I am new to Pyomo and python and am currently trying to build a MILP model. It'd be great if someone can help me out on this.
So in my production model, I have packing families,pf, and a packing line,l, can handle a packing family at a time. I also have a set of products, p.
In my model, capacity is reserved on a family level, so I want to construct sets in such a way that pf1 in set pf includes product p1,p2,p3,p4 and pf2 includes p5,p6,p7,p8. For instance, a constraint for implementing packing capacity restriction would be:
model.ct6rePackCap = ConstraintList()
for pf in model.PF for l in model.L for t in model.T for s in model.S for n in model.N:
lhs = sum(r[p,l,t,s,n] for p in model.P)
rhs = RPack[l,pf,t,s]
model.ct6reCap.add (lhs <= rhs)
Here r is the quantity of product with product index p and RPack is the capacity reserved for the packing family pf, to which each p belongs. How can I connect p and pf here such that each element of pf (pf1, pf2..) contains a set of products e.g. (pf1 = (p1,p2,p3,p4), pf2 =(p5,p6,p7,p8)) ?
I read pyomo document and read something about subset but it didn't seem like it would achieve what I want.
Thanks a lot in advance!
I have been trying to get into python optimization, and I have found that pyomo is probably the way to go; I had some experience with GUROBI as a student, but of course that is no longer possible, so I have to look into the open source options.
I basically want to perform an non-linear mixed integer problem in which I will minimized a certain ratio. The problem itself is setting up a power purchase agreement (PPA) in a renewable energy scenario. Depending on the electricity generated, you will have to either buy or sell electricity acording to the PPA.
The only starting data is the generation; the PPA is the main decision variable, but I will need others. "buy", "sell", "b1" and "b2" are unknown without the PPA value. These are the equations:
Equations that rule the problem (by hand).
Using pyomo, I was trying to set up the problem as:
# Dataframe with my Generation information:
January = Data['Full_Data'][(Data['Full_Data']['Month'] == 1) & (Data['Full_Data']['Year'] == 2011)]
Gen = January['Producible (MWh)']
Time = len(Generacion)
M=100
# Model variables and definition:
m = ConcreteModel()
m.IDX = range(time)
m.PPA = Var(initialize = 2.0, bounds =(1,7))
m.compra = Var(m.IDX, bounds = (0, None))
m.venta = Var(m.IDX, bounds = (0, None))
m.b1 = Var(m.IDX, within = Binary)
m.b2 = Var(m.IDX, within = Binary)
And then, the constraint; only the first one, as I was already getting errors:
m.b1_rule = Constraint(
expr = (((Gen[i] - PPA)/M for i in m.IDX) <= m.b1[i])
)
which gives me the error:
---------------------------------------------------------------------------
AttributeError Traceback (most recent call last)
<ipython-input-5-5d5f5584ebca> in <module>
1 m.b1_rule = Constraint(
----> 2 expr = (((Generacion[i] - PPA)/M for i in m.IDX) <= m.b1[i])
3 )
pyomo\core\expr\numvalue.pyx in pyomo.core.expr.numvalue.NumericValue.__ge__()
pyomo\core\expr\logical_expr.pyx in pyomo.core.expr.logical_expr._generate_relational_expression()
AttributeError: 'generator' object has no attribute 'is_expression_type'
I honestly have no idea what this means. I feel like this should be a simple problem, but I am strugling with the syntax. I basically have to apply a constraint to each individual data from "Generation", there is no sum involved; all constraints are 1-to-1 contraints set so that the physical energy requirements make sense.
How do I set up the constraints like this?
Thank you very much
You have a couple things to fix. First, the error you are getting is because you have "extra parenthesis" around an expression that python is trying to convert to a generator. So, step 1 is to remove the outer parenthesis, but that will not solve your issue.
You said you want to generate this constraint "for each" value of your index. Any time you want to generate copies of a constraint "for each" you will need to either do that by making a constraint list and adding to it with some kind of loop, or use a function-rule combination. There are examples of each in the pyomo documentation and plenty on this site (I have posted a ton if you look at some of my posts.) I would suggest the function-rule combo and you should end up with something like:
def my_constr(m, i):
return m.Gen[i] - m.PPA <= m.b1[i] * M
m.C1 = Constraint(m.IDX, rule=my_constr)
I am trying to simulate a battery dispatch models with charging and discharging constraints. The BESS is charging from a Solar PV system. When I run the model currently, there are some time periods when the BESS is charging and discharging at the same time. How can I add a flag such that when Charge >, Discharge =0 and vice-versa.
def market_constraintx0(model, t):
return (model.Charge[t] <= df.loc[t,'PVGeneration']*stripeff)
model.market_rulex0 = Constraint(model.T, rule=market_constraintx0)
def market_constraintx1(model, t):
return (model.Charge[t] + model.RegDown[t] <= model.ChargeMax)
model.market_rulex1 = Constraint(model.T, rule=market_constraintx1)
def market_constraintx2(model, t):
return ( model.Discharge[t] + model.RegUp[t] <= model.DischargeMax)
model.market_rulex2 = Constraint(model.T, rule=market_constraintx2)
def charge_soc(model, t):
return model.RegUp[t] + model.Discharge[t] <= model.SoC[t] * stripeff ###Battery discharge and regup capacity is limited by SOC
model.charge_soc = Constraint(model.T, rule=charge_soc)
def discharge_soc(model, t):
return model.RegDown[t] + model.Charge[t] <= (model.SoCmax - model.SoC[t])/stripeff ### Battery can be charged by the amount of capacity left to charge.
model.discharge_soc = Constraint(model.T, rule=discharge_soc)
The constraint
x >= 0 or y >= 0
is sometimes called a complementarity condition. It can also be written as:
x * y = 0
(I assume x and y are non-negative variables). There are different ways to solve this:
complementarity solver. Some solvers support this kind of constraints directly. Complementarity constraints inside a math programming model is known as MPEC (Mathematical Programming with Equilibrium Constraints). So these solvers are sometimes called MPEC solvers.
nonlinear formulation. The constraint x*y=0 is not very easy, but a global solver should be able to handle this reliably. However these solvers only handle relatively small models (compared to local solvers).
discrete formulation. Formulate the OR condition using binary variables or a SOS1 construct. This is especially useful if the rest of the model is linear.
You may want to look into pyomo.mpec. For further information see link.
If you want to stick to (mixed-integer) linear formulations, you can also look for indicator constraints, which are discussed generally in this question. Some solvers like CPLEX and Gurobi seem to have specific constraint types for indicator constraints, but I'm not familiar with how to use those within Pyomo.
In general, you can get similar functionality by using a "Big M" formulation. In your case, something like:
model.Indicator = Var(model.T, within=Binary)
model.M = Param(initialize=1000)
def charge_indicator_constraint(model, t):
return model.M * model.Indicator[t] >= model.Charge[t]
...
def discharge_indicator_constraint(model, t):
return (1 - model.M) * model.Indicator >= model.Discharge[t]
...
As the discussed in the question I linked to, picking the right value of model.M is important to keep your model formulation "tight", and in your case, you would probably tie it directly to the power rating of your BESS.
I am working on a code to solve for the optimum combination of diameter size of number of pipelines. The objective function is to find the least sum of pressure drops in six pipelines.
As I have 15 choices of discrete diameter sizes which are [2,4,6,8,12,16,20,24,30,36,40,42,50,60,80] that can be used for any of the six pipelines that I have in the system, the list of possible solutions becomes 15^6 which is equal to 11,390,625
To solve the problem, I am using Mixed-Integer Linear Programming using Pulp package. I am able to find the solution for the combination of same diameters (e.g. [2,2,2,2,2,2] or [4,4,4,4,4,4]) but what I need is to go through all combinations (e.g. [2,4,2,2,4,2] or [4,2,4,2,4,2] to find the minimum. I attempted to do this but the process is taking a very long time to go through all combinations. Is there a faster way to do this ?
Note that I cannot calculate the pressure drop for each pipeline as the choice of diameter will affect the total pressure drop in the system. Therefore, at anytime, I need to calculate the pressure drop of each combination in the system.
I also need to constraint the problem such that the rate/cross section of pipeline area > 2.
Your help is much appreciated.
The first attempt for my code is the following:
from pulp import *
import random
import itertools
import numpy
rate = 5000
numberOfPipelines = 15
def pressure(diameter):
diameterList = numpy.tile(diameter,numberOfPipelines)
pressure = 0.0
for pipeline in range(numberOfPipelines):
pressure += rate/diameterList[pipeline]
return pressure
diameterList = [2,4,6,8,12,16,20,24,30,36,40,42,50,60,80]
pipelineIds = range(0,numberOfPipelines)
pipelinePressures = {}
for diameter in diameterList:
pressures = []
for pipeline in range(numberOfPipelines):
pressures.append(pressure(diameter))
pressureList = dict(zip(pipelineIds,pressures))
pipelinePressures[diameter] = pressureList
print 'pipepressure', pipelinePressures
prob = LpProblem("Warehouse Allocation",LpMinimize)
use_diameter = LpVariable.dicts("UseDiameter", diameterList, cat=LpBinary)
use_pipeline = LpVariable.dicts("UsePipeline", [(i,j) for i in pipelineIds for j in diameterList], cat = LpBinary)
## Objective Function:
prob += lpSum(pipelinePressures[j][i] * use_pipeline[(i,j)] for i in pipelineIds for j in diameterList)
## At least each pipeline must be connected to a diameter:
for i in pipelineIds:
prob += lpSum(use_pipeline[(i,j)] for j in diameterList) ==1
## The diameter is activiated if at least one pipelines is assigned to it:
for j in diameterList:
for i in pipelineIds:
prob += use_diameter[j] >= lpSum(use_pipeline[(i,j)])
## run the solution
prob.solve()
print("Status:", LpStatus[prob.status])
for i in diameterList:
if use_diameter[i].varValue> pressureTest:
print("Diameter Size",i)
for v in prob.variables():
print(v.name,"=",v.varValue)
This what I did for the combination part which took really long time.
xList = np.array(list(itertools.product(diameterList,repeat = numberOfPipelines)))
print len(xList)
for combination in xList:
pressures = []
for pipeline in range(numberOfPipelines):
pressures.append(pressure(combination))
pressureList = dict(zip(pipelineIds,pressures))
pipelinePressures[combination] = pressureList
print 'pipelinePressures',pipelinePressures
I would iterate through all combinations, I think you would run into memory problems otherwise trying to model ALL combinations in a MIP.
If you iterate through the problems perhaps using the multiprocessing library to use all cores, it shouldn't take long just remember only to hold information on the best combination so far, and not to try and generate all combinations at once and then evaluate them.
If the problem gets bigger you should consider Dynamic Programming Algorithms or use pulp with column generation.
Thanks for the answers, I have not used StackOverflow before so I was suprised by the number of answers and the speed of them - its fantastic.
I have not been through the answers properly yet, but thought I should add some information to the problem specification. See the image below.
I can't post an image in this because i don't have enough points but you can see an image
at http://journal.acquitane.com/2010-01-20/image003.jpg
This image may describe more closely what I'm trying to achieve. So you can see on the horizontal lines across the page are price points on the chart. Now where you get a clustering of lines within 0.5% of each, this is considered to be a good thing and why I want to identify those clusters automatically. You can see on the chart that there is a cluster at S2 & MR1, R2 & WPP1.
So everyday I produce these price points and then I can identify manually those that are within 0.5%. - but the purpose of this question is how to do it with a python routine.
I have reproduced the list again (see below) with labels. Just be aware that the list price points don't match the price points in the image because they are from two different days.
[YR3,175.24,8]
[SR3,147.85,6]
[YR2,144.13,8]
[SR2,130.44,6]
[YR1,127.79,8]
[QR3,127.42,5]
[SR1,120.94,6]
[QR2,120.22,5]
[MR3,118.10,3]
[WR3,116.73,2]
[DR3,116.23,1]
[WR2,115.93,2]
[QR1,115.83,5]
[MR2,115.56,3]
[DR2,115.53,1]
[WR1,114.79,2]
[DR1,114.59,1]
[WPP,113.99,2]
[DPP,113.89,1]
[MR1,113.50,3]
[DS1,112.95,1]
[WS1,112.85,2]
[DS2,112.25,1]
[WS2,112.05,2]
[DS3,111.31,1]
[MPP,110.97,3]
[WS3,110.91,2]
[50MA,110.87,4]
[MS1,108.91,3]
[QPP,108.64,5]
[MS2,106.37,3]
[MS3,104.31,3]
[QS1,104.25,5]
[SPP,103.53,6]
[200MA,99.42,7]
[QS2,97.05,5]
[YPP,96.68,8]
[SS1,94.03,6]
[QS3,92.66,5]
[YS1,80.34,8]
[SS2,76.62,6]
[SS3,67.12,6]
[YS2,49.23,8]
[YS3,32.89,8]
I did make a mistake with the original list in that Group C is wrong and should not be included. Thanks for pointing that out.
Also the 0.5% is not fixed this value will change from day to day, but I have just used 0.5% as an example for spec'ing the problem.
Thanks Again.
Mark
PS. I will get cracking on checking the answers now now.
Hi:
I need to do some manipulation of stock prices. I have just started using Python, (but I think I would have trouble implementing this in any language). I'm looking for some ideas on how to implement this nicely in python.
Thanks
Mark
Problem:
I have a list of lists (FloorLevels (see below)) where the sublist has two items (stockprice, weight). I want to put the stockprices into groups when they are within 0.5% of each other. A groups strength will be determined by its total weight. For example:
Group-A
115.93,2
115.83,5
115.56,3
115.53,1
-------------
TotalWeight:12
-------------
Group-B
113.50,3
112.95,1
112.85,2
-------------
TotalWeight:6
-------------
FloorLevels[
[175.24,8]
[147.85,6]
[144.13,8]
[130.44,6]
[127.79,8]
[127.42,5]
[120.94,6]
[120.22,5]
[118.10,3]
[116.73,2]
[116.23,1]
[115.93,2]
[115.83,5]
[115.56,3]
[115.53,1]
[114.79,2]
[114.59,1]
[113.99,2]
[113.89,1]
[113.50,3]
[112.95,1]
[112.85,2]
[112.25,1]
[112.05,2]
[111.31,1]
[110.97,3]
[110.91,2]
[110.87,4]
[108.91,3]
[108.64,5]
[106.37,3]
[104.31,3]
[104.25,5]
[103.53,6]
[99.42,7]
[97.05,5]
[96.68,8]
[94.03,6]
[92.66,5]
[80.34,8]
[76.62,6]
[67.12,6]
[49.23,8]
[32.89,8]
]
I suggest a repeated use of k-means clustering -- let's call it KMC for short. KMC is a simple and powerful clustering algorithm... but it needs to "be told" how many clusters, k, you're aiming for. You don't know that in advance (if I understand you correctly) -- you just want the smallest k such that no two items "clustered together" are more than X% apart from each other. So, start with k equal 1 -- everything bunched together, no clustering pass needed;-) -- and check the diameter of the cluster (a cluster's "diameter", from the use of the term in geometry, is the largest distance between any two members of a cluster).
If the diameter is > X%, set k += 1, perform KMC with k as the number of clusters, and repeat the check, iteratively.
In pseudo-code:
def markCluster(items, threshold):
k = 1
clusters = [items]
maxdist = diameter(items)
while maxdist > threshold:
k += 1
clusters = Kmc(items, k)
maxdist = max(diameter(c) for c in clusters)
return clusters
assuming of course we have suitable diameter and Kmc Python functions.
Does this sound like the kind of thing you want? If so, then we can move on to show you how to write diameter and Kmc (in pure Python if you have a relatively limited number of items to deal with, otherwise maybe by exploiting powerful third-party add-on frameworks such as numpy) -- but it's not worthwhile to go to such trouble if you actually want something pretty different, whence this check!-)
A stock s belong in a group G if for each stock t in G, s * 1.05 >= t and s / 1.05 <= t, right?
How do we add the stocks to each group? If we have the stocks 95, 100, 101, and 105, and we start a group with 100, then add 101, we will end up with {100, 101, 105}. If we did 95 after 100, we'd end up with {100, 95}.
Do we just need to consider all possible permutations? If so, your algorithm is going to be inefficient.
You need to specify your problem in more detail. Just what does "put the stockprices into groups when they are within 0.5% of each other" mean?
Possibilities:
(1) each member of the group is within 0.5% of every other member of the group
(2) sort the list and split it where the gap is more than 0.5%
Note that 116.23 is within 0.5% of 115.93 -- abs((116.23 / 115.93 - 1) * 100) < 0.5 -- but you have put one number in Group A and one in Group C.
Simple example: a, b, c = (0.996, 1, 1.004) ... Note that a and b fit, b and c fit, but a and c don't fit. How do you want them grouped, and why? Is the order in the input list relevant?
Possibility (1) produces ab,c or a,bc ... tie-breaking rule, please
Possibility (2) produces abc (no big gaps, so only one group)
You won't be able to classify them into hard "groups". If you have prices (1.0,1.05, 1.1) then the first and second should be in the same group, and the second and third should be in the same group, but not the first and third.
A quick, dirty way to do something that you might find useful:
def make_group_function(tolerance = 0.05):
from math import log10, floor
# I forget why this works.
tolerance_factor = -1.0/(-log10(1.0 + tolerance))
# well ... since you might ask
# we want: log(x)*tf - log(x*(1+t))*tf = -1,
# so every 5% change has a different group. The minus is just so groups
# are ascending .. it looks a bit nicer.
#
# tf = -1/(log(x)-log(x*(1+t)))
# tf = -1/(log(x/(x*(1+t))))
# tf = -1/(log(1/(1*(1+t)))) # solved .. but let's just be more clever
# tf = -1/(0-log(1*(1+t)))
# tf = -1/(-log((1+t))
def group_function(value):
# don't just use int - it rounds up below zero, and down above zero
return int(floor(log10(value)*tolerance_factor))
return group_function
Usage:
group_function = make_group_function()
import random
groups = {}
for i in range(50):
v = random.random()*500+1000
group = group_function(v)
if group in groups:
groups[group].append(v)
else:
groups[group] = [v]
for group in sorted(groups):
print 'Group',group
for v in sorted(groups[group]):
print v
print
For a given set of stock prices, there is probably more than one way to group stocks that are within 0.5% of each other. Without some additional rules for grouping the prices, there's no way to be sure an answer will do what you really want.
apart from the proper way to pick which values fit together, this is a problem where a little Object Orientation dropped in can make it a lot easier to deal with.
I made two classes here, with a minimum of desirable behaviors, but which can make the classification a lot easier -- you get a single point to play with it on the Group class.
I can see the code bellow is incorrect, in the sense the limtis for group inclusion varies as new members are added -- even it the separation crieteria remaisn teh same, you heva e torewrite the get_groups method to use a multi-pass approach. It should nto be hard -- but the code would be too long to be helpfull here, and i think this snipped is enoguh to get you going:
from copy import copy
class Group(object):
def __init__(self,data=None, name=""):
if data:
self.data = data
else:
self.data = []
self.name = name
def get_mean_stock(self):
return sum(item[0] for item in self.data) / len(self.data)
def fits(self, item):
if 0.995 < abs(item[0]) / self.get_mean_stock() < 1.005:
return True
return False
def get_weight(self):
return sum(item[1] for item in self.data)
def __repr__(self):
return "Group-%s\n%s\n---\nTotalWeight: %d\n\n" % (
self.name,
"\n".join("%.02f, %d" % tuple(item) for item in self.data ),
self.get_weight())
class StockGrouper(object):
def __init__(self, data=None):
if data:
self.floor_levels = data
else:
self.floor_levels = []
def get_groups(self):
groups = []
floor_levels = copy(self.floor_levels)
name_ord = ord("A") - 1
while floor_levels:
seed = floor_levels.pop(0)
name_ord += 1
group = Group([seed], chr(name_ord))
groups.append(group)
to_remove = []
for i, item in enumerate(floor_levels):
if group.fits(item):
group.data.append(item)
to_remove.append(i)
for i in reversed(to_remove):
floor_levels.pop(i)
return groups
testing:
floor_levels = [ [stock. weight] ,... <paste the data above> ]
s = StockGrouper(floor_levels)
s.get_groups()
For the grouping element, could you use itertools.groupby()? As the data is sorted, a lot of the work of grouping it is already done, and then you could test if the current value in the iteration was different to the last by <0.5%, and have itertools.groupby() break into a new group every time your function returned false.