I'm trying to port a minizinc model in choco. I know how to define variables and other basic stuff but despite having read the tutorial and some code examples I've some trouble defining some non trivial constraints.
Could someone give me some advice how to translate the following code (just z) in a choco solver style?
array[1..n,1..n] of int: c;
array[1..n] of var 0..10: next;
var 0..sum(c): z = sum(i in 1..n)(c[i,next[i]]);
Thanks!
I believe you know how to post a sum constraint so the non trivial part lies in the c[i,next[i]] which retrieves the integer in matrix c at row i and column next[i]. The problem is that next[i] is a variable so you cannot use it directly to access a (Java) array.
You need to use the element constraint (that is also in minizinc):
/**
* Creates an element constraint: value = table[index]
*
* #param value an integer variable taking its value in table
* #param table an array of integer values
* #param index an integer variable representing the value of value in table
*/
default Constraint element(IntVar value, int[] table, IntVar index)
As you work with a matrix, you need to do that for each row and then post a sum on them.
Note also that in Java, array cells are accessed from 0 to n-1 (in minizinc it is from 1 to n), so you may need to update the model accordingly or use an offset.
Hope this helps
https://www.cosling.com/
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I am trying to write some unit tests for my constraints using the CheckSatisfied function. How do I know the variable order of the input vector x?
E.g.
q = prog.NewContinuousVariables(1, 'q')
r = prog.NewContinuousVariables(2, 'r')
formula = le(q, r[0] + r[1])
constraint = prog.AddConstraint(formula)
assert(constraint.evaluator().CheckSatisfied([0.3, 0.5, 1]))
How do I know the which variable 0.3, 0.5, 1 corresponds to?
Is it dependent on how the constraints are added, and if so, how do I know the variable order for constraints added in the myriad of ways?
The order of the variables is stored in the return argument of AddConstraint. If you check constraint.variables(), you would see the variable order. The pseudo code is
constraint = prog.AddConstraint(formula)
print(f"{constraint.variables()}")
In a transport problem, I'm trying to insert the following rule into the objective function:
If a supply of BC <19,000 tons, then we will have a penalty of $ 125 / MT
I added a constraint to check the condition but would like to apply the penalty in the objective function.
I was able to do this in Excel Solver, but the values do not match. I've already checked both, and debugged the code, but I could not figure out what's wrong.
Here is the constraint:
def bc_rule(model):
return sum(model.x[supplier, market] for supplier in model.suppliers \
for market in model.markets \
if 'BC' in supplier) >= 19000
model.bc_rules = Constraint(rule=bc_rule, doc='Minimum production')
The problem is in the objective rule:
def objective_rule(model):
PENALTY_THRESHOLD = 19000
PENALTY_COST = 125
cost = sum(model.costs[supplier, market] * model.x[supplier, market] for supplier in model.suppliers for market in model.markets)
# what is the problem here?
bc = sum(model.x[supplier, market] for supplier in model.suppliers \
for market in model.markets \
if 'BC' in supplier)
if bc < PENALTY_THRESHOLD:
cost += (PENALTY_THRESHOLD - bc) * PENALTY_COST
return cost
model.objective = Objective(rule=objective_rule, sense=minimize, doc='Define objective function')
I'm getting a much lower value than found in Excel Solver.
Your condition (if) depends on a variable in your model.
Normally, ifs should never be used in a mathematical model, and that is not only for Pyomo. Even in Excel, if statements in formulas are simply converted to scalar value before optimization, so I would be very careful when saying that it is the real optimal value.
The good news is that if statements are easily converted into mathematical constraints.
For that, you need to add a binary variable (0/1) to your model. It will take the value of 1 if bc <= PENALTY_TRESHOLD. Let's call this variable y, and is defined as model.y = Var(domain=Binary).
You will add model.y * PENALTY_COST as a term of your objective function to include the penalty cost.
Then, for the constraint, add the following piece of code:
def y_big_M(model):
bigM = 10000 # Should be a big number, big enough that it will be bigger than any number in your
# model, but small enough that it will stay around the same order of magnitude. Avoid
# utterly big number like 1e12 and + if you don't need to, since having numbers too
# large causes problems.
PENALTY_TRESHOLD = 19000
return PENALTY_TRESHOLD - sum(
model.x[supplier, market]
for supplier in model.suppliers
for market in model.markets
if 'BC' in supplier
) <= model.y * bigM
model.y_big_M = Constraint(rule=y_big_M)
The previous constraint ensures that y will take a value greater than 0 (i.e. 1) when the sum that calculates bc is smaller than the PENALTY_TRESHOLD. Any value of this difference that is greater than 0 will force the model to put 1 in the value of variable y, since if y=1, the right hand side of the constraint will be 1 * bigM, which is a very big number, big enough that bc will always be smaller than bigM.
Please, also check your Excel model to see if your if statements really works during the solver computations. Last time I checked, Excel solver do not convert if statements into bigM constraints. The modeling technique I showed you works for absolutely all programming method, even in Excel.
I want to calculate a matrix with symbolic entries and export the matrix to an excel file.
Approach:
syms x_1 y_1
A_sym = sym(zeros(2,2));
A_sym(1,1) = x_1;
A_sym(2,1) = x_1 * y_1
A_sym(2,2) = y_1;
I tried to use the xlswrite('test.xls',A_sym,'A1:C5') function but it is somehow not designed for symbolic expressions and I get the following error:
Input data must be a numeric, cell, or logical array.
Afterwards I tried to typecast the content of my matrix to char and export it again:
B = char(A);
xlswrite('test.xls',B,'A1:C5');
The result was that the function exported each character into a single excel cell which leads to the problem that the symbolic variables containing more than one char are not in one single excel cell but are divided into many cells which is useless for my purposes.
I guess there must be a better solution to export the variables into a single cell.
Does someone has a good solution ?
If what you want is an output based on text, then you are on the right trach, but you need to do what you are doing per matrix element.
for ii=1:size(A_sym,1)
for jj=1:size(A_sym,2)
B{ii,jj}=char(A_sym(ii,jj));
end
end
xlswrite('test.xls',B);
This will put a char version of the symbolic matrix with the same size in excel (in this case 2x2)
I need to construct a loop (simulation) that will iterate a certain number of times and display a value of warrant once the new firm value is close to the guess firm value. Specifically, the idea is to start out with a guess for the firm value (for example the stock price multiplied by the number of shares). Then you value the warrant as a call option (the code below) on this value multiplied by dilution factor, using the same volatility as the vol of the share price. You recompute then the value of the firm (number of shares times share price plus number of warrants times warrant price). This value will be different from the value of the firm you started with. Then you redo the procedure and after a few iterations you will see that the difference in values of the firm tends to zero. For this, I have a following code, but what I get is the following:
TypeError: 'int' object is not subscriptable
Please, help me to figure out the error given the code below:
def bsm_call_value(S0, K, T, r, sigma):
from math import log, sqrt, exp
from scipy import stats
S0 = float(S0)
d1 = (log(S0 / K) + (r + 0.5 * sigma ** 2) * T) / (sigma * sqrt(T))
d2 = (log(S0 / K) + (r - 0.5 * sigma ** 2) * T) / (sigma * sqrt(T))
value = (S0 * stats.norm.cdf(d1, 0.0, 1.0) - K * exp(-r * T) *stats.norm.cdf(d2, 0.0, 1.0))
return value
def warrant_1unobservable(S0, K, T, r, sigma, k, N, M, Iteration):
for i in range(1, Iteration):
Guess_FirmValue = S0*N
dilution = N/(N +k*M)
warrant[i] = bsm_call_value(Guess_FirmValue[i]/N,100,1,0.1,0.2)*dilution
New_FirmValue[i] = Guess_FirmValue[i]+ warrant[i]
Guess_FirmValue[i] - New_FirmValue[i] == 0
return warrant
print(warrant_1unobservable(100,100,1,0.1,0.2,1,100,10, 1000))
I'm not really a python expert and I'm not familiar with the algorithm you're using, but I'll point out a few things that could be causing the issue.
1) In warrant_1observable, you first assign Guess_FirmValue a scalar value (since both S0 and N are scalars the way you call the function), and then you try to access it with an index as Guess_FirmValue[i]. My guess would be that this is causing the error you displayed, since you're trying to index/subscript a variable that, based on your function input values, would be an integer.
2) Both warrant[i] and New_FirmValue[i] are attempts to assign values to an indexed position in a list, but nowhere do you initialize these variables as lists. Lists in python are initialized as warrant = []. Also, it's likely that you would have to either a) pre-allocate the lists to the correct size based on the Iteration or b) use append to push new values onto the back of the list.
3) Guess_FirmValue[i] - New_FirmValue[i] == 0 is a vacuous line of code. All this does is evaluate to either true or false, while performing no other operation. I imagine you're trying to check if the values are equal and then return, but that won't happen even if you stick this in an if statement. It is extremely unlikely that the floating-point representation of the values will ever be identical. This kind of break is accomplished by checking if the difference of the values is below some tolerance, which is set to be a very small number. Ex.:
if (abs(Guess_FirmValue[i] - New_FirmValue[i]) <= 1e-9):
return ...
Using Sybase ASE 12.5 I have the following situation.
2 values stored in float cols when multiplied give a value.
Converting that value to a varchar (or retrieving it with Java) gives the underlying precise value which the floats approximated to.
My issue is that the value as represented by the floats is correct, but the precise value is causing issues (due to strict rounding rules).
For example
declare #a float,#b float
select #a = 4.047000, #b = 1033000.000000
select #a*#b as correct , str(#a*#b,40,20) as wrong
gives:
correct: 4180551.000000,
wrong: 4180550.9999999995343387
Similarly when
#a = 4.047000, #b = 1
...you get
correct: 4.047000,
wrong: 4.0469999999999997
(same thing happens using convert(varchar(30), #a*#b) and cast(#a*#b, varchar(30) )
I appreciate it would be easy to just round the first example in java but for various business reasons that cannot be done and in any case it wouldn't work for the second.
I also cannot change the float table column datatype.
Is there anyway to get the float representation of the multiplication product either as a string or the actual 'correct' value above?
Thanks
Chris