In MiniZinc it is possible to use the search annotation impact, it is explained as follows on the official website:
annotation impact
Choose the variable with the highest impact so far during the search
What does this mean in practice? What is the highest impact? How is this calculated?
To understand the impact based variable selection, you have to understand first_fail. In constraint programming we generally want to solve the hardest sub-problem first, failing quickly if no solution can be found. The problem with first_fail is that it doesn't take into account the number of constraints that a variable is involved in, more would indicate that the a decision for the variable "harder", or the effect that choices on the variable had in other parts of the search-tree.
As a sidenote, dom_w_deg is can be seen as compromise between first_fail and impact, where the constraints are taken into account, but the past decision are not.
impact variable selection is supposed to be an improvement on first_fail where not just domain sizes are considered, but also the constraints it's involved in and how much "impact" historical choices had. The variable with the highest impact is the one that is expected to be the hardest to assign the right value, taking all of this information into account.
As you've seen, MiniZinc does not provide an exact specification of how the variable choice has to made. It is up to solver implementer to select a heuristic that fit the solver. Note that it would be hard to provide an exact heuristic guideline as it would heavily depend on how the solver tracks its variables and constraints.
For ideas on possible implementations of impact based heuristics, I would suggest reading the paper "On the Efficiency of Impact Based Heuristics" by Marco Correia and Pedro Barahona. You can also check your specific MiniZinc/FlatZinc solver for their implementation of the heuristic.
Related
I am coding a spell-casting system where you draw a symbol with your wand (mouse), and it can recognize said symbol.
There are two methods I believe might work; neural networking and an "invisible grid system"
The problem with the neural networking system is that It would be (likely) suboptimal in Roblox Luau, and not be able to match the performance nor speed I wish for. (Although, I may just be lacking in neural networking knowledge. Please let me know whether I should continue to try implementing it this way)
For the invisible grid system, I thought of converting the drawing into 1s and 0s (1 = drawn, 0 = blank), then seeing if it is similar to one of the symbols. I create the symbols by making a dictionary like:
local Symbol = { -- "Answer Key" shape, looks like a tilted square
00100,
01010,
10001,
01010,
00100,
}
The problem is that user error will likely cause it to be inaccurate, like this "spell"'s blue boxes, showing user error/inaccuracy. I'm also sure that if I have multiple Symbols, comparing every value in every symbol will surely not be quick.
Do you know an algorithm that could help me do this? Or just some alternative way of doing this I am missing? Thank you for reading my post.
I'm sorry if the format on this is incorrect, this is my first stack-overflow post. I will gladly delete this post if it doesn't abide to one of the rules. ( Let me know if there are any tags I should add )
One possible approach to solving this problem is to use a template matching algorithm. In this approach, you would create a "template" for each symbol that you want to recognize, which would be a grid of 1s and 0s similar to what you described in your question. Then, when the user draws a symbol, you would convert their drawing into a grid of 1s and 0s in the same way.
Next, you would compare the user's drawing to each of the templates using a similarity metric, such as the sum of absolute differences (SAD) or normalized cross-correlation (NCC). The template with the lowest SAD or highest NCC value would be considered the "best match" for the user's drawing, and therefore the recognized symbol.
There are a few advantages to using this approach:
It is relatively simple to implement, compared to a neural network.
It is fast, since you only need to compare the user's drawing to a small number of templates.
It can tolerate some user error, since the templates can be designed to be tolerant of slight variations in the user's drawing.
There are also some potential disadvantages to consider:
It may not be as accurate as a neural network, especially for complex or highly variable symbols.
The templates must be carefully designed to be representative of the expected variations in the user's drawings, which can be time-consuming.
Overall, whether this approach is suitable for your use case will depend on the specific requirements of your spell-casting system, including the number and complexity of the symbols you want to recognize, the accuracy and speed you need, and the resources (e.g. time, compute power) that are available to you.
I have estimated a complex hierarchical model with many random effects, but don't really know what the best approach is to checking for convergend. I have complex longitudinal data from a few hundred individuals and estimate quite a few parameters for every individual. Because of that, I have way to many traceplots to inspect visually. Or should I really spend a day going through all the traceplots? What would be a better way to check for convergence? Do I have to calculate Gelman and Rubin's Rhat for every parameter on the person level? And when can I conclude that the model converged? When absolutely all of the thousends of parameters reached convergence? Is it even sensible to expect that? Or is there something like "overall convergence"? And what does it mean when some person-level parameters did not converge? Does it make sense to use autorun.jags from the R2jags package with such a model or will it just run for ever? I know, these are a lot of question, but I just don't know how to approach that.
The measure I am using for convergence is a potential scale reduction factor (psrf)* using the gelman.diag function from the R package coda.
But nevertheless, I am also quickly visually inspecting all the traceplots, even though I also have tens/hundreds of them. It can be really fast if you put them in PNG files and then quickly go through them using e.g. IrfanView (let me know if you need me to expand on this).
The reason you should inspect the traceplots is pretty well described by an example from Marc Kery (author of great Bayesian books): see "Never blindly trust Rhat for convergence in a Bayesian analysis", here I include a self explanatory image from this email:
This is related to Rhat statistics while I use psrf, but it's pretty likely that psrf suffers from this too... and better to check the chains.
*) Gelman, A. & Rubin, D. B. Inference from iterative simulation using multiple sequences. Stat. Sci. 7, 457–472 (1992).
At the moment, my problem has four metrics. Each of these measures something entirely different (each has different units, a different range, etc.) and each is weighted externally. I am using Drools for scoring.
I only have only one score level (SimpleLongScore) and I have to find a way to appropriately combine the individual scores of these metrics onto one long value
The most significant problem at the moment is that the range of values for the metrics can be wildly different.
So if, for example, after a move the score of a metric with a small possible range improves by, say, 10%, that could be completely dwarfed by an alternate move which improves the metric with a larger range's score by only 1% because OptaPlanner only considers the actual score value rather than the possible range of values and how changes affect them proportionally (to my knowledge).
So, is there a way to handle this cleanly which is already part of OptaPlanner that I cannot find?
Is the only feasible solution to implement Pareto scoring? Because that seems like a hack-y nightmare.
So far I have code/math to compute the best-possible and worst-possible scores for a metric that I access from within the Drools and then I can compute where in that range a move puts us, but this also feel quite hack-y and will cause issues with incremental scoring if we want to scale non-linearly within that range.
I keep coming back to thinking I should just just bite the bullet and implement Pareto scoring.
Thanks!
Take a look at #ConstraintConfiguration and #ConstraintWeight in the docs.
Also take a look at the chapter "explaning the score", which can exactly tell you which constraint had which score impact on the best solution found.
If, however, you need pareto optimization, so you need multiple best solutions that don't dominate each other, then know that OptaPlanner doesn't support that yet, but I know of 2 cases that implemented it in OptaPlanner by hacking BestSolutionRecaller.
That being said, 99% of the cases that think of pareto optimization, are 100% happy with #ConstraintWeight instead, because users don't want multiple best solutions (except during simulations), they just want one in production.
I am using the SymbolicTransformer of gplearn to generate some automated features. The issue is, when I inspect the expression of the features via looking at _best_programs after fitting, I find that most of the features have the same expression. I am wondering whether there is a way to ensure that we output different features using SymbolicTransformer after fitting?
I don't know if there is a way to explicitly enforce this but you can probably try to enforce more diverse populations each generation in the hopes that this leads to a a collection of more diverse _best_programs. In my opinion a few parameters you could look into are:
p_crossover
p_subtree_mutation
p_hoise_mutation
p_point_mutation
p_point_replace
If you increase the chance of crossover or mutation you will increase your expected diversity but you must not overdue it. There is a balance between a diverse population and an accurate one. The higher the crossover or mutation the more likely that you will take a strong individual candidate and change it into something meaningless.
How to set values to all the variables that could be possibly used as iteration variables, for example, there is a heat exchanger which includes a few connectors, and each connector includes a few variables, I can't know which variables could be used as iteration variables, when dealing with initialization, do I need to set values to every variable so that no matter which variable is chosen as iteration variable, there is a reasonable value?
Marvel,
I think that you are a bit on the wrong track for finding a solution: setting values to all variables that possibly could become iteration variables is often too many, and will lead to errors and problems. But I think I can give you some useful advice in any case.
Alias variables: there are many alias variable sin Modelica models. You should always try to only select one of them to set start values.
Feedback between start values and iteration variables: most Modelica tools will prefer to select iteration variables that have start values set. Selecting fewer thus can guide the algorithm towards selecting good one. Therefore: don't overdo it.
General advice for selecting iteration variables. For a pure ODE, the states will always be a complete set of start variables, even if sometimes not the best one. For DAE you can start with the following exercise: think of all equations that result from a singular perturbation of the complete physics as differential equations with states. For example, in a heat exchanger, you need to consider the dynamic momentum balance and not the most often used static reduction to an algebraic pressure loss only, i.e. add the mass flow as a state. Similar in chemical reactions: think of it as Kinetics, not equilibrium reactions. That gives you a pretty good starting point, even though often not the best one.
If your troubles don't quite resolve from that, I recommend that you contact us via www.modelon.com: we have advanced ways of dealing with hard initialization and steady state problems in our Modelic tool. :-)
There is also a simplest way to answer your question, working quite well with fluid models.
Giving the fact that you are using a dynamic model, what you need to initialize are the state variables of your system. To know the state variables, either you know the type of model you are wirking with or you can dig through them using options like 'List continuous time states selected' in Dymola (I do not know about other tools), giving you the state variables in the translation log.
In case of fluid models, most of the times those are pressure and energy (enthalpy or temperature). All other variables will be calculated based on them.
For complex (or not) models, this approach show limits, which can sometimes be solved by changing/correcting the structure of the model.
Static models are something else...
Hope this can help :)