I am trying to explore a riddle with MiniZinc. I have a weighing platter, and I need 4 weighs satisfying two constraints:
their sum is 40kg
it should be able to weigh any weight between 1 and 40 with them
But the second constraint is in my mind rephrased as "there exists a combination of the weights so that..." and this seems difficult/inadapted for me in MiniZinc. Is there a natural way to express this constraint in MiniZinc?
Thanks in advance!
It very much depends on what you mean by "natural". I wrote a model of this problem some years ago and to me it's natural (at least after some thoughts).
Here is a hint that might help.
Think of each of the four weights as either at the right pan, the left pan or not involved in the measurement of each specific weight (1..40kg). If the weight is at the right pan then it has "positive" weight, if at the left pan it has "negative weight". And 0 otherwise.
Does that help at all?
Related
Sorry for long post. I am newbie in agent-based modelling. So please accept my apology in advance if my question sounds stupid. I am trying to model a scenario where framer (i.e. agent) decides which type of crop should be harvest in different types of fields to increase the profit. The farmer agent has a budget i.e. the amount of money that can be spent on farming each time step equal to $100.
The farmer operates a farm that is subdivided into nine fields, which are arranged in a 3x3
cellular grid. Each field is of the same size. Water availability varies spatially across the fields with a rating of either 1 (driest), 2 (moderate),
or 3 (wettest). The manner in which water availability varies across the fields (i.e. randomly).
The farmer must choose among three crops. As initial parameter settings, the crops have the
following characteristics:
Yield Price Costs Minimum Water Req.
Crop 1 300 20 15 3
Crop 2 200 12 10 2
Crop 3 100 7 5 1
Each crop requires a certain amount of water to grow. Crop yields will only be realized if the crop is
planted in a field with at least the crop’s minimum water requirement.
Now the problem is that I couldn't find any function in Netlogo that calculates the permutation or combination of crop, field, and water requirements to calculate the expected profit. Any help would be high appreciated.
I believe you describe a linear programming problem.
Useful functions for solving Simplex Linear Programming problems are in NumAnal extension, which does not come bundled with NetLogo but which you can get as follows:
In NetLogo, under Tools / Extensions ... you can find NumAnal, probably with no green check-mark. Select it. On the right, you have buttons to install it, and then one to add it to your code. When you click those, it should now get a green checkmark and you should have a new line in your code "extensions [ numanal ]", and you are now able to use those commands, with the "numanal:" prefix, for example, numanal:simplex.
The documentation for it is in the folder where it was installed. But where is that?
Sadly, the documentation for where extensions are downloaded is not current.
https://ccl.northwestern.edu/netlogo/docs/extensions.html#where-extensions-are-located
After exhaustive search by date-modified, I actually found the folder on my Windows 10 laptop here: c:\Users\condor\AppData\Roaming\NetLogo\6.1\extensions
( Note the "\Roaming\" ).
That folder has a README.md text file, and a pdf document named "NumAnal-v3.4.0" explaining how to use it, and an examples folder with code. It is a little dense.
Here's a link to the basics of how to describe a Linear Programming problem, which is beyond the scope of StackOverflow. You can find help via Google.
Here's one 8 minute video ( as of 24-Nov-2019) that might help you figure out if this is what you need.
Simplex Algorithm Explanation (How to Solve a Linear Program)
https://www.youtube.com/watch?v=RO5477EKlXE
I am attempting to cluster a group of customers based on spend, order frequency, order breadth and what % of purchases they make in each category (there are around 20).
It will probably be a simple answer but I cannot figure out whether I should standardize (subtract mean and divide by sd) the % category buy columns or not. When I dont standardize I can get around 90% of the variance explained in 4-5 principal components (using SVD), but when I standardize each column I only get around 40% for the same number of principal components. My worry is that because each column is related, I am removing the relationship by standardizing. At the same time I am worried that not standardizing will cause issues with the other variables in the data that I have standardized.
I would assume if others tried clustering in this way they would face a similar issue but I cant seem to find one so it might be that I just dont understand the situation. Thanks for any clarification in advance!
Chris,
Percentage scale has a well defined range and nice properties.
By heuristically scaling these features you usually make things worse.
Can we get top 3 best scores using constraints in Optaplanner?
For eg i have a use case where i need to show top 3 results which has highest score to user so that user can select the solution according to their need.
Sounds like pareto optimization (see docs). Not yet supported in OptaPlanner officially.
But users have hacked it before, by implementing their own BestSolutionRecaller (= that class that holds the best solution(s)) and replacing the DefaultSolver's bestSolutionRecaller with it. This implies "taking the red pill" and "following the rabbit hole down to wonderland". Good luck :)
Important note: Pareto optimization goes much further than just remember the n best solutions. It's about remember the n best solutions which aren't dominated by one of the other best solutions. So it entails changing the score comparison (and breaking the transitive aspect of score comparison).
I am implementing an app which measures the how much distance it has moved .For example if my device felldown from my table to ground ,then I would like to calculate the distance.So Kindly help me to do this. Let me know if my question is not clear.
Thanks in advance.
Your question is very clear : you want to compute the second level integral of the acceleration, which theorically is possible, by supposing the speed null at some time, but I really doubt you could get something precise enough to make any sense (as in many integral computations).
This isn't done today because the error is too big. Done in hardware (for permanent integration of the acceleration) it could be a little more precise but probably not enough to really compute a distance in any acceptable sense of the word "accuracy".
If you want to try it by yourself, here's a document describing more in detail the approach : http://perso-etis.ensea.fr/~pierandr/cours/M1_SIC/AN3397.pdf
I'm doing a map-coloring problem with Scheme, and I used minimum remaining values (Select the vertex with the fewest legal colors) and degree heuristics select the vertex that has the largest number of neighbors). If there exists a solution for a certain configuration, will these heuristics ensures that it won't need to backtrack?
Let's do a simple theoretical analysis.
Graph coloring is NP-complete for general graphs (if not asking for a coloring with less than 4 colors). This means there exists no known polynomial time algorithm.
Your heuristic is computable in polynomial time.
Assuming you need no backtracking, then you need to make n steps, each of which requires polynomial time (n is number of vertices). Thus you can solve the problem in polynomial time.
Either you have proven P=NP or your assumption is wrong.
I leave it up to you to decide upon which option in point (4) is more plausible.
In general: no, MRV and your other heuristic will not guarantee a straight walk to the goal. (I imagine they might if your problem has some very specific structure, but don't count on it until you've seen the theorem.)
Heuristics prune the search space, or change the order of the search to make an early termination more likely. This is not the same thing as backtracking.
But it's a related concept.
We prune some spaces because we are confident that the solution does not lie in those branches of the search tree, or change the order because we have some reason to believe that it will be quicker if we look in some subtrees before others.
We also cut ourselves off from backtracking because we are confident that the solution is in the branch of the space we are in now (so that if we don't find it in this subtree, we can declare failure and don't bother).
Both kinds of strategies are ultimately about searching less of the space somehow and getting to the answer (positive or negative) without searching everything.
MRV and the degrees heuristic are about reordering the sub-searches, not about avoiding backtracking. Heuristics can be right and make a short search but that's not the same
thing as eliminating backtracking (e.g. the "cut" operator in Prolog). When you find what you're looking for, you can declare success, and of course that eliminates further backtracking. But real backtracking elimination means making a decision not to backtrack no matter what, before the search completes.
E.g. if you're doing a depth-first search, and you find what you're looking for by dumb luck without backtracking, we cannot say that dumb luck is a fence operation that eliminates backtracking. :)