I am wondering whether it is possible to create constraints over years and hours at the same time in Pyomo.
For example, my current time variable is:
model.T = pyo.RangeSet(len(hourly_data.index))
However, this does not allow me to distinguish between hours and years. I do have a timestamp variable, that contains the date and the time. So, I thought perhaps I could do:
model.T2 = pyo.Set(initialize=hourly_data.DateTime)
Now the problem comes on how to manipulate this TimeStamp object. Consider that the parameters are given and the variables are outputs from the solver. Let's first assume that our objective function is a maximisation function. We would like to create the following constraint:
Get the maximum water used, in normal circumstances, if we would like to get the maximum water usage of during all hours, we can do:
model.c_maxWater = pyo.ConstraintList()
for t in model.T:
model.c_maxWater.add(model.waterUsage[t] <=
model.maxWater)
With a penalty in the objective function associated with model.maxWater. The problem becomes what if we want to penalise every year differently, because we have different water costs? I can imagine that our constraint would be somewhat like:
model.c_maxWater = pyo.ConstraintList()
for t in model.T2:
model.c_maxWater.add(model.waterUsage[t] <=
model.maxWater[y])
My problem is: how can I associate the t variable with certain years y. One index is hourly (in this case the t and the other is annually (y)?
Note: a multi index set is possible, but how to deal with leap years etc.? Can a multi index set have different lengths in it's hourly dimensions for leap years?
You could double-index your variables and data with [hour, year], but that would be redundant information, right? As you should be able to calculate the years from the hours (with or without some initial offset for the yearly rollover, if that is important.)
I would go about this making subsets of your time index associated with years. Do this outside of pyomo using set/list comprehensions and a little math and/or some of the functionality in DateTime if (as you say) you are spanning many years and leap years, etc. [Aside: If you are making an hourly model that spans years--it will probably collapse under it's own weight, but that is a secondary issue. :) ] Then you can use these subsets to build constraints in your model without muddying things up with extra indices.
Comment back if stuck...
Related
I am applying the VRP example of optaplanner with time windows and I get feasible solutions whenever I define time windows in a range of 24 hours (00:00 to 23:59). But I am needing:
Manage long trips, where I know that the duration between leaving the depot to the first visit, or durations between visits, will be more than 24 hours. So currently it does not give me workable solutions, because the TW format is in 24 hour format. It happens that when applying the scoring rule "arrivalAfterDueTime", always the "arrivalTime" is higher than the "dueTime", because the "dueTime" is in a range of (00:00 to 23:59) and the "arrivalTime" is the next day.
I have thought that I should take each TW of each Customer and add more TW to it, one for each day that is planned.
Example, if I am planning a trip for 3 days, then I would have 3 time windows in each Customer. Something like this: if Customer 1 is available from [08:00-10:00], then say it will also be available from [32:00-34:00] and [56:00-58:00] which are the equivalent of the same TW for the following days.
Likewise I handle the times with long, converted to milliseconds.
I don't know if this is the right way, my consultation would be more about some ideas to approach this constraint, maybe you have a similar problematic and any idea for me would be very appreciated.
Sorry for the wording, I am a Spanish speaker. Thank you.
Without having checked the example, handing multiple days shouldn't be complicated. It all depends on how you model your time variable.
For example, you could:
model the time stamps as a long value denoted as seconds since epoch. This is how most of the examples are model if I remember correctly. Note that this is not very human-readable, but is the fastest to compute with
you could use a time data type, e.g. LocalTime, this is a human-readable time format but will work in the 24-hour range and will be slower than using a primitive data type
you could use a date time data tpe, e.g LocalDateTime, this is also human-readable and will work in any time range and will also be slower than using a primitive data type.
I would strongly encourage to not simply map the current day or current hour to a zero value and start counting from there. So, in your example you denote the times as [32:00-34:00]. This makes it appear as you are using the current day midnight as the 0th hour and start counting from there. While you can do this it will affect debugging and maintainability of your code. That is just my general advice, you don't have to follow it.
What I would advise is to have your own domain models and map them to Optaplanner models where you use a long value for any time stamp that is denoted as seconds since epoch.
Let's assume a variation on Nurse Rostering example in which instead of assigning a nurse to a shift on a day, the nurse is assigned to a variable number of timeblocks on that day (which consists of 24 timeblocks). eg: Nurse1 is assigned to timeblocks [8,9,10,11,12,13,14]. Let's call these consecutive assignments a ShiftPeriod. There is a hard minimum and maximum on these shiftperiods. However, optaplanner has difficulties finding a feasible solution.
When having hard consecutive constraints, is it better to model the planning entity as a startTimeBlock with a duration instead of my current way with assignment to a timeblock and a day and then imposing min/max consecutive?
Take a look at the meeting scheduling example on github master for 6.4.0.Beta1 (but the example will work perfectly with 6.3.0.Final too). Video and docs coming soon. That example uses the design pattern TimeGrains, which is what you're looking for I think.
I was wondering if anyone has code for a BUGS/JAGS model for a repeated measures ANOVA? Basically, I have a response (y) that I want to model against Time of day, Day, and Treatment. I would also like to include two interaction terms, Treatment x Time of Day and Treatment x Day. There are about 20 individuals in the study, who were measured 4 times per day over about 1 week. I'm not entirely sure where to start, and I'm concerned that the Time of day covariate should also be nested within the Day covariate? If anyone has code for the likelihood portion of the BUGS/JAGS model, it would be greatly appreciated. I can take care of priors. Just can't seem to get off the ground with this one.
There are a few ambiguities in your question.
Do you want Time of Day and Day to enter as continuous covariates or as discrete factors?
Do you want individual identity to enter the model as a fixed or random effect?
If either Day or Time of Day is a factor, do you want to include it as a fixed or random effect?
You ask about whether Time of Day should be nested within Day. This is impossible to answer without knowing more about your data and your aims.
Here's an example of code that assumes that you want to treat individuals as a random effect.
Also assumed: Treatment, Time.of.day, and Day have constant slopes across all individuals. It would be straightforward to extend this model to a fixed- or random-slopes model where different individuals get separate modeled slopes. For example, for a random-slopes model, you'd just modify the beta parameters below to treat them in a manner similar to the alpha parameter.
Following the OP's request, this is the likelihood portion only, and does not include the priors.
for(i in 1:n.observations){
y[i] ~ dnorm(alpha[individual[[i]] + beta1*Day[i] + beta2*Time.of.day[i] + beta3*Treatment[i] + beta4*Treatment[i]*Day[i] + beta5*Treatment[i]*Time.of.day[i], tau.obs)
}
# individual[i] contains the numerical index representing the individual that corresponds to observation i.
for(j in 1:n.individuals){
alpha[j] ~ dnorm(mu, tau)
}
I'm using AMPL to model a production where I have two particular constraints that I am not very sure how to handle.
subject to Constraint1 {t in T}:
prod[t] = sum{i in I} x[i,t]*u[i] + Recycle[f]*RecycledU[f];
subject to Constraint2 {t in T}:
Solditems[t]+Recycle[t]=prod[t];
EDIT: where x[i,t] is the amount of products from supply point i. u[i] denotes the "exchange rate" of the raw material from supply point i to create the product. I.E. a percentage of the raw material will become the finished products, whereas some raw material will go to waste. The same is true for RecycledU[f] where f is in F, which denotes the refinement station where it has been refined. The difference is that RecycledU[f] has a much lower percentage that will go to waste due to Recycled already being a finished product from f (albeitly a much less profitable one). I.e. Recycle has already "went through" the process of being a raw material earlier, x, but has become a finished product in some earlier stage, or hopefully (if it can be modelled) in the same time period as this. In the actual models things as "products" and "refinement station" is existent as well, but I figured for this question those could be abandoned to keep it more simple.
What I want to accomplish is that the amount of products produced is the sum of all items sold in time period t and the amount of products recycled in time period t (by recycled I mean that the finished product is kept at the production site for further refinement in some timestep g, g>t).
Is it possible to write two equal signs for prod[t] like I have done? Also, how to handle Recycle[t]? Can AMPL "understand" that since these are represented at the same time step, that AMPL must handle the constraints recursively, i.e. compute a solution for Recycle[t] and subsequently try to improve that solution in every timestep?
EDIT: The time periods are expressed in years which is why I want to avoid having an expression with Recycle[t-1].
EDIT2: prod and x are parameters and Recycle and Solditems are variables.
Hope anyone can shed some light into this!
Cenderze
The two constraints will be considered simultaneously (unless you explicitly exclude one from the problem). AMPL or optimization solvers don't have the notion of time steps and the complete problem is considered at the same time, so you might need to add some linking constraints between time periods yourself to model time periods. In particular, you might need to make sure that the inventory (such as the amount finished product is kept at the production site for further refinement) is carried over from one period to another, something like:
Recycle[t + 1] = Recycle[t] - RecycleDecrease + RecycleIncrease;
You have to figure out the expressions for the amounts by which Recycle is increased (RecycleIncrease) and decreased (RecycleDecrease).
Also if you want some kind of an iterative procedure with one constraint considered at a time instead, then you should use AMPL script.
Ok, I'm just curious what the formula would be for calculating an expected income over the next X weeks/months/etc, if the only data I have in mySQL DB is all past transactions (dates of transactions, amounts, etc)
I am thinking taking some averages and whatnot, but I can't think of a specific formula (there must be something along those lines) to take say average rise of income over time (weekly/monthly) and then apply it to a select future period and display it weekly/monthly/etc?
Any suggestions?
use AVG() on the income in the past devide it to proper weekly/monthly amounts if neccessary.
see http://dev.mysql.com/doc/refman/5.1/en/group-by-functions.html#function_avg for more info on AVG()
Linear regression + simple integration is probably sufficient for your needs. I leave sorting out exact implementation for your DB up to you, but that follow that link to the "Estimation Methods" section, and probably use Ordinary Least Squares.
Alternatively, you can always slurp your data into something like R where the details are already implemented.
EDIT:
For more detail: you're trying to model INCOME = BASE + SCALING*T where we are assuming that a linear model is "good" (it's probably not great, but it's probably good enough on a short time scale). For two value linear regression, you're pretty much just taking averages; follow that link to "Fitting the Regression Line" and you'll see which things you need to average (y = INCOME and x = T). There are some tricks you can play to simplify the calculation for the computer if you can enforce some other conditions (e.g., having equally spaced time periods + no missing data), but you'll need to math a bit more yourself first if you want to do that (and you'll be less flexible in the face of changing db assumptions).