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 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 | // Low Autocorrelation Binary Sequences /* Code written by Ian Gent, Feb 1999, ipg@cs.strath.ac.uk For description of techniques used, see Symmetry Breaking during Search in Constraint Programming Ian P Gent and Barbara M Smith University of Leeds Research Report, 1999. This code does NOT contain the symmetry breaking techniques described in the report, so if you are interested in those contact the authors. Instead two simple constraints break some symmetries, by asserting that the first two bits are both -1. */ #include <ilsolver/ilcint.h> IlcInt nBits; IlcConstraint SimpleMod(IlcIntVar var, IlcInt mod, IlcIntVar remainder) { return (0 <= remainder) && (remainder < mod) && ( (var-remainder) == ((var-remainder)/mod)*mod) ;} IlcConstraint SimpleMod(IlcIntVar var, IlcInt mod, IlcInt remainder) { if ((0 <= remainder) && (remainder < mod)) { return ( (var-remainder) == ((var-remainder)/mod)*mod) ;} else {var.getManager().fail(); } ;} // impossible to satisfy IlcConstraint SimpleMod(IlcInt var, IlcInt mod, IlcIntVar remainder) { return (0 <= remainder) && (remainder < mod) && ( (var-remainder) == ((var-remainder)/mod)*mod) ;} void ModCorrelation(IlcIntVarArray Bits, IlcInt k, IlcIntVar Correlation) { IlcManager m = Bits.getManager(); IlcIntArray BitValues(m,2,-1,1); IlcInt numCorrelations = IlcMin(k,nBits-k); IlcIntVar Mod4Value(m,0,3); IlcIntVarArray Mod4Values(m,numCorrelations,0,3); IlcIntVarArray SequenceCorrelations(m,numCorrelations); IlcInt length ; for (IlcInt ki = 0; ki < numCorrelations; ki++) { length = (nBits-1-ki)/k; // hope that's right -- CHECK!! // length = 0 -> no correlation at this distance // although I think formula still holds as first value = 0? if (length > 0) { IlcIntVarArray products(m,0,length,1,IlcIntVar(m,BitValues)); for (IlcInt j = 0; j < length; j++) { products[j] = Bits[j*k + ki]*Bits[(j+1)*k+ki]; } SequenceCorrelations[ki] = IlcSum(products); m.add(SimpleMod(SequenceCorrelations[ki],2,length%2)); m.add( SimpleMod((length%4) - (2*(Bits[ki] != Bits[ki+(length*k)])), 4, Mod4Values[ki]) ); m.add(SimpleMod(SequenceCorrelations[ki],4,Mod4Values[ki])); } else { assert (1 == 0) ; // error if we get here! SequenceCorrelations[ki] = IlcIntVar(m,0,0); m.add( Mod4Values[ki] == 0) ; } ; }; m.add(Correlation == IlcSum(SequenceCorrelations)); m.add(SimpleMod(IlcSum(Mod4Values),4,Mod4Value)); m.add(SimpleMod(Correlation,4,Mod4Value)); } void SimpleCorrelation(IlcIntVarArray Bits, IlcInt k, IlcIntVar Correlation) { IlcManager m = Bits.getManager(); IlcIntArray BitValues(m,2,-1,1); IlcInt numCorrelations = IlcMin(k,nBits-k); IlcIntVarArray SequenceCorrelations(m,numCorrelations); IlcInt length ; for (IlcInt ki = 0; ki < numCorrelations; ki++) { length = (nBits-1-ki)/k; // hope that's right -- CHECK!! // length = 0 -> no correlation at this distance // although I think formula still holds as first value = 0? if (length > 0) { IlcIntVarArray products(m,0,length,1,IlcIntVar(m,BitValues)); for (IlcInt j = 0; j < length; j++) { products[j] = Bits[j*k + ki]*Bits[(j+1)*k+ki]; } SequenceCorrelations[ki] = IlcSum(products); m.add(SimpleMod(SequenceCorrelations[ki],2,length%2)); } else { assert (1 == 0) ; // error if we get here! SequenceCorrelations[ki] = IlcIntVar(m,0,0); } }; m.add(Correlation == IlcSum(SequenceCorrelations)); } //$doc:CHOOSE IlcChooseIndex1(IlcChooseOutermost, IlcMin(varIndex,nBits-varIndex), IlcIntVar) //end:CHOOSE //$doc:MAIN1 int main( int argc, char ** argv){ IlcManager m(IlcNoEdit); IlcInt i ; // loop variable #if defined(ILCLOGFILE) m.openLogFile( "labs.log" ); #endif nBits = (argc > 1) ? atoi (argv[1]) : 10; IlcIntVar zeroVar(m,0,0); IlcIntArray BitValues(m,2,-1,1); IlcIntVarArray Bits(m,0,nBits,1,IlcIntVar(m,BitValues)); // Set up domains of even/odd squares IlcIntArray EvenSquares(m,(nBits/2)+1) ; IlcIntArray OddSquares(m,(nBits+1)/2) ; for (i=0;i<(nBits/2)+1;i++) { EvenSquares[i]= IlcSquare(i*2); } for (i=0;i<(nBits+1)/2;i++) { OddSquares[i]= IlcSquare(i*2+1); } // IlcIntVarArray *shiftedBits = new(m.getHeap()) IlcIntVarArray[nBits]; // IlcIntVarArray *differences = new(m.getHeap()) IlcIntVarArray[nBits]; IlcIntVarArray Correlations(m,nBits,-nBits,nBits); Correlations[0] = zeroVar; // so that Correlations[i] matches distance i //shiftedBits[0] = Bits; // differences[0] = Bits; IlcIntVarArray SquareCorrelations(m,nBits); SquareCorrelations[0] = zeroVar; // general correlation mod work for (i=1; i < nBits; i++) { if (i <= (nBits/2)) { ModCorrelation(Bits,i,Correlations[i]) ; } else { SimpleCorrelation(Bits,i,Correlations[i]) ; } ; if (((nBits-i) %2) == 0L) { SquareCorrelations[i] = IlcIntVar(m,EvenSquares); } else { SquareCorrelations[i] = IlcIntVar(m,OddSquares); } m.add(SquareCorrelations[i] == IlcSquare(Correlations[i])); } IlcIntVar TotalSquareCorrelation = IlcSum(SquareCorrelations); m.setObjMin(TotalSquareCorrelation); // simple symmetry breaking: m.add(Bits[0] == -1); m.add(Bits[1] == -1); //end:MAIN1 /* */ //$doc:GEN2 m.add(IlcGenerate(Bits,IlcChooseOutermost)); //end:GEN2 //$doc:MAIN2 while (m.nextSolution()) { m.out() << "Cost:\t" << TotalSquareCorrelation.getValue() << endl; m.storeSolution(); m.printInformation(); m.out() << endl; } m.restart(); m.nextSolution(); m.out() << "Optimal Correlation Cost:\t" << TotalSquareCorrelation.getValue() << endl; m.out() << Bits << endl; m.out() << SquareCorrelations << endl; m.printInformation(); #if defined(ILCLOGFILE) m.closeLogFile(); #endif m.end(); return 0; } //end:MAIN2 |