如何在PuLP Python中指定約束來乘以兩個變量？

Question

我試圖用Python紙漿

我寫了下面的代碼下面的整數規劃模型型號：

from pulp import * 

#knapsack problem 

def knapsolve(item): 

    prob = LpProblem('BinPacking', LpMinimize) 

    ys = [LpVariable("y{0}".format(i+1), cat="Binary") for i in range(item.bins)] 

    xs = [LpVariable("x{0}{1}".format(i+1, j+1), cat="Binary") 
      for i in range(item.items) for j in range(item.bins)] 

    #minimize objective 
    nbins = sum(ys) 
    prob += nbins 

    print(nbins) 

    #constraints 

    t = nbins >= 1 
    print(t) 
    prob += t 

    for i in range(item.items): 
     con1 = sum(xs[(i + j*item.bins)]* ys[j] for j in range(item.bins)) 
     t = con1 == 1 
     prob += t 
     print(t) 

    status = prob.solve() 

    print(LpStatus[status]) 
    print("Objective value:", value(prob.objective)) 
    print ('\nThe values of the variables : \n') 

    for v in prob.variables(): 
     print(v.name, "=", v.varValue) 

    return 

class Probelm: 
    #bins, binweight, items, weight, itemheight, binheight 

    bins = 5 
    items = 5 

    binweight = [2,3,2,5,3] 
    itemweight = [1,2,2,1,3] 

    itemheight = [2,1,4,5,3] 
    binheight = [4,9,10,8,10] 


item = Problem() 

knapsolve(item) 

在運行時，這提供了錯誤：

y1 + y2 + y3 + y4 + y5 
y1 + y2 + y3 + y4 + y5 >= 1 
Traceback (most recent call last): 
    File "C:\Python34\BinPacking6.py", line 58, in <module> 
    knapsolve(item) 
    File "C:\Python34\BinPacking6.py", line 27, in knapsolve 
    con1 = sum(xs[(i + j*item.bins)]* ys[j] for j in range(item.bins)) 
    File "C:\Python34\BinPacking6.py", line 27, in <genexpr> 
    con1 = sum(xs[(i + j*item.bins)]* ys[j] for j in range(item.bins)) 
    File "C:\Python34\lib\site-packages\pulp-1.6.1-py3.4.egg\pulp\pulp.py", line 209, in __mul__ 
    return LpAffineExpression(self) * other 
    File "C:\Python34\lib\site-packages\pulp-1.6.1-py3.4.egg\pulp\pulp.py", line 786, in __mul__ 
    return self * LpAffineExpression(other) 
    File "C:\Python34\lib\site-packages\pulp-1.6.1-py3.4.egg\pulp\pulp.py", line 774, in __mul__ 
    raise TypeError("Non-constant expressions cannot be multiplied") 
TypeError: Non-constant expressions cannot be multiplied 

據我所知，問題出在con1 = sum(xs[(i + j*item.bins)]* ys[j] for j in range(item.bins))。我如何指定約束條件？

Answer 1

來自PuLP的消息是正確的。您正嘗試將非線性結構（兩個變量的乘法）傳遞給PuLP，而PuLP僅針對線性模型設計。幸運的是，您想要解決的簡單裝箱模型可以制定爲線性MIP模型，請參閱here。在開始輸入一些Python代碼之前，它通常會幫助我首先將數學模型寫得比您發佈的數據模型更精確（這太籠統了）。