[i] * cg_impact_4u[start // 4]) else: new_cg = 0 # 计算新的总重心变化量 temp_cg_change = total_cg_change - ( weights[i] * cg_impact[current_start] if cargo_type == 1 else weights[i] * cg_impact_2u[current_start // 2] if cargo_type == 2 else weights[i] * cg_impact_4u[current_start // 4] if cargo_type == 4 else 0 ) + new_cg # 如果新的重心变化量更小，进行更新 if temp_cg_change < best_cg: best_cg = temp_cg_change best_start = start # 如果找到了更好的位置，进行更新 if best_start != current_start: # 释放当前占用的位置 occupied[current_start:current_start + cargo_type] = 0 solution[i, current_start:current_start + cargo_type] = 0 # 分配到新的位置 solution[i, best_start:best_start + cargo_type] = 1 occupied[best_start:best_start + cargo_type] = 1 # 更新总重心变化量 total_cg_change = best_cg improved = True if not improved: break # 如果在一个完整的迭代中没有改进，结束优化 return solution, total_cg_change # 示例输入和调用 def main(): weights = [500, 800, 1200, 300, 700, 1000, 600, 900] # 每个货物的质量 cargo_names = ['LD3', 'LD3', 'PLA', 'LD3', 'P6P', 'PLA', 'LD3', 'BULK'] # 货物名称 cargo_types_dict = {"LD3": 1, "PLA": 2, "P6P": 4, "BULK": 1} # 货物占位关系 positions = list(range(44)) # 44个货位编号 cg_impact = [i * 0.1 for i in range(44)] # 每kg货物对重心index的影响系数 (单个位置) cg_impact_2u = [i * 0.08 for i in range(22)] # 两个位置组合的影响系数 cg_impact_4u = [i * 0.05 for i in range(11)] # 四个位置组合的影响系数 max_positions = 44 # 总货位数量 solution, cg_change = cargo_load_planning_heuristic( weights, cargo_names, cargo_types_dict, positions, cg_impact, cg_impact_2u, cg_impact_4u, max_positions, max_iterations=1000 ) if solution is not None and solution.size > 0: print("成功找到最优装载方案！") print("装载方案矩阵:") print(solution) print(f"重心的变化量: {cg_change:.2f}") # 输出实际分布 for i in range(len(weights)): assigned_positions = [] for j in range(len(positions)): if solution[i, j] > 0.5: # 判断位置是否被分配 assigned_positions.append(j) print(f"货物 {cargo_names[i]} (占 {cargo_types_dict[cargo_names[i]]} 单位): 放置位置 -> {assigned_positions}") else: print("未找到可行的装载方案。") if __name__ == "__main__": main()