Geodesic distances are not always the ultimate distance but they often help.

Let me share some code that compute those geodesic distances:

.mod

tuple point {
float latitude;
float longitude;
};

float PI;

execute
{
PI=Math.PI;
}

{point} points = ...;

{point} pointsRadian={<p.latitude*PI/180,p.longitude*PI/180> | p in points};

float  earthRadiusKms = 6376.5;

// Cities
int     n       = card(points);
range   Cities  = 1..n;

point pRadian[c in Cities]=item(pointsRadian,c-1);

// Edges -- sparse set
tuple       edge        {int i; int j;}
setof(edge) Edges       = {<i,j> | ordered i,j in Cities};
float         dist[Edges];

execute compute_distances
{
writeln(n," points");

for(e in Edges)
{
  dist[e]=earthRadiusKms*Math.acos(
  Math.sin(pRadian[e.i].latitude)*Math.sin(pRadian[e.j].latitude)+
  Math.cos(pRadian[e.i].latitude)*Math.cos(pRadian[e.j].latitude)*
  Math.cos(pRadian[e.j].longitude-pRadian[e.i].longitude));
 
  writeln("distance from ",e.i," to ",e.j," = ",dist[e]);
 
}
}

.dat

points = {

<90.00, 90.00>,
<45.00, 45.00>,
<30,20>,
<20,-20>
<45,0>,
<-90,0>,
<0,-90>,
<90.00, 0.00>,
<71.17, -156.47>,
<64.51, -147.43>,
<61.13, -149.53>,

};

which gives

11 points
distance from 1 to 2 = 5008.091388904
distance from 1 to 3 = 6677.455185205
distance from 1 to 4 = 7790.364382739
distance from 1 to 5 = 5008.091388904
distance from 1 to 6 = 20032.365555615
distance from 1 to 7 = 10016.182777808
distance from 1 to 8 = 0
distance from 1 to 9 = 2095.608018957
distance from 1 to 10 = 2836.805544515
distance from 1 to 11 = 3212.968853281
distance from 2 to 3 = 2748.227646927
distance from 2 to 4 = 6509.319132227
distance from 2 to 5 = 3494.503141191
distance from 2 to 6 = 15024.274166711
distance from 2 to 7 = 13354.91037041
distance from 2 to 8 = 5008.091388904
distance from 2 to 9 = 6990.683723353
distance from 2 to 10 = 7796.577300153
distance from 2 to 11 = 8148.457920375
distance from 3 to 4 = 4162.273650918
distance from 3 to 5 = 2417.380052239
distance from 3 to 6 = 13354.91037041
distance from 3 to 7 = 11933.658168096
distance from 3 to 8 = 6677.455185205
distance from 3 to 9 = 8769.616053004
distance from 3 to 10 = 9457.100063805
distance from 3 to 11 = 9846.019348887
distance from 4 to 5 = 3336.043897524
distance from 4 to 6 = 12242.001172876
distance from 4 to 7 = 7929.785501304
distance from 4 to 8 = 7790.364382739
distance from 4 to 9 = 9352.971477397
distance from 4 to 10 = 9614.599355622
distance from 4 to 11 = 9947.715796963
distance from 5 to 6 = 15024.274166711
distance from 5 to 7 = 10016.182777808
distance from 5 to 8 = 5008.091388904
distance from 5 to 9 = 6968.154654933
distance from 5 to 10 = 7518.038417735
distance from 5 to 11 = 7905.702847421
distance from 6 to 7 = 10016.182777808
distance from 6 to 8 = 20032.365555615
distance from 6 to 9 = 17936.757536658
distance from 6 to 10 = 17195.560011101
distance from 6 to 11 = 16819.396702334
distance from 7 to 8 = 10016.182777808
distance from 7 to 9 = 9192.24326288
distance from 7 to 10 = 8525.381590705
distance from 7 to 11 = 8438.966484735
distance from 8 to 9 = 2095.608018957
distance from 8 to 10 = 2836.805544515
distance from 8 to 11 = 3212.968853281
distance from 9 to 10 = 830.681781355
distance from 9 to 11 = 1158.377782719
distance from 10 to 11 = 390.965210663

regards

Alex Fleischer

PS:

Many how to with OPL at https://www.linkedin.com/pulse/how-opl-alex-fleischer/

Many examples from a very good book : https://www.linkedin.com/pulse/model-building-oplcplex-alex-fleischer/

Making optimization simple : https://www.linkedin.com/pulse/making-decision-optimization-simple-alex-fleischer/

Originally posted by: gustavgans123

Hi Alex,

this is great, thanks for the example.

I know it might be stupid, but could you help me transform this code into one without using any tuple notation? Or maybe even provide an example without the use of tuples, such that:

dis[I in N][j in N] = geodesic distance betw. node I and node j.

I got this far:

int n = ...;

{int} N = asSet(0..n);

float latitude[i in N] = ...;

float longitude[i in N] = ...;

float PI;

execute

{

PI=Math.PI;

}

float pointsRadianlat[i in N] = latitude[i]*PI/180;

float pointsRadianlong[i in N] = longitude[i]*PI/180;

float earthRadiusKms = 6376.5;

Introducing tuples in my model now would mean, that I have to basically change all the notation.

Thanks a lot,

gustav

Hi,

then you could write

.mod

int n = ...;

{int} N = asSet(1..n);

float latitude[N] = ...;

float longitude[N] = ...;

float dist[N][N];

float PI;

execute
{
PI=Math.PI;
}

float pointsRadianlat[i in N] = latitude[i]*PI/180;

float pointsRadianlong[i in N] = longitude[i]*PI/180;

float earthRadiusKms = 6376.5;

execute compute_distances
{
writeln(n," points");

for(a in N) for(b in N)
{
  dist[a][b]=earthRadiusKms*Math.acos(
  Math.sin(pointsRadianlat[a])*Math.sin(pointsRadianlat[b])+
  Math.cos(pointsRadianlat[a])*Math.cos(pointsRadianlat[b])*
  Math.cos(pointsRadianlong[b]-pointsRadianlong[a]));
 
  writeln("distance from ",a," to ",b," = ",dist[a][b]);
 
}
}

.dat

n=11;

    latitude = [

    90.00,
    45.00,
    30,
    20,
    45,
    -90,
    0,
    90.00,
    71.17,
    64.51,
    61.13,

    ];
    
    longitude = [

     90.00,
     45.00,
    20,
    -20
    0,
    0,
    -90,
     0.00,
     -156.47,
     -147.43,
     -149.53,

    ];

which would give

11 points
distance from 1 to 1 = 0
distance from 1 to 2 = 5008.091388904
distance from 1 to 3 = 6677.455185205
distance from 1 to 4 = 7790.364382739
distance from 1 to 5 = 5008.091388904
distance from 1 to 6 = 20032.365555615
distance from 1 to 7 = 10016.182777808
distance from 1 to 8 = 0
distance from 1 to 9 = 2095.608018957
distance from 1 to 10 = 2836.805544515
distance from 1 to 11 = 3212.968853281
distance from 2 to 1 = 5008.091388904
distance from 2 to 2 = NaN
distance from 2 to 3 = 2748.227646927
distance from 2 to 4 = 6509.319132227
distance from 2 to 5 = 3494.503141191
distance from 2 to 6 = 15024.274166711
distance from 2 to 7 = 13354.91037041
distance from 2 to 8 = 5008.091388904
distance from 2 to 9 = 6990.683723353
distance from 2 to 10 = 7796.577300153
distance from 2 to 11 = 8148.457920375
distance from 3 to 1 = 6677.455185205
distance from 3 to 2 = 2748.227646927
distance from 3 to 3 = 0
distance from 3 to 4 = 4162.273650918
distance from 3 to 5 = 2417.380052239
distance from 3 to 6 = 13354.91037041
distance from 3 to 7 = 11933.658168096
distance from 3 to 8 = 6677.455185205
distance from 3 to 9 = 8769.616053004
distance from 3 to 10 = 9457.100063805
distance from 3 to 11 = 9846.019348887
distance from 4 to 1 = 7790.364382739
distance from 4 to 2 = 6509.319132227
distance from 4 to 3 = 4162.273650918
distance from 4 to 4 = 0
distance from 4 to 5 = 3336.043897524
distance from 4 to 6 = 12242.001172876
distance from 4 to 7 = 7929.785501304
distance from 4 to 8 = 7790.364382739
distance from 4 to 9 = 9352.971477397
distance from 4 to 10 = 9614.599355622
distance from 4 to 11 = 9947.715796963
distance from 5 to 1 = 5008.091388904
distance from 5 to 2 = 3494.503141191
distance from 5 to 3 = 2417.380052239
distance from 5 to 4 = 3336.043897524
distance from 5 to 5 = NaN
distance from 5 to 6 = 15024.274166711
distance from 5 to 7 = 10016.182777808
distance from 5 to 8 = 5008.091388904
distance from 5 to 9 = 6968.154654933
distance from 5 to 10 = 7518.038417735
distance from 5 to 11 = 7905.702847421
distance from 6 to 1 = 20032.365555615
distance from 6 to 2 = 15024.274166711
distance from 6 to 3 = 13354.91037041
distance from 6 to 4 = 12242.001172876
distance from 6 to 5 = 15024.274166711
distance from 6 to 6 = 0
distance from 6 to 7 = 10016.182777808
distance from 6 to 8 = 20032.365555615
distance from 6 to 9 = 17936.757536658
distance from 6 to 10 = 17195.560011101
distance from 6 to 11 = 16819.396702334
distance from 7 to 1 = 10016.182777808
distance from 7 to 2 = 13354.91037041
distance from 7 to 3 = 11933.658168096
distance from 7 to 4 = 7929.785501304
distance from 7 to 5 = 10016.182777808
distance from 7 to 6 = 10016.182777808
distance from 7 to 7 = 0
distance from 7 to 8 = 10016.182777808
distance from 7 to 9 = 9192.24326288
distance from 7 to 10 = 8525.381590705
distance from 7 to 11 = 8438.966484735
distance from 8 to 1 = 0
distance from 8 to 2 = 5008.091388904
distance from 8 to 3 = 6677.455185205
distance from 8 to 4 = 7790.364382739
distance from 8 to 5 = 5008.091388904
distance from 8 to 6 = 20032.365555615
distance from 8 to 7 = 10016.182777808
distance from 8 to 8 = 0
distance from 8 to 9 = 2095.608018957
distance from 8 to 10 = 2836.805544515
distance from 8 to 11 = 3212.968853281
distance from 9 to 1 = 2095.608018957
distance from 9 to 2 = 6990.683723353
distance from 9 to 3 = 8769.616053004
distance from 9 to 4 = 9352.971477397
distance from 9 to 5 = 6968.154654933
distance from 9 to 6 = 17936.757536658
distance from 9 to 7 = 9192.24326288
distance from 9 to 8 = 2095.608018957
distance from 9 to 9 = 0
distance from 9 to 10 = 830.681781355
distance from 9 to 11 = 1158.377782719
distance from 10 to 1 = 2836.805544515
distance from 10 to 2 = 7796.577300153
distance from 10 to 3 = 9457.100063805
distance from 10 to 4 = 9614.599355622
distance from 10 to 5 = 7518.038417735
distance from 10 to 6 = 17195.560011101
distance from 10 to 7 = 8525.381590705
distance from 10 to 8 = 2836.805544515
distance from 10 to 9 = 830.681781355
distance from 10 to 10 = 0
distance from 10 to 11 = 390.965210663
distance from 11 to 1 = 3212.968853281
distance from 11 to 2 = 8148.457920375
distance from 11 to 3 = 9846.019348887
distance from 11 to 4 = 9947.715796963
distance from 11 to 5 = 7905.702847421
distance from 11 to 6 = 16819.396702334
distance from 11 to 7 = 8438.966484735
distance from 11 to 8 = 3212.968853281
distance from 11 to 9 = 1158.377782719
distance from 11 to 10 = 390.965210663
distance from 11 to 11 = 0

regards

Originally posted by: gustavgans123

Perfect, Thanks a lot Alex! Really appreciate your time and help!!

BR

Hi

you re welcome

I tweeted

https://twitter.com/alexfleischer1/status/910816045488893953

regards