## Novice User seeking assistance Topic is solved

Problems with modeling
GAMSnovice655
User
Posts: 8
Joined: 6 months ago

### Novice User seeking assistance

Hello All!

I feel really lucky I stumbled across this forum. I am attempting to create a model that involves a table I will eventually expand to simulate points on a grid (as an artificial map of sorts). I've been racking my brain for days trying to figure out the right combination of parameters, equations, etc. that can perform what I hope to achieve. I am attempting to have an input where I place a number greater than 0, that will then add one to any of the intersections of two sets in a table. Once the one is added I would like to set it up so it adds one to each intersection to the right, left, above, and below the point on the table that is increased. Here is my model:

* TITLE test;

Set i / 1*4 / ;
Set j / 1*4 / ;

Table d(i,j)

1 2 3 4
1 0 0 0 0
2 0 0 0 0
3 0 0 0 0
4 0 0 0 0;

Binary Variable Y(j);
Variables
z "test"

Parameter
d(i,j) # (y =G= 0) = 1;

Equation coverage(i) , Def_obj;

coverage(i)..sum(j, Y(j)+d(i,j)) =g= 1 ;
Def_obj..z =e= sum(j, Y(j));

Model testcoverage / all / ;
Solve testcoverage using mip minimizing z;
Display z.l, y.l ;

With this visual aid it may be easier to understand what my goal is. I want to have any point on table d(i,j) be able to have one added to it, and thus each point to the right, left, above, and below it also have one added to it, with these operations hinging on a user choosing a number greater than zero. I don't know if this is possible but I am hoping someone on here may have some creative ideas. Thank you for taking a moment to entertain a newbie.

Renger
Posts: 266
Joined: 2 years ago

### Re: Novice User seeking assistance

Hi

I do not understand what you are trying to achieve. The code you show is obviously not doing anything as d(i,j), a parameter, should, during the solve, change according to values of Y, a variable. d(i,j) should, therefore, be a variable.
Perhaps you are looking for an iterative (loop) for doing this. If not, please try to explain, what exactly has to change in what way (if Y>0 for j = 1, then the variable D(i,j) should change as follows....)

Cheers
Renger

PS. If you copy the code into a question, please put code tags around the code. Or by clicking on the </> symbol in the editor icons lists and pasting the code between those two code tags. In this way, your code is easier copied as the formatting of tabs and empty spaces is kept.

GAMSnovice655
User
Posts: 8
Joined: 6 months ago

### Re: Novice User seeking assistance

I should have replied a few days ago and explained that I had already figured out what I needed to change in order to make this work the way I wanted it to. I ended up shifting gears and creating a set-covering model. What I was trying to achieve was covering every "node" with either something in its place or something right next to it for a value. I ended up doing something like this:

Code: Select all

``````* TITLE Drone Coverage;
Set i / 1*100 / ;
Set j / 1*100 / ;
Table A(i,j)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

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94  0 0 0 0 0 0 0 0 0 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  1  1  1  0  0  0  0  0
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98  0 0 0 0 0 0 0 0 0 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  1  1  1  0
99  0 0 0 0 0 0 0 0 0 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  1  1  1
100 0 0 0 0 0 0 0 0 0 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  1  1

;
Binary Variable Y(j);
Variables
z "Drone Coverage"
Equation Coverage(i) , Def_obj ;
Coverage(i)..sum(j, Y(j)*A(i,j)) =g= 1 ;
Def_obj..z =e= sum(j, Y(j));
Model DroneCoverage / all / ;
Solve DroneCoverage using mip minimizing z;
Display z.l, y.l ;``````
Now I am playing with equations trying to translate it into real distances in real world scenarios. Any creative ideas on that would be appreciated. I am working on this for school and want to add some "Bells and Whistles" so to speak. Thanks for the reply Renger

GAMSnovice655
User
Posts: 8
Joined: 6 months ago

### Re: Novice User seeking assistance

To explain what my goal is, I am trying to construct a model that uses the 2 sets of 100 to illustrate a type of grid, like so:

91 92 93 94 95 96 97 98 99 100
81 82 83 84 85 86 87 88 89 90
71 72 73 74 75 76 77 78 79 80
61 62 63 64 65 66 67 68 69 70
51 52 53 54 55 56 57 58 59 60
41 42 43 44 45 46 47 48 49 50
31 32 33 34 35 36 37 38 39 40
21 22 23 24 25 26 27 28 29 30
11 12 13 14 15 16 17 18 19 20
1 2 3 4 5 6 7 8 9 10

The results of the model tell a user on what number to place a drone that would cover the square it is on and one to the right, left, above, and below it. The formula for FOV shows what viewing area a camera will have. The perimeter is a result of the viewing area of a drone. I ultimately want to be able to use the 100 square grid as a section of a disaster area that would be considered covered by a team of drone operators.

Code: Select all

``````* TITLE Drone Coverage;
Set i / 1*100 / ;
Set j / 1*100 / ;
Table A(i,j)

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100

1   1 1 0 0 0 0 0 0 0 0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
2   1 1 1 0 0 0 0 0 0 0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
3   0 1 1 1 0 0 0 0 0 0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
4   0 0 1 1 1 0 0 0 0 0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
5   0 0 0 1 1 1 0 0 0 0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
6   0 0 0 0 1 1 1 0 0 0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
7   0 0 0 0 0 1 1 1 0 0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
8   0 0 0 0 0 0 1 1 1 0  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
9   0 0 0 0 0 0 0 1 1 1  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
10  0 0 0 0 0 0 0 0 1 1  0  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
11  1 0 0 0 0 0 0 0 0 0  1  1  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
12  0 1 0 0 0 0 0 0 0 0  1  1  1  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0
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98  0 0 0 0 0 0 0 0 0 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  1  1  1  0
99  0 0 0 0 0 0 0 0 0 0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  1  0  0  0  0  0  0  0  0  1  1  1
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;
Binary Variable
Y(j) "Location that drone should be placed";
Variables
z "Drone Placement"
p "Perimeter in Miles"
f "Field of view for drone cameras in SqMi"
h "Operating height of drones"
t "Angle of view for camera on drones in SqMi"
Equation Coverage(i) , Obj, Perimeter, FOV;
Coverage(i)..sum(j, Y(j)*A(i,j)) =g= 1 ;
Perimeter.. p =e= (sqrt(card(i))*2+sqrt(card(j))*2)*f;
FOV.. f =e= (pi*(tan(45)*1150)**2)/27878400;
Obj..z =e= sum(j, Y(j));

Model DroneCoverage / all / ;
Solve DroneCoverage using mip minimizing z;
Display z.l, y.l, p.l, f.l;``````
If you have any cool ideas for translating this model into real world distances and "Bells and Whilstles" for optimizing using drones in a disaster situation, then please feel free to contribute!

Thanks for checking out my post