In need of help in dealing with logic statements using GAMS

GAMS
,
1

Good day,
I am currently a new user GAMS. I am solving a problem that have to do the use of logic fucntion as shown in the code below.(The problem starts from the objective function definition).

The problem is an example of the TRAVELKLING SALESMAN PROBLEM in optimization.

Your urgent help or advice will be appreciated.

Sets
  i   Stations /E1, E2, E3, E4, E5, E6/;
       Alias(i,j)
Parameters
  xCoord(i)  /E1 20, E2 40, E3 180, E4 130, E5 160, E6 80/
  yCoord(i)  /E1 90, E2 10, E3 30, E4 40, E5 10, E6 80/;


Scalar n /6/;


* Calculate the distances between stations
Table Dist(i, j) Distance
     E1     E2     E3     E4     E5     E6
E1   0      0      0      0      0      0
E2   0      0      0      0      0      0
E3   0      0      0      0      0      0
E4   0      0      0      0      0      0
E5   0      0      0      0      0      0
E6   0      0      0      0      0      0;


* Fill the table with Euclidean distances
Loop(i,
  Loop(j,
     Dist(i,j) = sqrt((xCoord(i) - xCoord(j))**2 + (yCoord(i) - yCoord(j))**2);
  );
);


Binary Variables
  x(i, j)  "1 if edge (i, j) is used, 0 otherwise";


Variables
  Z  "Total distance traveled";


* Objective function
Equations
  obj "Objective function"
  visit(i) "Ensure each station is visited exactly once";


obj..
  Z =E= sum((i,j)$(i <> j), Dist(i,j) * x(i,j));


visit(i)..
  sum(j$(j <> i), x(i,j)) =E= 1;


* Each station should be left exactly once
visit2(j)..
  sum(i$(i <> j), x(i,j)) =E= 1;


* Subtour elimination constraints
Equations
  subtour(i) "Subtour elimination constraints";


* Define a variable for subtour elimination
Positive Variables
  u(i) "Number of stations visited before station i";


subtour(i)..
  u(i) - u(j) + n * x(i,j) <= n - 1;


Model TSP /all/;
Solve TSP using mip minimizing Z;


Display x.l, Z.l;```
2

You can’t compare labels/set with <> like in your code $(i <> j). You need to use the sameas functionality. So write this as $(not sameas(i,j)). There were more issues in the model but hopefully this gets you over the hurdle to continue with your homework.

-Michael

3

Good Micheal,

Thank you very much the response.

I would try this technique subsequently as I have executed the code by using the ordered set command instead : $(ord(i) <>ord(j))

Kind regards,

Edward.