go

data/2024-Algorithms/src/bestbippol.zpl

+#param vfile := "ins1-v.txt";
+#param efile := "ins1-e.txt";
+
+# set V := { "a1", "a2", "a3", "a4" };
+set V := { read vfile as "<1s>"  };
+param vsize := card(V);
+do print "Num vertices: ",vsize;
+
+do print V;
+set Edges := { read efile as "<1s,2s>"  };
+do print Edges;
+param esize := card(Edges);
+do print "Num non-zero edges: ",esize;
+
+
+# param vcost[V] := <"a1"> 2, <"a2"> 4, <"a3"> -5 , <"a4"> -3;
+param vcost[V] := read vfile as "<1s> 2n";
+do forall <v> in V do print v, " -> ", vcost[v];
+
+#param ecost[Edges] := <"a1","a1"> 0, <"a1","a2"> 0, <"a1","a3"> 2, <"a1","a4"> 0,
+#                      <"a2","a1"> 0, <"a2","a2"> 0, <"a2","a3"> 2, <"a2","a4"> 0,
+#                      <"a3","a1"> 2, <"a3","a2"> 0, <"a3","a3"> 0, <"a3","a4"> 0,
+#                      <"a4","a1"> 0, <"a4","a2"> 0, <"a4","a3"> 0, <"a4","a4"> 0;
+param ecost[Edges] := read efile as "<1s,2s> 3n";
+do forall <v1,v2> in Edges do print v1,v2," -> ",ecost[v1,v2];
+
+set Vpos := {  <v> in V with vcost[v] > 0 };
+set Vneg := {  <v> in V with vcost[v] <= 0 };
+
+#do print "Vpos: ";
+#do print Vpos;
+#do print "Vneg: ";
+#do print Vneg;
+#do forall <v> in V do print "Cost for: ", v, " is: ",vcost[v];
+#do print Vneg*Vpos;
+#do print ((-1)*vcost["a3"]*vcost["a1"])*(1.0-(-1))*(1.0+1)/4.0;
+#do print sum<i,j> in Vneg*Vpos : ((-1)*vcost[i]*vcost[j]);
+
+var x[V] integer >= -1 <= 1;
+var dummy integer >=0  <= 1;
+
+subto polarized:  forall <v> in V: x[v]^2 == 1;
+subto fixed: dummy == 1;
+
+# double quadratic model 
+maximize cost: 
+(sum <i,j> in Vneg*Vpos :  (((-1.0)*vcost[i]*vcost[j])*(dummy-x[i])*(dummy+x[j])/4.0)) / (1.0*vsize*vsize) *
+  ((sum <i,j> in Edges : ecost[i,j]*(dummy-(x[i]*x[j]))/2.0)/(esize) + (dummy*2.0) );
+
+
+
+# maximize cost:  (dummy-(x["a3"]*x["a1"]));
+
+# optimal:
+# -(-5)*2 + -(-5)*4 + -(-3)*2 + -(-3)*4 = 10 + 20 + 6 + 12 = 36+12 = 48
+# 48 * (2+2+2) = 288
+
+
+# Normalized values
+#
+#  -(-1)*1 * (1-(-1))*(1+1)/4 + -(-1)*1 * (1-(-1))*(1+1)/4 + -(-1)*1 * (1-(-1))*(1+1)/4 + -(-1)*1 * (1-(-1))*(1+1)/4  = 1+1+1+1 = 4     y 4/(4*4) = 1/4  
+
+# edges:   -(-2)*3 = 6   y  6 / 3 = 2    2 + 2 = 4 
+
+

data/2024-Algorithms/src/solve_bippol.sh

+#!/bin/bash
+zimpl bestbippol.zpl -t pip -D vfile=$1 -D efile=$2
+scip -c "set limits time 600  read bestbippol.pip   optimize display solution quit"
+