210 lines
10 KiB
Python
210 lines
10 KiB
Python
from ortools.linear_solver import pywraplp
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def solve_program(preference_mat:list, depart_mat:list, want_num_array:list, is_new_array:list,
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num_min=None, num_max=None,
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num_tech_old_min=None, num_tech_old_max=None,
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num_old_min=None, num_old_max=None,
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num_new_min=None, num_new_max=None,
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weights=[1.0, 1.0, 1.0, 0.5, 0.5]
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):
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is_old_array = [not is_new for is_new in is_new_array]
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is_tech_array = [depart_mat[i][0] == 1 or depart_mat[i][1] == 1 for i in range(len(depart_mat))]
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is_hr_array = [depart_mat[i][2] == 1 for i in range(len(depart_mat))]
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# 使用 SCIP 求解器求解组合优化问题
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solver = pywraplp.Solver.CreateSolver("SCIP")
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if not solver:
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return
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N = len(preference_mat) # 学生人数
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M = len(preference_mat[0]) # 班次数
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avg_num = sum(want_num_array) / M
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print(f"平均人数：{avg_num}")
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# 各个目标的期望值/归一化系数
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m = [2.5, 3, 4, 1, 8] # [班次人数偏差, 技术部老人, 技术部小朋友, 人资部小朋友, 部门均衡]
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# 创建决策变量：variables[i][j] 表示第 i 个学生是否选择第 j 个班次
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variables = [[solver.IntVar(0.0, 1.0, f"choice_{i}_{j}")
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for j in range(M)] for i in range(N)]
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# 创建辅助变量用于优化目标1（均衡班次人数）
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aux_vars_x1 = [solver.NumVar(0.0, solver.infinity(), f"aux_x1_{j}")
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for j in range(M)]
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# 创建辅助变量用于优化目标2（每班次技术部老人数量缺口）
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aux_vars_x2 = [solver.NumVar(0.0, solver.infinity(), f"aux_x2_{j}")
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for j in range(M)]
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# 创建辅助变量用于优化目标3（每班次技术部小朋友数量缺口）
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aux_vars_x3 = [solver.NumVar(0.0, solver.infinity(), f"aux_x3_{j}")
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for j in range(M)]
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# 创建辅助变量用于优化目标4（每班次人资部小朋友数量缺口）
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aux_vars_x4 = [solver.NumVar(0.0, solver.infinity(), f"aux_x4_{j}")
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for j in range(M)]
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# 创建辅助变量用于优化目标5（均衡各部门人数）
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# 如果提供了部门信息，则创建相应的辅助变量
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aux_vars_x5 = []
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num_departments = 5 # 电脑部、电器部、人资部、财外部、文宣部
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# 为每个班次的每个部门创建辅助变量
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aux_vars_x5 = [[solver.NumVar(0.0, solver.infinity(), f"aux_x5_{j}_{k}")
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for k in range(num_departments)] for j in range(M)]
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print("Number of variables =", solver.NumVariables())
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# 约束：每个同学意愿一定要满足
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for i in range(N):
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for j in range(M):
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solver.Add(variables[i][j] <= preference_mat[i][j])
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# 约束：辅助变量 X1 用于计算与平均人数的偏差（绝对值）
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for j in range(M):
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actual_num = sum(variables[i][j] for i in range(N))
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solver.Add(aux_vars_x1[j] >= actual_num - avg_num)
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solver.Add(aux_vars_x1[j] >= avg_num - actual_num)
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# 约束：辅助变量 X2 用于计算每班次技术部老人数量超出期望值的部分
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# 辅助变量表示超出期望值(期望每班有m2个技术部老人,超过即计入)
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# 目标是让尽可能多的班次达到但不超过这个期望值
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tech_old_target = m[1] # 使用归一化系数作为期望值
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for j in range(M):
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tech_old_count = sum(variables[i][j] * is_old_array[i] * is_tech_array[i] for i in range(N))
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# 辅助变量捕获超出部分和不足部分
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solver.Add(aux_vars_x2[j] >= tech_old_count - tech_old_target)
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solver.Add(aux_vars_x2[j] >= tech_old_target - tech_old_count)
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# 约束：辅助变量 X3 用于计算每班次技术部小朋友数量超出期望值的部分
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tech_new_target = m[2] # 使用归一化系数作为期望值
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for j in range(M):
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tech_new_count = sum(variables[i][j] * is_new_array[i] * is_tech_array[i] for i in range(N))
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solver.Add(aux_vars_x3[j] >= tech_new_count - tech_new_target)
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solver.Add(aux_vars_x3[j] >= tech_new_target - tech_new_count)
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# 约束：辅助变量 X4 用于计算每班次人资部小朋友数量超出期望值的部分
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hr_new_target = m[3] # 使用归一化系数作为期望值
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for j in range(M):
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hr_new_count = sum(variables[i][j] * is_new_array[i] * is_hr_array[i] for i in range(N))
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solver.Add(aux_vars_x4[j] >= hr_new_count - hr_new_target)
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solver.Add(aux_vars_x4[j] >= hr_new_target - hr_new_count)
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# 约束：辅助变量 X5 用于计算各部门人数与平均值的偏差（绝对值）
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if aux_vars_x5 is not None:
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for j in range(M):
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# 计算第 j 班次的总人数
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shift_total = sum(variables[i][j] for i in range(N))
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# 计算平均每个部门应有的人数
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avg_dept = shift_total / num_departments
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# 对每个部门 k
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for k in range(num_departments):
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# 计算第 j 班次中第 k 个部门的实际人数
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dept_count = sum(variables[i][j] * depart_mat[i][k] for i in range(N))
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# 添加绝对值约束
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solver.Add(aux_vars_x5[j][k] >= dept_count - avg_dept)
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solver.Add(aux_vars_x5[j][k] >= avg_dept - dept_count)
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# 约束：满足每位同学的意愿班次数
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for i in range(N):
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total_shifts = sum(variables[i])
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if want_num_array[i] == 3:
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solver.Add(total_shifts >= 2)
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solver.Add(total_shifts <= 3)
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else:
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solver.Add(total_shifts == want_num_array[i])
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# 添加约束的辅助函数
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def add_shift_constraint(array, min_val, max_val):
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for j in range(M):
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shift_count = sum(variables[i][j] * array[i] for i in range(N))
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if min_val is not None:
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solver.Add(shift_count >= min_val)
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if max_val is not None:
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solver.Add(shift_count <= max_val)
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# 约束：每个班次的总人数
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add_shift_constraint([1] * N, num_min, num_max)
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# 约束：每班次电脑或电器的老人数量
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tech_old_array = [is_old_array[i] * is_tech_array[i] for i in range(N)]
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add_shift_constraint(tech_old_array, num_tech_old_min, num_tech_old_max)
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# 约束：每班次老人数量
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add_shift_constraint(is_old_array, num_old_min, num_old_max)
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# 约束：每班次小朋友数量
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add_shift_constraint(is_new_array, num_new_min, num_new_max)
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# 构建多目标优化函数
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m1, m2, m3, m4, m5 = m[0], m[1], m[2], m[3], m[4]
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# X1: 每班次人数与平均人数的偏差
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x1 = sum(aux_vars_x1)
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obj_x1 = x1 / (m1 * M) # 归一化处理，防止数值过大
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# X2: 每班次技术部老人数量的缺口总和（优化目标是让每班都达到目标值）
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x2 = sum(aux_vars_x2)
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obj_x2 = x2 / (m2 * M) # 归一化处理，缺口越小越好
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# X3: 每班次技术部小朋友数量的缺口总和
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x3 = sum(aux_vars_x3)
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obj_x3 = x3 / (m3 * M) # 归一化处理，缺口越小越好
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# X4: 每班次人资部小朋友数量的缺口总和
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x4 = sum(aux_vars_x4)
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obj_x4 = x4 / (m4 * M) # 归一化处理，缺口越小越好
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# X5: 每班次各部门人数的平均程度
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obj_x5 = 0
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if aux_vars_x5:
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x5 = sum(sum(aux_vars_x5[j]) for j in range(M))
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obj_x5 = x5 / (m5 * M) # 归一化处理
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# 线性加权组合所有目标
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total_objective = (
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weights[0] * obj_x1 + weights[1] * obj_x2 + weights[2] * obj_x3 + weights[3] * obj_x4 + weights[4] * obj_x5
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)
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print(f"优化目标权重: X1={weights[0]}, X2={weights[1]}, X3={weights[2]}, X4={weights[3]}, X5={weights[4]}")
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solver.Minimize(total_objective)
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# 求解
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status = solver.Solve()
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if status == pywraplp.Solver.OPTIMAL:
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print("Optimal solution found:")
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variables_return = [[variables[i][j].solution_value() for j in range(M)]
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for i in range(N)]
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aux_vars_x1_return = sum([aux_vars_x1[j].solution_value() for j in range(M)]) / M
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print(f"Optimized objective value: {solver.Objective().Value()}")
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print(f"X1 (每班次人数平均偏差): {aux_vars_x1_return}")
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# 输出各个优化目标的详细信息
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tech_old_array = [is_old_array[i] * is_tech_array[i] for i in range(N)]
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tech_new_array = [is_new_array[i] * is_tech_array[i] for i in range(N)]
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hr_new_array = [is_new_array[i] * is_hr_array[i] for i in range(N)]
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x2_value = sum(sum(variables[i][j].solution_value() * tech_old_array[i] for i in range(N)) for j in range(M)) / M
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x3_value = sum(sum(variables[i][j].solution_value() * tech_new_array[i] for i in range(N)) for j in range(M)) / M
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x4_value = sum(sum(variables[i][j].solution_value() * hr_new_array[i] for i in range(N)) for j in range(M)) / M
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aux_vars_x2_return = sum([aux_vars_x2[j].solution_value() for j in range(M)]) / M
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aux_vars_x3_return = sum([aux_vars_x3[j].solution_value() for j in range(M)]) / M
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aux_vars_x4_return = sum([aux_vars_x4[j].solution_value() for j in range(M)]) / M
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print(f"X2 (每班平均技术部老人): {x2_value}, 缺口平均: {aux_vars_x2_return}")
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print(f"X3 (每班平均技术部小朋友): {x3_value}, 缺口平均: {aux_vars_x3_return}")
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print(f"X4 (每班平均人资部小朋友): {x4_value}, 缺口平均: {aux_vars_x4_return}")
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if aux_vars_x5:
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x5_value = sum(sum(aux_vars_x5[j][k].solution_value() for k in range(num_departments)) for j in range(M))
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print(f"X5 (部门人数偏差): {x5_value}")
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return variables_return
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else:
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print("No solution found.")
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return None
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