code/optimization baselines/algorithm/IOM.py

import numpy as np
from scipy.optimize import linprog


def cargo_load_planning_linear2(weights, cargo_names, cargo_types_dict, positions, cg_impact, cg_impact_2u, cg_impact_4u,
                        max_positions):
    """
    使用整数线性规划方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。

    返回:
        result.x: 最优装载方案矩阵。
    """
    # 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

    # 决策变量：xij (是否将货物i放置在位置j)
    c = []  # 目标函数系数列表
    for i in range(num_cargos):
        for j in range(num_positions):
            if cargo_types[i] == 1:
                c.append(abs(weights[i] * cg_impact[j]))
            elif cargo_types[i] == 2 and j % 2 == 0 and j < len(cg_impact_2u) * 2:
                c.append(abs(weights[i] * cg_impact_2u[j // 2]))
            elif cargo_types[i] == 4 and j % 4 == 0 and j < len(cg_impact_4u) * 4:
                c.append(abs(weights[i] * cg_impact_4u[j // 4]))
            else:
                c.append(0)  # 不适合的索引默认影响为0

    # 决策变量约束：xij只能是0或1 (整型约束由 linprog 近似处理)
    bounds = [(0, 1) for _ in range(num_cargos * num_positions)]

    # 约束1：每个货物只能装载到一个位置
    A_eq = []
    b_eq = []
    for i in range(num_cargos):
        constraint = [0] * (num_cargos * num_positions)
        for j in range(num_positions):
            constraint[i * num_positions + j] = 1
        A_eq.append(constraint)
        b_eq.append(1)

    # 约束2：每个位置只能装载一个货物
    A_ub = []
    b_ub = []
    for j in range(num_positions):  # 遍历所有位置
        constraint = [0] * (num_cargos * num_positions)
        for i in range(num_cargos):  # 遍历所有货物
            constraint[i * num_positions + j] = 1
        A_ub.append(constraint)
        b_ub.append(1)  # 每个位置最多只能分配一个货物

    # 约束3：占用多个位置的货物
    for i, cargo_type in enumerate(cargo_types):
        if cargo_type == 2:  # 两个连续位置组合
            for j in range(0, num_positions - 1, 2):
                constraint = [0] * (num_cargos * num_positions)
                constraint[i * num_positions + j] = 1
                constraint[i * num_positions + j + 1] = 1
                A_ub.append(constraint)
                b_ub.append(1)
        elif cargo_type == 4:  # 上两个、下两个组合
            for j in range(0, num_positions - 3, 4):
                constraint = [0] * (num_cargos * num_positions)
                constraint[i * num_positions + j] = 1
                constraint[i * num_positions + j + 1] = 1
                constraint[i * num_positions + j + 2] = 1
                constraint[i * num_positions + j + 3] = 1
                A_ub.append(constraint)
                b_ub.append(1)

    # 转换为numpy数组
    A_eq = np.array(A_eq)
    b_eq = np.array(b_eq)
    A_ub = np.array(A_ub)
    b_ub = np.array(b_ub)
    c = np.array(c)

    # 求解线性规划问题
    result = linprog(c, A_ub=A_ub, b_ub=b_ub, A_eq=A_eq, b_eq=b_eq, bounds=bounds, method='highs-ds')

    if result.success:
        # print("成功找到最优装载方案！")
        solution = result.x.reshape((num_cargos, num_positions))
        # print("装载方案矩阵:")
        # print(solution)

        # 计算最终重心变化
        cg_change = 0
        for i in range(num_cargos):
            for j in range(num_positions):
                if cargo_types[i] == 1:
                    cg_change += solution[i, j] * weights[i] * cg_impact[j]
                elif cargo_types[i] == 2 and j % 2 == 0 and j < len(cg_impact_2u) * 2:
                    cg_change += solution[i, j] * weights[i] * cg_impact_2u[j // 2]
                elif cargo_types[i] == 4 and j % 4 == 0 and j < len(cg_impact_4u) * 4:
                    cg_change += solution[i, j] * weights[i] * cg_impact_4u[j // 4]
        # print(f"重心的变化量: {cg_change:.2f}")
        return result,cg_change
        # 输出实际分布
        # print("货物实际分布:")
        # for i in range(num_cargos):
        #     assigned_positions = []
        #     for j in range(num_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[i]} 单位): 放置位置 -> {assigned_positions}")
    else:
        result = []
        return result,-1000000




# 示例输入
# 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
#
#     result = cargo_load_planning(weights, cargo_names, cargo_types_dict, positions, cg_impact, cg_impact_2u,
#                                  cg_impact_4u, max_positions)
#
#
# if __name__ == "__main__":
#     main()