python 设施开单 SCIP 优化

问题描述

我正在尝试使用 SCIP optimization 找到设施的最佳打开顺序 给定距离住宅区的距离并为数量加权 该地区的居民。

我已经设置了距离字典，以便从设施到 每个住宅区应为设施产生 [2,1,0] 订单的输出。

但是，我收到的输出是 [0,2]。

此外，如果我将 alpha 更改为正值，则没有任何影响。

import pandas as pd
from pyscipopt import Model,quicksum,multidict,exp
num_fac_to_open = 3
order_to_open = []
opened_fac = []
closed_fac = [0,2]
# Facility id
S = [0,2]
# Residential block id
R = [10,11,12]
distance_dict = {(0,10): 0.8,(1,10): 150.6,(2,10): 100007.8,(0,11): 1.0,11): 2012.1,11): 10009.2,12): 3.2,12): 1798.3,12): 10006.3}
population_dict = {10:54,11:46,12:22}
alpha = -1
# n is the desired number of facilities to open
n = len(opened_fac) + num_fac_to_open
# create a model
model = Model()
z,y= {},{}
for s in S:
    # x_i is binary,1 if service facility i is opened,0 otherwise
    z[s] = model.addVar(vtype="B")
    for r in R:
        # y_i,j is binary,1 if service facility i is assigned to residential area j,0 otherwise
        y[s,r] = model.addVar(vtype="B")

for r in R:
    model.addCons(quicksum(y[s,r] for s in S) == 1)
#
for s in S:
    for r in R:
        model.addCons(y[s,r]-z[s] <= 0)
#
model.addCons(quicksum(z[s] for s in S) == n)
#
for facility in opened_fac:
    model.addCons(z[facility] == 1)

x,w = {},{}
for r in R:
    x[r] = model.addVar(vtype="C",name="x(%s)"%(r))
    w[r] = model.addVar(vtype="C",name="w(%s)"%(r))
for r in R:
    x[r] = quicksum(distance_dict[s,r]*y[s,r] for s in S)
    exp_power = alpha*population_dict[r]*x[r]
    model.addCons((w[r] - exp(exp_power)) >= 0)
#
#print(quicksum(w[r] for r in R))
model.setObjective(quicksum(w[r] for r in R),'minimize')
model.optimize()

new_facilities = []
for s in S:
    if ((model.getVal(z[s]) == 1) and (not s in opened_fac)):
        new_facilities.append(s)
        if len(new_facilities) == num_fac_to_open:
            break
print(new_facilities)

我正在尝试优化以下问题：

目标是minimize sum_{r=1}^N W_r

哪里W_r = exp(population_dict[r]*sum_{s∈S} d_r,s * y_r,s) ∀r ∈ R

对这个问题的任何帮助都会很棒！

解决方法

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