104 lines
3.7 KiB
Python
104 lines
3.7 KiB
Python
from ortools.linear_solver import pywraplp
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def solve_program(preference_mat:list,
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want_num_array:list,
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is_new_array:list,
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is_tech_array:list,
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is_hr_array:list,
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num_min=None,
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num_max=None,
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num_tech_min=None,
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num_tech_max=None,
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num_old_min=None,
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num_old_max=None,
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num_hr_min=None,
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num_hr_max=None,
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num_new_min=None,
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num_new_max=None
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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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# 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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# 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（均衡班次人数）
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aux_vars = [solver.NumVar(0.0, solver.infinity(), f"aux_{j}")
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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[j] >= actual_num - avg_num)
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solver.Add(aux_vars[j] >= avg_num - actual_num)
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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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# 添加班次人数约束的辅助函数
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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_min, num_tech_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：每班次人资部小朋友数量
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add_shift_constraint(is_hr_array, num_hr_min, num_hr_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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# 优化目标：最小化各班次人数与平均人数的偏差总和
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solver.Minimize(sum(aux_vars))
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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_return = [aux_vars[j].solution_value() for j in range(M)]
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print(f"Optimized objective value: {solver.Objective().Value()}")
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print(aux_vars_return)
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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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