143 lines
5.2 KiB
Python
143 lines
5.2 KiB
Python
from ortools.sat.python import cp_model
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from ortools.linear_solver import pywraplp
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from utils import read_excel, save_to_excel
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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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is_not_tech_array = [not is_tech for is_tech in is_tech_array]
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# 这是一个组合优化问题，我们使用 SCIP 求解器来解决这个问题
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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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# 定义变量的规模，一共有 N*M 个变量需要求解器求解
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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 # 每班次的平均人数
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print(f"平均人数：{avg_num}")
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variables = []
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aux_vars = [] # 辅助变量
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infinity = solver.infinity()
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for i in range(N):
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row_vars = []
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for j in range(M):
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var = solver.IntVar(0.0, 1.0, f"choice_{i}_{j}")
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row_vars.append(var)
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variables.append(row_vars)
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for j in range(M):
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aux_var = solver.NumVar(0.0, infinity, f"aux_{j}")
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aux_vars.append(aux_var)
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print("Number of variables =", solver.NumVariables())
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# 添加约束：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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# 辅助变量添加约束：
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for j in range(M):
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actual_num = sum(variables[i][j] for i in range(N)) # 每班次的实际人数
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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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# 添加约束：满足每位同学的意愿班次
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for i in range(N):
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solver.Add(sum(variables[i]) == want_num_array[i])
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# 添加约束：每个班次至少有？位同学
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if num_min is not None:
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for j in range(M):
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solver.Add(sum(variables[i][j] for i in range(N)) >= num_min)
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# 添加约束：每个班次至多有？位同学
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if num_max is not None:
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for j in range(M):
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solver.Add(sum(variables[i][j] for i in range(N)) <= num_max)
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# 添加约束：每班次最少包含？个电脑或电器的老人
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if num_tech_min is not None:
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for j in range(M):
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solver.Add(sum(variables[i][j]*is_old_array[i]*is_tech_array[i] for i in range(N)) >= num_tech_min)
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# 添加约束：每班次最多包含？个电脑或电器的老人
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if num_tech_max is not None:
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for j in range(M):
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solver.Add(sum(variables[i][j]*is_old_array[i]*is_tech_array[i] for i in range(N)) <= num_tech_max)
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# 添加约束：每班次至少包含？个老人
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if num_old_min is not None:
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for j in range(M):
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solver.Add(sum(variables[i][j]*is_old_array[i] for i in range(N)) >= num_old_min)
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# 添加约束：每班次至多包含？个老人
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if num_old_max is not None:
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for j in range(M):
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solver.Add(sum(variables[i][j]*is_old_array[i] for i in range(N)) <= num_old_max)
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# 添加约束：每班次至少包含？个人资部小朋友
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if num_hr_min is not None:
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for j in range(M):
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solver.Add(sum(variables[i][j]*is_hr_array[i] for i in range(N)) >= num_hr_min)
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# 添加约束：每班次至多包含？个人资部小朋友
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if num_hr_max is not None:
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for j in range(M):
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solver.Add(sum(variables[i][j]*is_hr_array[i] for i in range(N)) <= num_hr_max)
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# 添加约束：每班次至少包含？个小朋友
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if num_new_min is not None:
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for j in range(M):
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solver.Add(sum(variables[i][j]*is_new_array[i] for i in range(N)) >= num_new_min)
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# 添加约束：每班次至多包含？个小朋友
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if num_new_max is not None:
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for j in range(M):
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solver.Add(sum(variables[i][j]*is_new_array[i] for i in range(N)) <= num_new_max)
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# 优化目标：每班次人数尽可能平均
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solver.Minimize(sum(aux_vars)) # Maximize the sum of these variables.
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# 求解优化问题
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status = solver.Solve()
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# 输出结果
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variables_return = []
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aux_vars_return = []
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if status == pywraplp.Solver.OPTIMAL:
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print("Optimal solution found:")
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for i in range(N):
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row_solution = [variables[i][j].solution_value() for j in range(M)]
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variables_return.append(row_solution)
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for j in range(M):
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aux_vars_return.append(aux_vars[j].solution_value())
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# Print the optimized value of the objective function.
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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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