python多目标线性规划_用Pulp求解线性规划python问题

Routes

所有可能的路线,而你只有

cost_to_send

为某些路线定义。

路线

Routes = [(i, j) for i in origin for j in destination if j in cost_to_send[i]]

我能看到的另一个问题是第二组约束:

for i in origin:

prob += lpSum(quantity[i][j] for j in destination) == 1

所有目的地必须只有一个来源,而不是所有来源

必须使用

from pulp import *

import pandas as pd

origin = ["a","b","c","d","e","f","g","h"]

destination = ["1","2","3","4","5","6","7","8","9","10"]

offer = {"a":3,"b":3,"c":3,"d":3,"e":3,"f":4,"g":3,"h":3}

demand = {"1":1,"2":1,"3":1,"4":1,"5":1,"6":1,"7":1,"8":1,"9":1,"10":1}

cost_to_send = {

"a":{"1":1,"2":1,"3":1},

"b":{"2":1,"3":1,"9":1},

"c":{"5":1,"6":1,"7":1},

"d":{"7":1,"9":1,"10":1},

"e":{"3":1,"6":1,"8":1},

"f":{"1":1,"4":1,"7":1,"9":1},

"g":{"4":1,"5":1,"9":1},

"h":{"1":1,"4":1,"8":1}

}

prob = LpProblem("Exercise", LpMinimize)

# Routes = [(i,j) for i in origin for j in destination]

Routes = [(i, j) for i in origin for j in destination if j in cost_to_send[i]]

quantity = LpVariable.dicts("quantity de envio",Routes,0)

prob += lpSum(quantity[(i,j)]*cost_to_send[i][j] for (i,j) in Routes)

for j in destination:

prob += lpSum(quantity[(i,j)] for i in origin if (i,j) in Routes) == demand[j]

#for i in origin:

# prob += lpSum(quantity[i][j] for j in destination) == 1

prob.solve()

print("Status: ", LpStatus[prob.status])

for v in prob.variables():

if v.varValue > 0:

print(v.name, "=", v.varValue)

print("Answer ", value(prob.objective))

Returns:

Status: Optimal

quantity_de_envio_('a',_'1') = 1.0

quantity_de_envio_('a',_'2') = 1.0

quantity_de_envio_('a',_'3') = 1.0

quantity_de_envio_('b',_'9') = 1.0

quantity_de_envio_('c',_'5') = 1.0

quantity_de_envio_('c',_'6') = 1.0

quantity_de_envio_('d',_'10') = 1.0

quantity_de_envio_('f',_'4') = 1.0

quantity_de_envio_('f',_'7') = 1.0

quantity_de_envio_('h',_'8') = 1.0

Answer 10.0

请注意,如果您希望对一个给定的目的地有大于1的请求,但是希望强制目的地只接收来自单个源的输入,那么您需要添加

二元的