PLEASE HELP ME: i have a boolean decision variable. moreover, set t itself in the domain of this variable should be calculated from an equation.**
Xro^t={1 if request r∈R_τ is assigned to offer o ∈ O_τ at time period t∈ Γ_ro,
0 Otherwise}
Γ_ro= [p, a]∩z
in this case, i am not sure if Γ_ro is a set or is a parameter?
You could rely on tuple set in order not to do the full Euclidian product:
range R=1..4;
range O=1..3;
int Tstart[r in R][o in O]=rand(5);
int Tend[r in R][o in O]=Tstart[r][o]+rand(4);
tuple rot
{
int r;
int o;
int t;
}
sorted {rot} rots={<r,o,t> | r in R,o in O,t in Tstart[r][o]..Tend[r][o]};
dvar boolean x[rots];
minimize sum(i in rots) x[i];
subject to
{
}
Related
My distance matrix in my no overlap constraint does not seem to work in my model outcome. I have formulated the distance matrix by means of a tuple set. I have tried this in 2 different ways as can be seen in the code. Both tuple sets seem to be correct and the distance matrix is added in the noOverlap constraint for the dvar sequence.
Nevertheless I do not see the added transition distance between products in the optimal results. Jobs seem to continue at the same time when a job is finished. Instead of waiting for a transition time. I would like this transition matrix to hold both for machine 1 and machine 2.
Could someone tell me what I did wrong in my model formulation? I have looked into the examples, but they seem to be constructed in the same way. So I do not know what I am doing wrong.
mod.
using CP;
// Number of Machines (Packing + Manufacturing)
int nbMachines = ...;
range Machines = 1..nbMachines;
// Number of Jobs
int nbJobs = ...;
range Jobs = 1..nbJobs;
int duration[Jobs,Machines] = ...;
int release = ...;
int due = ...;
tuple Matrix { int job1; int job2; int value; };
//{Matrix} transitionTimes ={<1,1,0>,<1,2,6>,<1,3,2>,<2,1,2>,<2,2,0>,<2,3,1>,<3,1,2>,<3,2,3>,<3,3,0>};
{Matrix} transitionTimes ={ <i,j, ftoi(abs(i-j))> | i in Jobs, j in Jobs };
dvar interval task[j in Jobs] in release..due;
dvar interval opttask[j in Jobs][m in Machines] optional size duration[j][m];
dvar sequence tool[m in Machines] in all(j in Jobs) opttask[j][m];
execute {
cp.param.FailLimit = 5000;
}
// Minimize the max timespan
dexpr int makespan = max(j in Jobs, m in Machines)endOf(opttask[j][m]);
minimize makespan;
subject to {
// Each job needs one unary resource of the alternative set s (28)
forall(j in Jobs){
alternative(task[j], all(m in Machines) opttask[j][m]);
}
forall(m in Machines){
noOverlap(tool[m],transitionTimes);
}
};
execute {
writeln(task);
};
dat.
nbMachines = 2;
nbJobs = 3;
duration = [
[5,6],
[3,4],
[5,7]
];
release = 1;
due = 30;
``
You should specify interval types for each sequence.
In your case, the type is the job id:
int JobId[j in Jobs] = j;
dvar sequence tool[m in Machines] in all(j in Jobs) opttask[j][m] types JobId;
I am trying to add an Endbeforestartconstraint to my contrained programming problem. However, I receive an error saying that my end beforestart is not an array type. I do not understand this as I almost copied the constraint and data from the sched_seq example in CPLEX, I only changed it to integers.
What I try to accomplish with the constraint, is that task 3 and task 1 will be performed before task 2 will start.
How I can fix the array error for this constraint?
Please find below the relevant parts of my code
tuple Precedence {int pre;int post;};
{Precedence} Precedences = {<3,2>,<1,2>};
dvar interval task[j in Jobs] in release..due;
dvar interval opttask[j in Jobs][m in Machines] optional size duration[j][m];
dvar sequence tool[m in Machines] in all(j in Jobs) opttask[j][m]
dexpr int makespan = max(j in Jobs, m in Machines)(endOf(opttask[j][m]));
minimize makespan;
subject to {
// Each job needs one unary resource of the alternative set s (28)
forall(j in Jobs){
alternative(task[j], all(m in Machines) opttask[j][m]);
}
// No overlap on machines
forall(j in Jobs)
forall(p in Precedences)
endBeforeStart(opttask[j][p.pre],opttask[j][p.post]);
forall(m in Machines){
noOverlap(tool[m],transitionTimes);
}
};
execute {
writeln(task);
dat.
nbMachines = 2;
nbJobs = 3;
duration = [
[5,6],
[4,4],
[5,8]
];
release = 1;
due = 30;
There are several errors in your model, on ranges or on inverted indices.
Also, next time, please post a complete program showing the problem, not just a partial one, this may help you to get quicker answers.
A corrected program:
using CP;
int nbMachines = 2;
int nbJobs = 3;
range Machines = 0..nbMachines-1;
range Jobs = 0..nbJobs-1;
int duration[Jobs][Machines] = [
[5,6],
[4,4],
[5,8]
];
int release = 1;
int due = 30;
tuple Precedence {int pre;int post;};
{Precedence} Precedences = {<2,1>,<0,1>};
dvar interval task[j in Jobs] in release..due;
dvar interval opttask[j in Jobs][m in Machines] optional size duration[j][m];
dvar sequence tool[m in Machines] in all(j in Jobs) opttask[j][m];
dexpr int makespan = max(j in Jobs, m in Machines)(endOf(opttask[j][m]));
minimize makespan;
subject to {
// Each job needs one unary resource of the alternative set s (28)
forall(j in Jobs){
alternative(task[j], all(m in Machines) opttask[j][m]);
}
// No overlap on machines
forall(m in Machines)
forall(p in Precedences)
endBeforeStart(opttask[p.pre][m],opttask[p.post][m]);
};
execute {
writeln(task);
}
You must have values in p.pre or p.post that are outside of the array indexing range.
I am trying to solve the following question on LeetCode; Write a function that takes an unsigned integer and returns the number of '1' bits it has. Constraints: The input must be a binary string of length 32.
I have written the following code for that which works fine for inputs 00000000000000000000000000001011 and 00000000000000000000000010000000 (provided internally by the website) but give output 0 for input 11111111111111111111111111111101 and in my local compiler for the last input it says "out of range"
class Solution {
// you need treat n as an unsigned value
fun hammingWeight(n:Int):Int {
var num = n
var setCountBit = 0
while (num > 0) {
setCountBit++
num= num and num-1
}
return setCountBit
}
}
To correctly convert binary string to Int and avoid "out of range error", you need to do the following (I believe LeetCode does the same under the hood):
fun binaryStringToInt(s: String): Int = s.toUInt(radix = 2).toInt()
"11111111111111111111111111111101" is equivalent to 4294967293. This is greater than Int.MAX_VALUE, so it will be represented as negative number after .toInt() convertion (-3 in this case).
Actually, this problem could be solved with one-liner in Kotlin 1.4:
fun hammingWeight(n: Int): Int = n.countOneBits()
But LeetCode uses Kotlin 1.3.10, so you need to adjust your solution to handle negative Ints as well.
Please change the type of your input variable from Int to a type like Double .At the moment The given value is bigger than the maximum value that a type Int number can store.
I need to declarate a 3 dimensional decision variable, which is defined according to the following:
x[m][p][q] in {0,1} with m in M, p in P(m) and q in Q(m,p)
dvar boolean x[M][P][Q] does not work.
Is there a possiblity to define it similar to a constraint, like:
forall(m in M, p in P(m) and q in Q(m,p))
x[m][p][q] in {0,1}
or something?
Regards
array variable indexer size - 3 ways : union , tuple set, decision expression
in Simple OPL CPLEX
could help
/*
Variable indexer size:
we'd like to be able to write
dvar int+ nbBus[s in scenarii][sizes[s]];
but we get an error "Variable indexer size not allowed"
So what can we do ?
We saw 2 options:
1) Rely on a tuple set that contains all options
instead of a multi dimension array
2) For the variable dimension use the union of all options
1) Is good but the drawback is that relying on a tuple set makes the
constraint harder to read for a human being
2) Is good but a bit suboptimal since we use options that are useless and
consume memory for no gain.
We can mix 1) and 2) with decision expressions
*/
int nbKids=300;
tuple busscenario
{
key int nbSeats;
key int scenario;
float cost;
}
{busscenario} busscenarii={<40,1,500>,<30,1,400>,<30,2,410>,<35,2,440>,<40,2,520>};
{int} scenarii={i.scenario | i in busscenarii};
{int} sizeBusesPerScenario[scen in scenarii]={i.nbSeats | i in busscenarii : i.scenario==scen};
{int} busSizes=union(scen in scenarii) sizeBusesPerScenario[scen];
// decision variable array with variable size
dvar int+ nbBus2[busscenarii];
// decision expression array with variable size
dexpr int nbBus[sc in scenarii][b in busSizes]=nbBus2[<b,sc>];
dexpr float cost[sc in scenarii][b in busSizes]=item(busscenarii,<b,sc>).cost;
// objective
minimize
1/card(scenarii)*sum(sc in scenarii,b in sizeBusesPerScenario[sc])
cost[sc][b]*nbBus[sc][b];
// constraints
subject to
{
forall(sc in scenarii) sum(b in sizeBusesPerScenario[sc]) b*nbBus[sc][b]>=nbKids;
}
execute
{
for(sc in scenarii)
{
writeln("scenario ",sc);
for(var b in sizeBusesPerScenario[sc]) writeln(nbBus[sc][b]," buses ",b," seats" );
writeln();
}
}
/*
which gives
// solution (optimal) with objective 3820
scenario 1
6 buses 40 seats
2 buses 30 seats
scenario 2
0 buses 30 seats
4 buses 35 seats
4 buses 40 seats
*/
I know that if I have a function like:
public int addOne(int a){
return (a+1)
}
The time complexity order will be O(1) since we only do one operation (the sum).
But what if I have a function that doesn't do any operations, just assigns some values to some global variables. Like this:
public void assignValues(){
a = 2;
b = 3;
c = 4;
//maybe more
}
What would the time complexity be for this function? My guess is that it would still O(1). Is that correct?
When you discuss the time complexity of an algorithm, you first have to define the variable parameter(s). For example, it doesn't make any sense to say that something is O(n) without defining what you measure by n (e.g. the length of an array? The size of the contents of an array? The bit-length of a number? The absolute value of an integer?).
In your particular case, you have a function that takes no parameters. Assuming that the operations within the function don't depend on any other external parameters, the complexity of such a function is always trivially O(1), no matter what operations you perform inside. For example, the following function is also O(1):
public static int DoSth() {
int x = 0;
const int n = 1000000;
for(int i = 0; i < n; i++)
for(int j = 0; j < n; j++)
x++;
return x;
}
As already mentioned, this assumes that the parameter-less function has no external dependencies. Consider e.g. the following function
public static void DoSth() {
int n = DateTime.Now.Ticks;
for(int i = 0; i < n; i++)
Console.WriteLine(i);
}
This function is O(n log n) if n is the amount of time that has passed since 1.1.0001.