如何根据决策变量（一个用于行，一个用于列）从矩阵（python 中的列表列表）中选取一个元素 | OR-工具，Python
How to pick an element from matrix (list of list in python) based on decision variables (one for row, and one for column) | OR-Tools, Python
我是约束编程和 OR-Tools 的新手。关于问题的简要说明。有 8 个位置，对于每个位置，我需要决定应该选择哪种 A 类移动（move_A）和哪种 B 类移动（move_B），以便从组合中获得的值2 次移动（在每个位置）被最大化。 （尽管这只是更大问题的一部分）。我想使用 AddElement 方法来进行子设置。
请看下面的尝试
from ortools.sat.python import cp_model
model = cp_model.CpModel()
# value achieved from combination of different moves of type A
# (moves_A (rows)) and different moves of type B (moves_B (columns))
# for e.g. 2nd move of type A and 3rd move of type B will give value = 2
value = [
[ -1, 5, 3, 2, 2],
[ 2, 4, 2, -1, 1],
[ 4, 4, 0, -1, 2],
[ 5, 1, -1, 2, 2],
[ 0, 0, 0, 0, 0],
[ 2, 1, 1, 2, 0]
]
# 6 moves of type A
num_moves_A = len(value)
# 5 moves of type B
num_moves_B = len(value[0])
num_positions = 8
type_move_A_position = [model.NewIntVar(0, num_moves_A - 1, f"move_A[{i}]") for i in range(num_positions)]
type_move_B_position = [model.NewIntVar(0, num_moves_B - 1, f"move_B[{i}]") for i in range(num_positions)]
value_position = [model.NewIntVar(0, 10, f"value_position[{i}]") for i in range(num_positions)]
# I am getting an error when I run the below
objective_terms = []
for i in range(num_positions):
model.AddElement(type_move_B_position[i], value[type_move_A_position[i]], value_position[i])
objective_terms.append(value_position[i])
错误如下：
Traceback (most recent call last):
File "<ipython-input-65-3696379ce410>", line 3, in <module>
model.AddElement(type_move_B_position[i], value[type_move_A_position[i]], value_position[i])
TypeError: list indices must be integers or slices, not IntVar
在 MiniZinc 中，下面的代码可以工作
var int: obj = sum(i in 1..num_positions ) (value [type_move_A_position[i], type_move_B_position[i]])
我知道在OR-Tools中我们必须先创建一些中间变量来存储结果，所以上面的minizinc方法是行不通的。但我正在努力这样做。
我总是可以创建一个二进制二进制变量的 2 矩阵，一个用于 num_moves_A * num_positions，另一个用于 num_moves_B * num_positions，添加 re;evant 约束并达到目的
但我想学习如何通过 AddElement 约束
做同样的事情
非常感谢任何有关如何重写 AddElement 片段的帮助。谢谢。
AddElement 仅为一维。
它从 minizinc 转换为 CP-SAT 的方式是创建一个中间变量 p == index1 * max(index2) + index2 并将其用于具有展平矩阵的元素约束。
遵循 Laurent 的建议（使用 AddElement 约束）：
from ortools.sat.python import cp_model
model = cp_model.CpModel()
# value achieved from combination of different moves of type A
# (moves_A (rows)) and different moves of type B (moves_B (columns))
# for e.g. 2 move of type A and 3 move of type B will give value = 2
value = [
[-1, 5, 3, 2, 2],
[2, 4, 2, -1, 1],
[4, 4, 0, -1, 2],
[5, 1, -1, 2, 2],
[0, 0, 0, 0, 0],
[2, 1, 1, 2, 0],
]
min_value = min([min(i) for i in value])
max_value = max([max(i) for i in value])
# 6 moves of type A
num_moves_A = len(value)
# 5 moves of type B
num_moves_B = len(value[0])
# number of positions
num_positions = 5
# flattened matrix of values
value_flat = [value[i][j] for i in range(num_moves_A) for j in range(num_moves_B)]
# flattened indices
flatten_indices = [
index1 * len(value[0]) + index2
for index1 in range(len(value))
for index2 in range(len(value[0]))
]
type_move_A_position = [
model.NewIntVar(0, num_moves_A - 1, f"move_A[{i}]") for i in range(num_positions)
]
model.AddAllDifferent(type_move_A_position)
type_move_B_position = [
model.NewIntVar(0, num_moves_B - 1, f"move_B[{i}]") for i in range(num_positions)
]
model.AddAllDifferent(type_move_B_position)
# below intermediate decision variable is created which
# will store index corresponding to the selected move of type A and
# move of type B for each position
# this will act as index in the AddElement constraint
flatten_index_num = [
model.NewIntVar(0, len(flatten_indices), f"flatten_index_num[{i}]")
for i in range(num_positions)
]
# another intermediate decision variable is created which
# will store value corresponding to the selected move of type A and
# move of type B for each position
# this will act as the target in the AddElement constraint
value_position_index_num = [
model.NewIntVar(min_value, max_value, f"value_position_index_num[{i}]")
for i in range(num_positions)
]
objective_terms = []
for i in range(num_positions):
model.Add(
flatten_index_num[i]
== (type_move_A_position[i] * len(value[0])) + type_move_B_position[i]
)
model.AddElement(flatten_index_num[i], value_flat, value_position_index_num[i])
objective_terms.append(value_position_index_num[i])
model.Maximize(sum(objective_terms))
# Solve
solver = cp_model.CpSolver()
status = solver.Solve(model)
solver.ObjectiveValue()
for i in range(num_positions):
print(
str(i)
+ "--"
+ str(solver.Value(type_move_A_position[i]))
+ "--"
+ str(solver.Value(type_move_B_position[i]))
+ "--"
+ str(solver.Value(value_position_index_num[i]))
)
以下版本使用 AddAllowedAssignments 约束来实现相同的目的（根据 Laurent 的替代方法）：
from ortools.sat.python import cp_model
model = cp_model.CpModel()
# value achieved from combination of different moves of type A
# (moves_A (rows)) and different moves of type B (moves_B (columns))
# for e.g. 2 move of type A and 3 move of type B will give value = 2
value = [
[-1, 5, 3, 2, 2],
[2, 4, 2, -1, 1],
[4, 4, 0, -1, 2],
[5, 1, -1, 2, 2],
[0, 0, 0, 0, 0],
[2, 1, 1, 2, 0],
]
min_value = min([min(i) for i in value])
max_value = max([max(i) for i in value])
# 6 moves of type A
num_moves_A = len(value)
# 5 moves of type B
num_moves_B = len(value[0])
# number of positions
num_positions = 5
type_move_A_position = [
model.NewIntVar(0, num_moves_A - 1, f"move_A[{i}]") for i in range(num_positions)
]
model.AddAllDifferent(type_move_A_position)
type_move_B_position = [
model.NewIntVar(0, num_moves_B - 1, f"move_B[{i}]") for i in range(num_positions)
]
model.AddAllDifferent(type_move_B_position)
value_position = [
model.NewIntVar(min_value, max_value, f"value_position[{i}]")
for i in range(num_positions)
]
tuples_list = []
for i in range(num_moves_A):
for j in range(num_moves_B):
tuples_list.append((i, j, value[i][j]))
for i in range(num_positions):
model.AddAllowedAssignments(
[type_move_A_position[i], type_move_B_position[i], value_position[i]],
tuples_list,
)
model.Maximize(sum(value_position))
# Solve
solver = cp_model.CpSolver()
status = solver.Solve(model)
solver.ObjectiveValue()
for i in range(num_positions):
print(
str(i)
+ "--"
+ str(solver.Value(type_move_A_position[i]))
+ "--"
+ str(solver.Value(type_move_B_position[i]))
+ "--"
+ str(solver.Value(value_position[i]))
)
我是约束编程和 OR-Tools 的新手。关于问题的简要说明。有 8 个位置，对于每个位置，我需要决定应该选择哪种 A 类移动（move_A）和哪种 B 类移动（move_B），以便从组合中获得的值2 次移动（在每个位置）被最大化。 （尽管这只是更大问题的一部分）。我想使用 AddElement 方法来进行子设置。
请看下面的尝试
from ortools.sat.python import cp_model
model = cp_model.CpModel()
# value achieved from combination of different moves of type A
# (moves_A (rows)) and different moves of type B (moves_B (columns))
# for e.g. 2nd move of type A and 3rd move of type B will give value = 2
value = [
[ -1, 5, 3, 2, 2],
[ 2, 4, 2, -1, 1],
[ 4, 4, 0, -1, 2],
[ 5, 1, -1, 2, 2],
[ 0, 0, 0, 0, 0],
[ 2, 1, 1, 2, 0]
]
# 6 moves of type A
num_moves_A = len(value)
# 5 moves of type B
num_moves_B = len(value[0])
num_positions = 8
type_move_A_position = [model.NewIntVar(0, num_moves_A - 1, f"move_A[{i}]") for i in range(num_positions)]
type_move_B_position = [model.NewIntVar(0, num_moves_B - 1, f"move_B[{i}]") for i in range(num_positions)]
value_position = [model.NewIntVar(0, 10, f"value_position[{i}]") for i in range(num_positions)]
# I am getting an error when I run the below
objective_terms = []
for i in range(num_positions):
model.AddElement(type_move_B_position[i], value[type_move_A_position[i]], value_position[i])
objective_terms.append(value_position[i])
错误如下：
Traceback (most recent call last):
File "<ipython-input-65-3696379ce410>", line 3, in <module>
model.AddElement(type_move_B_position[i], value[type_move_A_position[i]], value_position[i])
TypeError: list indices must be integers or slices, not IntVar
在 MiniZinc 中，下面的代码可以工作
var int: obj = sum(i in 1..num_positions ) (value [type_move_A_position[i], type_move_B_position[i]])
我知道在OR-Tools中我们必须先创建一些中间变量来存储结果，所以上面的minizinc方法是行不通的。但我正在努力这样做。
我总是可以创建一个二进制二进制变量的 2 矩阵，一个用于 num_moves_A * num_positions，另一个用于 num_moves_B * num_positions，添加 re;evant 约束并达到目的
但我想学习如何通过 AddElement 约束
非常感谢任何有关如何重写 AddElement 片段的帮助。谢谢。
AddElement 仅为一维。
它从 minizinc 转换为 CP-SAT 的方式是创建一个中间变量 p == index1 * max(index2) + index2 并将其用于具有展平矩阵的元素约束。
遵循 Laurent 的建议（使用 AddElement 约束）：
from ortools.sat.python import cp_model
model = cp_model.CpModel()
# value achieved from combination of different moves of type A
# (moves_A (rows)) and different moves of type B (moves_B (columns))
# for e.g. 2 move of type A and 3 move of type B will give value = 2
value = [
[-1, 5, 3, 2, 2],
[2, 4, 2, -1, 1],
[4, 4, 0, -1, 2],
[5, 1, -1, 2, 2],
[0, 0, 0, 0, 0],
[2, 1, 1, 2, 0],
]
min_value = min([min(i) for i in value])
max_value = max([max(i) for i in value])
# 6 moves of type A
num_moves_A = len(value)
# 5 moves of type B
num_moves_B = len(value[0])
# number of positions
num_positions = 5
# flattened matrix of values
value_flat = [value[i][j] for i in range(num_moves_A) for j in range(num_moves_B)]
# flattened indices
flatten_indices = [
index1 * len(value[0]) + index2
for index1 in range(len(value))
for index2 in range(len(value[0]))
]
type_move_A_position = [
model.NewIntVar(0, num_moves_A - 1, f"move_A[{i}]") for i in range(num_positions)
]
model.AddAllDifferent(type_move_A_position)
type_move_B_position = [
model.NewIntVar(0, num_moves_B - 1, f"move_B[{i}]") for i in range(num_positions)
]
model.AddAllDifferent(type_move_B_position)
# below intermediate decision variable is created which
# will store index corresponding to the selected move of type A and
# move of type B for each position
# this will act as index in the AddElement constraint
flatten_index_num = [
model.NewIntVar(0, len(flatten_indices), f"flatten_index_num[{i}]")
for i in range(num_positions)
]
# another intermediate decision variable is created which
# will store value corresponding to the selected move of type A and
# move of type B for each position
# this will act as the target in the AddElement constraint
value_position_index_num = [
model.NewIntVar(min_value, max_value, f"value_position_index_num[{i}]")
for i in range(num_positions)
]
objective_terms = []
for i in range(num_positions):
model.Add(
flatten_index_num[i]
== (type_move_A_position[i] * len(value[0])) + type_move_B_position[i]
)
model.AddElement(flatten_index_num[i], value_flat, value_position_index_num[i])
objective_terms.append(value_position_index_num[i])
model.Maximize(sum(objective_terms))
# Solve
solver = cp_model.CpSolver()
status = solver.Solve(model)
solver.ObjectiveValue()
for i in range(num_positions):
print(
str(i)
+ "--"
+ str(solver.Value(type_move_A_position[i]))
+ "--"
+ str(solver.Value(type_move_B_position[i]))
+ "--"
+ str(solver.Value(value_position_index_num[i]))
)
以下版本使用 AddAllowedAssignments 约束来实现相同的目的（根据 Laurent 的替代方法）：
from ortools.sat.python import cp_model
model = cp_model.CpModel()
# value achieved from combination of different moves of type A
# (moves_A (rows)) and different moves of type B (moves_B (columns))
# for e.g. 2 move of type A and 3 move of type B will give value = 2
value = [
[-1, 5, 3, 2, 2],
[2, 4, 2, -1, 1],
[4, 4, 0, -1, 2],
[5, 1, -1, 2, 2],
[0, 0, 0, 0, 0],
[2, 1, 1, 2, 0],
]
min_value = min([min(i) for i in value])
max_value = max([max(i) for i in value])
# 6 moves of type A
num_moves_A = len(value)
# 5 moves of type B
num_moves_B = len(value[0])
# number of positions
num_positions = 5
type_move_A_position = [
model.NewIntVar(0, num_moves_A - 1, f"move_A[{i}]") for i in range(num_positions)
]
model.AddAllDifferent(type_move_A_position)
type_move_B_position = [
model.NewIntVar(0, num_moves_B - 1, f"move_B[{i}]") for i in range(num_positions)
]
model.AddAllDifferent(type_move_B_position)
value_position = [
model.NewIntVar(min_value, max_value, f"value_position[{i}]")
for i in range(num_positions)
]
tuples_list = []
for i in range(num_moves_A):
for j in range(num_moves_B):
tuples_list.append((i, j, value[i][j]))
for i in range(num_positions):
model.AddAllowedAssignments(
[type_move_A_position[i], type_move_B_position[i], value_position[i]],
tuples_list,
)
model.Maximize(sum(value_position))
# Solve
solver = cp_model.CpSolver()
status = solver.Solve(model)
solver.ObjectiveValue()
for i in range(num_positions):
print(
str(i)
+ "--"
+ str(solver.Value(type_move_A_position[i]))
+ "--"
+ str(solver.Value(type_move_B_position[i]))
+ "--"
+ str(solver.Value(value_position[i]))
)