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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()
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