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Variable definition as constraint in pyomo

This question is related to my previous question found here. I have managed to solve this problem (big thanks to #AirSquid!) My objective function is something like:
So the avgPrice_n variable is indexed by n. However, it is actually defined as
Meaning that it is indexed by n and i.
So at the moment my objective function is very messy as I have three sums. It looks something like (I expanded the brackets in the objective function and added each component separately, so the avgPrice_n*demand_n looks like):
expr += sum(sum(sum((1/12)*model.c[i]*model.allocation[i,n] for i in model.MP[t]) for t in model.M)*model.demand_n[n] for n in model.N)
And while this works, debugging was quite difficult because the terms are very long. So intead of using the actual definition of avgPrice_n, I was wondering if it would be possible to create a avgPrice_n variable, use this in the objective function and then create a constraint where I define avgPrice_n as I showed above.
The issue I am having is that I created my decision variable, x_{i,n}, as a variable but apparently I can't create a avgPrice_n as a variable where I index it by x_{i,n} as this results in a TypeError: Cannot apply a Set operator to an indexed Var component (allocation) error.
So as of now my decision variable looks like:
model.x = Var(model.NP_flat, domain = NonNegativeReals)
And I tried to create:
model.avg_Price = Var(model.x, domain = NonNegativeReals)
Which resulted in the above error. Any ideas or suggestions would be much appreciated!

You have a couple options. Realize you do not need the model.avg_price variable because you can construct it from other variables and you would have to make some constraints to constrain the value, etc. etc. and pollute your model.
The basic building blocks in the model are pyomo expressions, so you could put in a little "helper function" to build expressions (the cost function shown, which is dependent on n) which are not defined within the model, but just pop out an expression...totally legal). You can also "break up" large expressions into smaller expressions (like the other_stuff below) and then just kludge them all together in the objective (or where needed) this gives you the opportunity to evaluate them independently. I've made several models with an objective function that has a "cost" component and a "penalty" component by dividing it into 2 expressions.... Then when solved, you can inspect them independently.
My suggestion (if you don't like the triple sum in your current model) is to make an avg_cost(n) function to build the expression similar to what is done in the nonsensical function below, and use that as a substitute for a new variable.
Note: the initialization of the variables here is generally unnecessary. I just did it to "simulate solving" or they would be None...
Code:
import pyomo.environ as pyo
m = pyo.ConcreteModel()
m.N = pyo.Set(initialize=[0,1,2])
m.x = pyo.Var(m.N, initialize = 2.0)
def cost(n):
return m.x[n] + 2*m.x[n+1]
m.other_stuff = 3 * m.x[1] + 4 * m.x[2]
m.costs = sum(cost(n) for n in {0,1})
m.obj_expr = m.costs + m.other_stuff
m.obj = pyo.Objective(expr= m.obj_expr)
# inspect cost at a particular value of n...
print(cost(1))
print(pyo.value(cost(1)))
# inspect the pyomo expressions "other_stuff" and total costs...
print(m.other_stuff)
print(pyo.value(m.other_stuff))
print(m.costs)
print(pyo.value(m.costs))
# inspect the objective... which can be accessed by pprint() and display()
m.obj.pprint()
m.obj.display()
Output:
x[1] + 2*x[2]
6.0
3*x[1] + 4*x[2]
14.0
12.0
obj : Size=1, Index=None, Active=True
Key : Active : Sense : Expression
None : True : minimize : x[0] + 2*x[1] + x[1] + 2*x[2] + 3*x[1] + 4*x[2]
obj : Size=1, Index=None, Active=True
Key : Active : Value
None : True : 26.0

Distance objective optimisation

I'm modeling a reoptimisation model and I would like to include a constraint in order to reduce the distance between the initial solution and the reoptimized solution. I'm doing a staff scheduling and to do so I wanna penalized each assignment in the reoptimized solution that is different from the initial solution.
Before I start, I'm new to optimisation model and the way I built the constraint may be wrong.
#1 Extract the data from the initial solution of my main variable
ModelX_DictExtVal = model.x.extract_values()
# 2 Create a new binary variable which activate when the main variable `ModelX_DictExtVal[x,s,d]` of the initial
#solution is =1 (an employee n works days d and sifht s) and the value of `model.x[n,s,d]` of the reoptimized solution are different.
model.alpha_distance = Var(model.N_S_D, within=Binary)
#3 Model a constraint to activate my variable.
def constraint_distance(model, n, s, d):
v = ModelX_DictExtVal[n,s,d]
if v == 1 and ModelX_DictExtVal[n,s,d] != model.x[n,s,d]:
return model.alpha_distance[n,s,d] == 1
elif v == 0:
return model.alpha_distance[n,s,d] == 0
model.constraint_distance = Constraint(model.N_S_D, rule = constraint_distance)
#4 Penalize in my objective function every time the varaible is equal to one
ObjFunction = Objective(expr = sum(model.alpha_distance[n,s,d] * WeightDistance
for n in model.N for s in model.S for d in model.D))
Issue: I'm not sure about what I'm doing in part 3 and I get an index error when v == 1.
ERROR: Rule failed when generating expression for constraint
constraint_distance with index (0, 'E', 6): ValueError: Constraint
'constraint_distance[0,E,6]': rule returned None
I am wondering since I am reusing the same model for re-optimization if the model keeps the value of the initial solution of model.x [n, s, d] to do the comparison ModelX_DictExtVal [n, s, d]! = model.x [n, s, d] during the re-optimization phase instead of the new assignments...

You are right to suspect part 3. :)
So you have some "initial values" that could be either the original schedule (before optimizing) or some other preliminary optimization. And your decision variable is binary, indexed by [n,s,d] if I understand your question.
In your constraint you cannot employ an if-else structure based on a comparison test of your decision variable. The value of that variable is unknown at the time the constraint is built, right?
You are on the right track, though. So, what you really want to do is to have your alpha_distance (or penalty) variable capture any changes, indicating 1 where there is a change. That is an absolute value operation, but can be captured with 2 constraints. Consider (in pseudocode):
penalty = |x.new - x.old| # is what you want
So introduce 2 constraints, (indexed fully by [n,s,d]):
penalty >= x.new - x.old
penalty >= x.old - x.new
Then, as you are doing now, include the penalty in your objective, optionally multiplied by a weight.
Comment back if that doesn't make sense...

Scipy Curve_fit. Separate bounds for multiple parameters

I am using Scipy to fit my data to a function. The function give me values for 2 parameters, in this case a and b. I want to use the bound argument to limit the values these parameters can take, each have their own range of acceptable values.
Acceptable values: 15< a <50 and 0.05< b <0.2
I want to know how to implement them. The official documentation only shows how to do them for 1 parameter. This question is similiar to: Python curve fit library that allows me to assign bounds to parameters. Which also only tackles boundaries for 1 parameter.
Here is what i tried:
def Ebfit(x,a,b):
Eb_mean = a*(0.0256/kt) # Eb at bake temperature
Eb_sigma = b*Eb_mean
Foursigma = 4*Eb_sigma
Eb_a = np.linspace(Eb_mean-Foursigma,Eb_mean+Foursigma,N_Device)
dEb = Eb_a[1] - Eb_a[0]
pdfEb_a = spys.norm.pdf(Eb_a,Eb_mean,Eb_sigma)
## Retention Time
DMom = np.zeros(len(x),float)
tau = (1/f0)*np.exp(Eb_a)
for bb in range(len(x)):
DMom[bb]= (1 - 2*(sum(pdfEb_a*(1 - np.exp(np.divide(-x[bb],tau))))*dEb))
return DMom
time = datafile['time'][0:501]
Moment = datafile['25Oe'][0:501]
params,extras = curve_fit(Ebfit,time,Moment, p0=[20,0.1], bounds=[(15,50),(0.05,0.2)])
I have also tried the following variations to see if the parenthesis was the issue:
params,extras = curve_fit(Ebfit,time,Moment, p0=[20,0.1], bounds=[[15,50],[0.02,0.2]])
params,extras = curve_fit(Ebfit,time,Moment, p0=[20,0.1], bounds=((15,50),(0.02,0.2)))
But I get the same error for all of these variations
ValueError: Each lower bound mush be strictly less than each upper
bound.
It only works with a single bound such as:
params,extras = curve_fit(Ebfit,time,Moment, p0=[20,0.1], bounds=[0,50])
Any help is appreciated.
Thank you!

bounds=[[0,50],[0,0.3]]) means the second parameter is greater than 50 but smaller then 0.3. Also the first parameter is fixed at zero.
The format is bounds=(lower, upper).

As per #ev-br suggestion. I tried the following changes for the bounds argument and it worked out great.
bounds=[[15,0.02],[50,0.2]]
So in the end, the argument give should be as follows:
bounds=[[a1,b1],[a2,b2]]
Where a1 is the lower limit for a and a2 the upper limit for a. Sames goes for b.

Why does my association model find subgroups in a dataset when there shouldn't any?

I give a lot of information on the methods that I used to write my code. If you just want to read my question, skip to the quotes at the end.
I'm working on a project that has a goal of detecting sub populations in a group of patients. I thought this sounded like the perfect opportunity to use association rule mining as I'm currently taking a class on the subject.
I there are 42 variables in total. Of those, 20 are continuous and had to be discretized. For each variable, I used the Freedman-Diaconis rule to determine how many categories to divide a group into.
def Freedman_Diaconis(column_values):
#sort the list first
column_values[1].sort()
first_quartile = int(len(column_values[1]) * .25)
third_quartile = int(len(column_values[1]) * .75)
fq_value = column_values[1][first_quartile]
tq_value = column_values[1][third_quartile]
iqr = tq_value - fq_value
n_to_pow = len(column_values[1])**(-1/3)
h = 2 * iqr * n_to_pow
retval = (column_values[1][-1] - column_values[1][1])/h
test = int(retval+1)
return test
From there I used min-max normalization
def min_max_transform(column_of_data, num_bins):
min_max_normalizer = preprocessing.MinMaxScaler(feature_range=(1, num_bins))
data_min_max = min_max_normalizer.fit_transform(column_of_data[1])
data_min_max_ints = take_int(data_min_max)
return data_min_max_ints
to transform my data and then I simply took the interger portion to get the final categorization.
def take_int(list_of_float):
ints = []
for flt in list_of_float:
asint = int(flt)
ints.append(asint)
return ints
I then also wrote a function that I used to combine this value with the variable name.
def string_transform(prefix, column, index):
transformed_list = []
transformed = ""
if index < 4:
for entry in column[1]:
transformed = prefix+str(entry)
transformed_list.append(transformed)
else:
prefix_num = prefix.split('x')
for entry in column[1]:
transformed = str(prefix_num[1])+'x'+str(entry)
transformed_list.append(transformed)
return transformed_list
This was done to differentiate variables that have the same value, but appear in different columns. For example, having a value of 1 for variable x14 means something different from getting a value of 1 in variable x20. The string transform function would create 14x1 and 20x1 for the previously mentioned examples.
After this, I wrote everything to a file in basket format
def create_basket(list_of_lists, headers):
#for filename in os.listdir("."):
# if filename.e
if not os.path.exists('baskets'):
os.makedirs('baskets')
down_length = len(list_of_lists[0])
with open('baskets/dataset.basket', 'w') as basketfile:
basket_writer = csv.DictWriter(basketfile, fieldnames=headers)
for i in range(0, down_length):
basket_writer.writerow({"trt": list_of_lists[0][i], "y": list_of_lists[1][i], "x1": list_of_lists[2][i],
"x2": list_of_lists[3][i], "x3": list_of_lists[4][i], "x4": list_of_lists[5][i],
"x5": list_of_lists[6][i], "x6": list_of_lists[7][i], "x7": list_of_lists[8][i],
"x8": list_of_lists[9][i], "x9": list_of_lists[10][i], "x10": list_of_lists[11][i],
"x11": list_of_lists[12][i], "x12":list_of_lists[13][i], "x13": list_of_lists[14][i],
"x14": list_of_lists[15][i], "x15": list_of_lists[16][i], "x16": list_of_lists[17][i],
"x17": list_of_lists[18][i], "x18": list_of_lists[19][i], "x19": list_of_lists[20][i],
"x20": list_of_lists[21][i], "x21": list_of_lists[22][i], "x22": list_of_lists[23][i],
"x23": list_of_lists[24][i], "x24": list_of_lists[25][i], "x25": list_of_lists[26][i],
"x26": list_of_lists[27][i], "x27": list_of_lists[28][i], "x28": list_of_lists[29][i],
"x29": list_of_lists[30][i], "x30": list_of_lists[31][i], "x31": list_of_lists[32][i],
"x32": list_of_lists[33][i], "x33": list_of_lists[34][i], "x34": list_of_lists[35][i],
"x35": list_of_lists[36][i], "x36": list_of_lists[37][i], "x37": list_of_lists[38][i],
"x38": list_of_lists[39][i], "x39": list_of_lists[40][i], "x40": list_of_lists[41][i]})
and I used the apriori package in Orange to see if there were any association rules.
rules = Orange.associate.AssociationRulesSparseInducer(patient_basket, support=0.3, confidence=0.3)
print "%4s %4s %s" % ("Supp", "Conf", "Rule")
for r in rules:
my_rule = str(r)
split_rule = my_rule.split("->")
if 'trt' in split_rule[1]:
print 'treatment rule'
print "%4.1f %4.1f %s" % (r.support, r.confidence, r)
Using this, technique I found quite a few association rules with my testing data.
THIS IS WHERE I HAVE A PROBLEM
When I read the notes for the training data, there is this note
...That is, the only
reason for the differences among observed responses to the same treatment across patients is
random noise. Hence, there is NO meaningful subgroup for this dataset...
My question is,
why do I get multiple association rules that would imply that there are subgroups, when according to the notes I shouldn't see anything?
I'm getting lift numbers that are above 2 as opposed to the 1 that you should expect if everything was random like the notes state.
Supp Conf Rule
0.3 0.7 6x0 -> trt1
Even though my code runs, I'm not getting results anywhere close to what should be expected. This leads me to believe that I messed something up, but I'm not sure what it is.

After some research, I realized that my sample size is too small for the number of variables that I have. I would need a way larger sample size in order to really use the method that I was using. In fact, the method that I tried to use was developed with the assumption that it would be run on databases with hundreds of thousands or millions of rows.

How to modify SPSS output files with Python?

I'm making custom tables in SPSS, but when the cell values (percentages) are rounded to 1 decimal, they sometimes add up to 99,9 or 100,1 in stead of 100,0. My boss asked my to have everything neatly add up to 100. This means slightly changing some values in the output tables.
I wrote some code to retrieve cell values from tables, which works fine, but I cannot find any method or class that allows me to change cells in already generated output. I've tried things like :
Table[(rij,6)] = CellText.Number(11)
and
SpssDataCells[(rij,6)] = CellText.Number(11)
but it keeps giving me "AttributeError: 'SpssClient.SpssTextItem' object has no attribute 'DataCellArray'"
How do I succesfully change cell values of output tables in SPSS?
My code so far:
import SpssClient, spss
# Python verbinden met SPSS.
SpssClient.StartClient()
OutputDoc = SpssClient.GetDesignatedOutputDoc()
OutputItemList = OutputDoc.GetOutputItems()
# Laatste tabel pakken.
lastTab = OutputItemList.Size()-2
OutputItem = OutputItemList.GetItemAt(lastTab)
Table = OutputItem.GetSpecificType()
SpssDataCells = Table.DataCellArray()
# For loop. Voor iedere rij testen of de afgeronde waarden optellen tot 100.
# Specifieke getallen pakken.
rij=0
try:
while (rij<20):
b14 = float(SpssDataCells.GetUnformattedValueAt(rij,0))
z14 = float(SpssDataCells.GetUnformattedValueAt(rij,1))
zz14 = float(SpssDataCells.GetUnformattedValueAt(rij,2))
b15 = float(SpssDataCells.GetUnformattedValueAt(rij,4))
z15 = float(SpssDataCells.GetUnformattedValueAt(rij,5))
zz15 = float(SpssDataCells.GetUnformattedValueAt(rij,6))
print [b14,z14,zz14,b15,z15,zz15]
rij=rij+1
except:
print 'Einde tabel'

The SetValueAt method is what you require to change the value of a cell in a table.
PS. I think your boss should focus on more important things than to spend billable time on having percentages add up neatly to 100% (due to rounding). Also ensure you are using as many decimal point precision as possible in your calculations so to minimize this "discrepancy".
Update:
Just to give an example of what you can do with manipulation like this (beyond fixing round errors):
The table above shows the Share of Voice (SoV) of a Respiratory drug brand (R3) and it's rank among all brands (first two columns of data) and SoV & Rank also within it's same class of brands only (third and forth column). This is compared against previous month (July 15) and if the rank has increased then it is highlighted in green and an upward facing arrow is added and if declined in rank then highlighted in red and downward red facing arrow added. Just adds a little, color and visualization to what otherwise can be dull tables.