## Traveling Salesman Problem Example (omode06)

```/***************************************************************/
/*                                                             */
/*          S A S   S A M P L E   L I B R A R Y                */
/*                                                             */
/*    NAME: omode06                                            */
/*   TITLE: Traveling Salesman Problem Example (omode06)       */
/* PRODUCT: OR                                                 */
/*  SYSTEM: ALL                                                */
/*    KEYS: OR                                                 */
/*   PROCS: OPTMODEL                                           */
/*    DATA:                                                    */
/*                                                             */
/* SUPPORT:                             UPDATE:                */
/*     REF:                                                    */
/*    MISC: Example 6 from the OPTMODEL chapter of             */
/*          Mathematical Programming.                          */
/*                                                             */
/***************************************************************/

/*
%let tsplib = location-of-st70-problem
*/

/* convert the TSPLIB instance into a data set */
data tspData(drop=H);
infile "&tsplib";
input H \$1. @;
if H not in ('N','T','C','D','E');
input @1 var1-var3;
run;

%macro plotTSP;
/* create Annotate data set to draw subtours */
data anno;
retain drawspace 'datavalue' linethickness 1 function 'line';
set solData;
run;

title1 h=2 "TSP: Iter = &i, Objective = &&obj&i";
title2;

proc sgplot data=tspData sganno=anno;
scatter x=var2 y=var3 / datalabel=var1;
xaxis display=none;
yaxis display=none;
run;
%mend plotTSP;

/* iterative solution using the subtour formulation */
proc optmodel;
set VERTICES;
set EDGES = {i in VERTICES, j in VERTICES: i > j};
num xc {VERTICES};
num yc {VERTICES};

num numsubtour init 0;
set SUBTOUR {1..numsubtour};

/* read in the instance and customer coordinates (xc, yc) */
read data tspData into VERTICES=[var1] xc=var2 yc=var3;

/* the cost is the euclidean distance rounded to the nearest integer */
num c {<i,j> in EDGES}
init floor( sqrt( ((xc[i]-xc[j])**2 + (yc[i]-yc[j])**2)) + 0.5);

var x {EDGES} binary;

/* minimize the total cost */
min obj =
sum {<i,j> in EDGES} c[i,j] * x[i,j];

/* each vertex has exactly one in-edge and one out-edge */
con two_match {i in VERTICES}:
sum {j in VERTICES: i > j} x[i,j]
+ sum {j in VERTICES: i < j} x[j,i] = 2;

/* no subtours (these constraints are generated dynamically) */
con subtour_elim {s in 1..numsubtour}:
sum {<i,j> in EDGES: (i in SUBTOUR[s] and j not in SUBTOUR[s])
or (i not in SUBTOUR[s] and j in SUBTOUR[s])} x[i,j] >= 2;

/* this starts the algorithm to find violated subtours */
set <num,num> EDGES1;
set VERTICES1 = union{<i,j> in EDGES1} {i, j};
num component {VERTICES1};
num numcomp  init 2;
num iter     init 1;
call symput('i',trim(left(put(round(iter),best.))));
num numiters init 1;

/* initial solve with just matching constraints */
solve;
call symput(compress('obj'||put(iter,best.)),
trim(left(put(round(obj),best.))));

/* create a data set for use by PROC SGPLOT */
create data solData from
[i j]={<i,j> in EDGES: x[i,j].sol > 0.5}
x1=xc[i] y1=yc[i] x2=xc[j] y2=yc[j];
submit;
%plotTSP;
endsubmit;
/* while the solution is disconnected, continue */
do while (numcomp > 1);
iter = iter + 1;
call symput('i',trim(left(put(round(iter),best.))));

/* find connected components of support graph   */
EDGES1 = {<i,j> in EDGES: round(x[i,j].sol) = 1};
solve with network /
nodes   = (include=VERTICES1)
concomp
out     = (concomp=component);

numcomp = _oroptmodel_num_["NUM_COMPONENTS"];
if numcomp = 1 then leave;

numiters = iter;
numsubtour = numsubtour + numcomp;
for {comp in 1..numcomp} do;
SUBTOUR[numsubtour-numcomp+comp]
= {i in VERTICES: component[i] = comp};
end;

solve;
call symput(compress('obj'||put(iter,best.)),
trim(left(put(round(obj),best.))));

/* create a data set for use by PROC SGPLOT */
create data solData from
[i j]={<i,j> in EDGES: x[i,j].sol > 0.5}
x1=xc[i] y1=yc[i] x2=xc[j] y2=yc[j];

call symput('numiters',put(numiters,best.));
submit;
%plotTSP;
endsubmit;
end;
quit;

```