I have a 2d grid where certain cell values produce different scores, and I want to maximize the score by assigning values to cells. Is it possible to trace each grid the solver tried during the solve? Below is a snippet of the model just to demonstrate the idea.
int: i_count;
int: e_count;
set of 1..3: ROW;
set of 1..3: COL;
enum CELL = { U, I, E };
array[ROW,COL] of var CELL: grid;
constraint sum(r in ROW, c in COL)(grid[r, c] = I) <= i_count;
constraint sum(r in ROW, c in COL)(grid[r, c] = E) <= e_count;
var int: assignment_gain = sum(r in ROW, c in COL)(
let {var CELL: cell = grid[r,c]} in (cell = I) * I_SCORE + (cell = E) * E_SCORE
);
solve maximize assignment_gain;
output
["Max assignment_gain: \(assignment_gain), with below grid:\n"] ++
["\(grid[r,c])" ++ if c = n then "\n" else "" endif
| r in ROW, c in COL];
I tried putting trace into the assignment_gain statement like below, but didn't work, the output sample is:
grid[1,1]=X_INTRODUCED_0_, grid[1,2]=X_INTRODUCED_1_, ...
var int: assignment_gain = sum(r in ROW, c in COL)(
let {var CELL: cell = trace("grid[\(r),\(c)]=\(grid[r,c]), ", grid[r,c])} in (cell = I) * I_SCORE + (cell = E) * E_SCORE
);
The trace function included in MiniZinc allows you to output expression at the compilation stage. This does not allow you to trace the expression during solving.
The options to see the values of variables during solving, depend on what values you want to see.
It is easy in MiniZinc to see intermediate solutions. So solutions found by the solver that are not yet optimal, but do satisfy all constraints. To see these solutions you can add the --intermediate-solutions on command line. In the MiniZincIDE, this should be default behaviour, but you can configure this by clicking "Show configuration editor".
If, on the other hand, you want to explore the values of variables during search (i.e., which values the solver tries for certain variables), then you have to dig a little deeper. MiniZinc supports many kinds of solvers, and they use different kinds of algorithms to find the solution. Therefore there is no standard way for MiniZinc to interact (or show) the search in the solver. Some solvers do however have tools to allow you to examine/debug the search. For example:
Chuffed, Gecode, and some other solvers use "CPProfiler", which has recently been integrated in the MiniZincIDE. You can activate it by clicking "MiniZinc > Profile Search" in the toolbar. This tool can help you visualise the search tree and even analyse the no-good learning in LCG solvers.
The standard MiniZinc distribution includes "Gecode Gist", which has specialised search analyses for Gecode. It will also show the search tree and decisions made, but has a few more sophisticated tools to inspect nodes in the search tree.
These are the tools shipped with MiniZinc, but for other MiniZinc solvers, more tools might be available.
Related
A little bit of background. I'm trying to make a model for clustering a Design Structure Matrix(DSM). I made a draft model and have a couple of questions. Most of them are not directly related to DSM per se.
include "globals.mzn";
int: dsmSize = 7;
int: maxClusterSize = 7;
int: maxClusters = 4;
int: powcc = 2;
enum dsmElements = {A, B, C, D, E, F,G};
array[dsmElements, dsmElements] of int: dsm =
[|1,1,0,0,1,1,0
|0,1,0,1,0,0,1
|0,1,1,1,0,0,1
|0,1,1,1,1,0,1
|0,0,0,1,1,1,0
|1,0,0,0,1,1,0
|0,1,1,1,0,0,1|];
array[1..maxClusters] of var set of dsmElements: clusters;
array[1..maxClusters] of var int: clusterCard;
constraint forall(i in 1..maxClusters)(
clusterCard[i] = pow(card(clusters[i]), powcc)
);
% #1
% constraint forall(i, j in clusters where i != j)(card(i intersect j) == 0);
% #2
constraint forall(i, j in 1..maxClusters where i != j)(
card(clusters[i] intersect clusters[j]) == 0
);
% #3
% constraint all_different([i | i in clusters]);
constraint (clusters[1] union clusters[2] union clusters[3] union clusters[4]) = dsmElements;
var int: intraCost = sum(i in 1..maxClusters, j, k in clusters[i] where k != j)(
(dsm[j,k] + dsm[k,j]) * clusterCard[i]
) ;
var int: extraCost = sum(el in dsmElements,
c in clusters where card(c intersect {el}) = 0,
k,j in c)(
(dsm[j,k] + dsm[k,j]) * pow(card(dsmElements), powcc)
);
var int: TCC = trace("\(intraCost), \(extraCost)\n", intraCost+extraCost);
solve maximize TCC;
Question 1
I was under the impression, that constraints #1 and #2 are the same. However, seems like they are not. The question here is why? What is the difference?
Question 2
How can I replace constraint #2 with all_different? Does it make sense?
Question 3
Why the trace("\(intraCost), \(extraCost)\n", intraCost+extraCost); shows nothing in the output? The output I see using gecode is:
Running dsm.mzn
intraCost, extraCost
clusters = array1d(1..4, [{A, B, C, D, E, F, G}, {}, {}, {}]);
clusterCard = array1d(1..4, [49, 0, 0, 0]);
----------
<sipped to save space>
----------
clusters = array1d(1..4, [{B, C, D, G}, {A, E, F}, {}, {}]);
clusterCard = array1d(1..4, [16, 9, 0, 0]);
----------
==========
Finished in 5s 419msec
Question 4
The expression constraint (clusters[1] union clusters[2] union clusters[3] union clusters[4]) = dsmElements;, here I wanted to say that the union of all clusters should match the set of all nodes. Unfortunately, I did not find a way to make this big union more dynamic, so for now I just manually provide all clusters. Is there a way to make this expression return union of all sets from the array of sets?
Question 5
Basically, if I understand it correctly, for example from here, the Intra-cluster cost is the sum of all interactions within a cluster multiplied by the size of the cluster in some power, basically the cardinality of the set of nodes, that represents the cluster.
The Extra-cluster cost is a sum of interactions between some random element that does not belong to a cluster and all elements of that cluster multiplied by the cardinality of the whole space of nodes to some power.
The main question here is are the intraCost and extraCost I the model correct (they seem to be but still), and is there a better way to express these sums?
Thanks!
(Perhaps you would get more answers if you separate this into multiple questions.)
Question 3:
Here's an answer on the trace question:
When running the model, the trace actually shows this:
intraCost, extraCost
which is not what you expect, of course. Trace is in effect when creating the model, but at that stage there is no value of these two decision values and MiniZinc shows only the variable names. They got some values to show after the (first) solution is reached, and can then be shown in the output section.
trace is mostly used to see what's happening in loops where one can trace the (fixed) loop variables etc.
If you trace an array of decision variables then they will be represented in a different fashion, the array x will be shown as X_INTRODUCED_0_ etc.
And you can also use trace for domain reflection, e.g. using lb and ub to get the lower/upper value of the domain of a variable ("safe approximation of the bounds" as the documentation states it: https://www.minizinc.org/doc-2.5.5/en/predicates.html?highlight=ub_array). Here's an example which shows the domain of the intraCost variable:
constraint
trace("intraCost: \(lb(intraCost))..\(ub(intraCost))\n")
;
which shows
intraCost: -infinity..infinity
You can read a little more about trace here https://www.minizinc.org/doc-2.5.5/en/efficient.html?highlight=trace .
Update Answer to question 1, 2 and 4.
The constraint #1 and #2 means the same thing, i.e. that the elements in clusters should be disjoint. The #1 constraint is a little different in that it loops over decision variables while the #2 constraint use plain indices. One can guess that #2 is faster since #1 use the where i != j which must be translated to some extra constraints. (And using i < j instead should be a little faster.)
The all_different constraint states about the same and depending on the underlying solver it might be faster if it's translated to an efficient algorithm in the solver.
In the model there is also the following constraint which states that all elements must be used:
constraint (clusters[1] union clusters[2] union clusters[3] union clusters[4]) = dsmElements;
Apart from efficiency, all these constraints above can be replaced with one single constraint: partition_set which ensure that all elements in dsmElements must be used in clusters.
constraint partition_set(clusters,dsmElements);
It might be faster to also combine with the all_different constraint, but that has to be tested.
Solving a triangle means finding all possible triangles when some of its sides a,b and c and angles A,B,C (A is the the angle opposite to a, and so on...) are known. This problem has 0, 1, 2 or infinitely many solutions.
I want to write a procedure to solve triangles. The user would feed the procedure with some datas amongst a,b,c,A,B,and C (if it is necessary for the sake of simplicity, you can assume that the user will avoid situations where there are infinitely many solutions) and the procedure will compute the other ones. The usual requires to use the Law of Sines or the Law of Cosines, depending on the situation.
Since it is for a Maths class where I also want to show graphs of functions, I will implement it in Maple. If Maple is not suitable for your answer, please suggest another language (I am reasonably competent in Java and beginner in Python for example).
My naive idea is to use conditional instructions if...then...else to determine the case in hand but it is a little bit boring. Java has a switch that could make things shorter and clearer, but I am hoping for a smarter structure.
Hence my question: Assume that some variables are related by known relations. Is there a simple and clear way to organize a procedure to determine missing variables when only some values are given?
PS: not sure on how I should tag this question. Any suggestion is welcome.
One approach could be to make all of the arguments to your procedure optional with default values that correspond to the names: A, B, C, a, b, c.
Since we can make the assumption that all missing variables are those that are not of type 'numeric', it is easy for us to then quickly determine which variables do not yet have values and give those as the values to a solve command that finds the remaining sides or angles.
Something like the following could be a good start:
trisolve := proc( { side1::{positive,symbol} := A, side2::{positive,symbol} := B, side3::{positive,symbol} := C,
angle1::{positive,symbol} := a, angle2::{positive,symbol} := b, angle3::{positive,symbol} := c } )
local missing := remove( hastype, [ side1, side2, side3, angle1, angle2, angle3 ], numeric );
return solve( { 180 = angle1 + angle2 + angle3,
side1/sin(angle1*Pi/180)=side2/sin(angle2*Pi/180),
side1/sin(angle1*Pi/180)=side3/sin(angle3*Pi/180),
side2/sin(angle2*Pi/180)=side3/sin(angle3*Pi/180),
side1^2=side2^2+side3^2-2*side2*side3*cos(angle1) },
missing );
end proc:
The following call:
trisolve( side1 = 1, angle1 = 90, angle2 = 45 );
returns:
[B = (1/2)*sqrt(2), C = (1/2)*sqrt(2), c = 45]
I'm using RandomForest for classification, and I got an unbalanced dataset, as: 5830-no, 1006-yes. I try to balance my dataset with class_weight and sample_weight, but I can`t.
My code is:
X_train,X_test,y_train,y_test = train_test_split(arrX,y,test_size=0.25)
cw='auto'
clf=RandomForestClassifier(class_weight=cw)
param_grid = { 'n_estimators': [10,50,100,200,300],'max_features': ['auto', 'sqrt', 'log2']}
sw = np.array([1 if i == 0 else 8 for i in y_train])
CV_clf = GridSearchCV(estimator=clf, param_grid=param_grid, cv= 10,fit_params={'sample_weight': sw})
But I don't get any improvement on my ratios TPR, FPR, ROC when using class_weight and sample_weight.
Why? Am I doing anything wrong?
Nevertheless, if I use the function called balanced_subsample, my ratios obtain a great improvement:
def balanced_subsample(x,y,subsample_size):
class_xs = []
min_elems = None
for yi in np.unique(y):
elems = x[(y == yi)]
class_xs.append((yi, elems))
if min_elems == None or elems.shape[0] < min_elems:
min_elems = elems.shape[0]
use_elems = min_elems
if subsample_size < 1:
use_elems = int(min_elems*subsample_size)
xs = []
ys = []
for ci,this_xs in class_xs:
if len(this_xs) > use_elems:
np.random.shuffle(this_xs)
x_ = this_xs[:use_elems]
y_ = np.empty(use_elems)
y_.fill(ci)
xs.append(x_)
ys.append(y_)
xs = np.concatenate(xs)
ys = np.concatenate(ys)
return xs,ys
My new code is:
X_train_subsampled,y_train_subsampled=balanced_subsample(arrX,y,0.5)
X_train,X_test,y_train,y_test = train_test_split(X_train_subsampled,y_train_subsampled,test_size=0.25)
cw='auto'
clf=RandomForestClassifier(class_weight=cw)
param_grid = { 'n_estimators': [10,50,100,200,300],'max_features': ['auto', 'sqrt', 'log2']}
sw = np.array([1 if i == 0 else 8 for i in y_train])
CV_clf = GridSearchCV(estimator=clf, param_grid=param_grid, cv= 10,fit_params={'sample_weight': sw})
This is not a full answer yet, but hopefully it'll help get there.
First some general remarks:
To debug this kind of issue it is often useful to have a deterministic behavior. You can pass the random_state attribute to RandomForestClassifier and various scikit-learn objects that have inherent randomness to get the same result on every run. You'll also need:
import numpy as np
np.random.seed()
import random
random.seed()
for your balanced_subsample function to behave the same way on every run.
Don't grid search on n_estimators: more trees is always better in a random forest.
Note that sample_weight and class_weight have a similar objective: actual sample weights will be sample_weight * weights inferred from class_weight.
Could you try:
Using subsample=1 in your balanced_subsample function. Unless there's a particular reason not to do so we're better off comparing the results on similar number of samples.
Using your subsampling strategy with class_weight and sample_weight both set to None.
EDIT: Reading your comment again I realize your results are not so surprising!
You get a better (higher) TPR but a worse (higher) FPR.
It just means your classifier tries hard to get the samples from class 1 right, and thus makes more false positives (while also getting more of those right of course!).
You will see this trend continue if you keep increasing the class/sample weights in the same direction.
There is a imbalanced-learn API that helps with oversampling/undersampling data that might be useful in this situation. You can pass your training set into one of the methods and it will output the oversampled data for you. See simple example below
from imblearn.over_sampling import RandomOverSampler
ros = RandomOverSampler(random_state=1)
x_oversampled, y_oversampled = ros.fit_sample(orig_x_data, orig_y_data)
Here it the link to the API: http://contrib.scikit-learn.org/imbalanced-learn/api.html
Hope this helps!
It's that time of the week where I realize just how little I understand in MATLAB. This week, we have homework on iteration, so using for-loops and while-loops. The problem I am currently experiencing difficulties with is one where I have to write a function that decides who to hire somebody. I'm given a list of names, a list of GPAs and a logical vector that tells me whether or not a student stayed to talk. What I have to output is the names of people to hire and the time they spent chatting with the recruiter.
function[candidates_hire, time_spent] = CFRecruiter(names, GPAs, stays_to_talk)
In order to be hired, a canidate must have a GPA that is higher than 2.5 (not inclusive). In order to be hired, the student must stick around to talk, if they don't talk, they don't get hired. The names are separated by a ', ' and the GPAs is a vector. The time spent talking is determined by:
Time in minutes = (GPA - 2.5) * 4;
My code so far:
function[candidates_hire, time_spent] = CFRecruiter(names, GPAs, stays_to_talk)
candidates = strsplit(names, ', ');
%// My attempt to split up the candidates names.
%// I get a 1x3 cell array though
for i = 1:length(GPAs)
%// This is where I ran into trouble, I need to separate the GPAs
student_GPA = (GPAs(1:length(GPAs)));
%// The length is unknown, but this isn't working out quite yet.
%// Not too sure how to fix that
return
end
time_spent = (student_GPA - 2.5) * 4; %My second output
while stays_to_talk == 1 %// My first attempt at a while-loop!
if student_GPA > 2.5
%// If the student has a high enough GPA and talks, yay for them
student = 'hired';
else
student = 'nothired'; %If not, sadface
return
end
end
hired = 'hired';
%// Here was my attempt to get it to realize how was hired, but I need
%// to concatenate the names that qualify into a string for the end
nothired = 'nothired';
canidates_hire = [hired];
What my main issue is here is figuring out how to let the function know them names(1) has the GPA of GPAs(1). It was recommended that I start a counter, and that I had to make sure my loops kept the names with them. Any suggestions with this problem? Please and thank you :)
Test Codes
[Names, Time] = CFRecruiter('Jack, Rose, Tom', [3.9, 2.3, 3.3],...
[false true true])
=> Name = 'Tom'
Time = 3.2000
[Names, Time] = CFRecruiter('Vatech, George Burdell, Barnes Noble',...
[4.0, 2.5, 3.6], [true true true])
=> Name = 'Vatech, Barnes Noble'
Time = 10.4000
I'm going to do away with for and while loops for this particular problem, mainly because you can solve this problem very elegantly in (I kid you not) three lines of code... well four if you count returning the candidate names. Also, the person who is teaching you MATLAB (absolutely no offense intended) hasn't the faintest idea of what they're talking about. The #1 rule in MATLAB is that if you can vectorize your code, do it. However, there are certain situations where a for loop is very suitable due to the performance enhancements of the JIT (Just-In-Time) accelerator. If you're curious, you can check out this link for more details on what JIT is about. However, I can guarantee that using loops in this case will be slow.
We can decompose your problem into three steps:
Determine who stuck around to talk.
For those who stuck around to talk, check their GPAs to see if they are > 2.5.
For those that have satisfied (1) and (2), determine the total time spent on talking by using the formula in your post for each person and add up the times.
We can use a logical vector to generate a Boolean array that simultaneously checks steps #1 and #2 so that we can index into our GPA array that you are specifying. Once we do this, we simply apply the formula to the filtered GPAs, then sum up the time spent. Therefore, your code is very simply:
function [candidates_hire, time_spent] = CFRecruiter(names, GPAs, stays_to_talk)
%// Pre-processing - split up the names
candidates = strsplit(names, ', ');
%// Steps #1 and #2
filtered_candidates = GPAs > 2.5 & stays_to_talk;
%// Return candidates who are hired
candidates_hire = strjoin(candidates(filtered_candidates), ', ');
%// Step #3
time_spent = sum((GPAs(filtered_candidates) - 2.5) * 4);
You had the right idea to split up the names based on the commas. strsplit splits up a string that has the token you're looking for (which is , in your case) into separate strings inside a cell array. As such, you will get a cell array where each element has the name of the person to be interviewed. Now, I combined steps #1 and #2 into a single step where I have a logical vector calculated that tells you which candidates satisfied the requirements. I then use this to index into our candidates cell array, then use strjoin to join all of the names together in a single string, where each name is separated by , as per your example output.
The final step would be to use the logical vector to index into the GPAs vector, grab those GPAs from those candidates who are successful, then apply the formula to each of these elements and sum them up. With this, here are the results using your sample inputs:
>> [Names, Time] = CFRecruiter('Jack, Rose, Tom', [3.9, 2.3, 3.3],...
[false true true])
Names =
Tom
Time =
3.2000
>> [Names, Time] = CFRecruiter('Vatech, George Burdell, Barnes Noble',...
[4.0, 2.5, 3.6], [true true true])
Names =
Vatech, Barnes Noble
Time =
10.4000
To satisfy the masses...
Now, if you're absolutely hell bent on using for loops, we can replace steps #1 and #2 by using a loop and an if condition, as well as a counter to keep track of the total amount of time spent so far. We will also need an additional cell array to keep track of those names that have passed the requirements. As such:
function [candidates_hire, time_spent] = CFRecruiter(names, GPAs, stays_to_talk)
%// Pre-processing - split up the names
candidates = strsplit(names, ', ');
final_names = [];
time_spent = 0;
for idx = 1 : length(candidates)
%// Steps #1 and #2
if GPAs(idx) > 2.5 && stays_to_talk(idx)
%// Step #3
time_spent = time_spent + (GPAs(idx) - 2.5)*4;
final_names = [final_names candidates(idx)];
end
end
%// Return candidates who are hired
candidates_hire = strjoin(final_names, ', ');
The trick with the above code is that we are keeping an additional cell array around that stores those candidates that have passed. We will then join all of the strings together with a , between each name as we did before. You'll also notice that there is a difference in checking for steps #1 and #2 between the two methods. In particular, there is a & in the first method and a && in the second method. The single & is for arrays and matrices while && is for single values. If you don't know what that symbol is, that is the symbol for logical AND. This means that something is true only if both the left side of the & and the right side of the & are both true. In your case, this means that someone who has a GPA of > 2.5 and stays to talk must both be true if they are to be hired.
hey guys i want your suggestion that how can change value of two variables without 3rd one. in objective cc.
is there any way so please inform me,
it can be done in any language. x and y are 2 variables and we want to swap them
{
//lets say x , y are 1 ,2
x = x + y; // 1+2 =3
y = x - y; // 3 -2 = 1
x = x -y; // 3-1 = 2;
}
you can use these equation in any language to achieve this
Do you mean exchange the value of two variables, as in the XOR swap algorithm? Unless you're trying to answer a pointless interview question, programming in assembly language, or competing in the IOCCC, don't bother. A good optimizing compiler will probably handle the standard tmp = a; a = b; b = tmp; better than whatever trick you might come up with.
If you are doing one of those things (or are just curious), see the Wikipedia article for more info.
As far as number is concerned you can swap numbers in any language without using the third one whether it's java, objective-C OR C/C++,
For more info
Potential Problem in "Swapping values of two variables without using a third variable"
Since this is explicitly for iPhone, you can use the ARM instruction SWP, but it's almost inconceivable why you'd want to. The complier is much, much better at this kind of optimization. If you just want to avoid the temporary variable in code, write an inline function to handle it. The compiler will optimize it away if it can be done more efficiently.
NSString * first = #"bharath";
NSString * second = #"raj";
first = [NSString stringWithFormat:#"%#%#",first,second];
NSRange needleRange = NSMakeRange(0,
first.length - second.length);
second = [first substringWithRange:needleRange];
first = [first substringFromIndex:second.length];
NSLog(#"first---> %#, Second---> %#",first,second);