我正在做一个名为'discrete optimization course的课程,在这个过程中,一个名为Minizinc的工具用于解决问题。
我想将类示例转换为python,从这个开始:
v = {'hammer':6, 'wrench':10, 'screwdriver':8, 'towel':40}
w = {'hammer':13, 'wrench':21, 'screwdriver':17, 'towel':100}
q = {'hammer':1000, 'wrench':400, 'screwdriver':500, 'towel':150}
limit = 1000
items = list(sorted(v.keys()))
# Create model
m = LpProblem("Knapsack", LpMaximize)
# Variables
x = LpVariable.dicts('x', items, lowBound=0, upBound=1, cat=LpInteger)
# Objective
m += sum(v[i]*x[i] for i in items)
# Constraint
m += sum(w[i]*x[i] for i in items) <= limit
# Optimize
m.solve()
# Print the status of the solved LP
print("Status = %s" % LpStatus[m.status])
# Print the value of the variables at the optimum
for i in items:
print("%s = %f" % (x[i].name, x[i].varValue))
# Print the value of the objective
print("Objective = %f" % value(m.objective))
但这是一个错误的答案,因为它只是一种类型。如何将每个项目(dict q)的可用金额添加到约束中?
您需要对代码进行两次非常小的更改。首先,您需要删除在x
变量上设置的上限。在你有二进制变量x[i]
的时刻,它只能是一个或零。
其次,您需要添加约束,这些约束有效地为每个项设置自定义上限。下面的工作代码和最终解决方案 - 你可以看到多个扳手(最高的v/w
比率)被选中,用一把锤子填满剩下的少量空间。
from pulp import *
v = {'hammer':6, 'wrench':10, 'screwdriver':8, 'towel':40}
w = {'hammer':13, 'wrench':21, 'screwdriver':17, 'towel':100}
q = {'hammer':1000, 'wrench':400, 'screwdriver':500, 'towel':150}
limit = 1000
items = list(sorted(v.keys()))
# Create model
m = LpProblem("Knapsack", LpMaximize)
# Variables
x = LpVariable.dicts('x', items, lowBound=0, cat=LpInteger)
# Objective
m += sum(v[i]*x[i] for i in items)
# Constraint
m += sum(w[i]*x[i] for i in items) <= limit
# Quantity of each constraint:
for i in items:
m += x[i] <= q[i]
# Optimize
m.solve()
# Print the status of the solved LP
print("Status = %s" % LpStatus[m.status])
# Print the value of the variables at the optimum
for i in items:
print("%s = %f" % (x[i].name, x[i].varValue))
# Print the value of the objective
print("Objective = %f" % value(m.objective))
print("Total weight = %f" % sum([x[i].varValue*w[i] for i in items]))
哪个回报:
状态=最佳
x_hammer = 1.000000
x_screwdriver = 0.000000
x_towel = 0.000000
x_wrench = 47.000000
Objective = 476.000000
Total weight = 1000.000000