Method encodeSigmoidConstraint

src/engine/MILPEncoder.cpp:462–591

}

void MILPEncoder::encodeSigmoidConstraint( GurobiWrapper &gurobi, SigmoidConstraint *sigmoid )
{
    unsigned sourceVariable = sigmoid->getB(); // x_b
    unsigned targetVariable = sigmoid->getF(); // x_f
    double sourceLb = _tableau.getLowerBound( sourceVariable );
    double sourceUb = _tableau.getUpperBound( sourceVariable );

    if ( sourceLb == sourceUb )
    {
        return;
    }
    else if ( FloatUtils::lt( sourceLb, 0 ) && FloatUtils::gt( sourceUb, 0 ) )
    {
        List<GurobiWrapper::Term> terms;
        String binVarName = Stringf( "a%u", _binVarIndex ); // a = 1 -> the case where x_b >= 0,
                                                            // otherwise where x_b <= 0
        gurobi.addVariable( binVarName, 0, 1, GurobiWrapper::BINARY );

        // Constraint where x_b >= 0
        // Upper line is tangent and lower line is secant for an overapproximation with a
        // linearization.

        int binVal = 1;

        // tangent line: x_f = tangentSlope * (x_b - tangentPoint) + yAtTangentPoint
        double tangentPoint = sourceUb / 2;
        double yAtTangentPoint = sigmoid->sigmoid( tangentPoint );
        double tangentSlope = sigmoid->sigmoidDerivative( tangentPoint );
        terms.append( GurobiWrapper::Term( 1, Stringf( "x%u", targetVariable ) ) );
        terms.append( GurobiWrapper::Term( -tangentSlope, Stringf( "x%u", sourceVariable ) ) );
        gurobi.addLeqIndicatorConstraint(
            binVarName, binVal, terms, -tangentSlope * tangentPoint + yAtTangentPoint );
        terms.clear();

        // secant line: x_f = secantSlope * (x_b - 0) + y_l
        double y_l = sigmoid->sigmoid( 0 );
        double y_u = sigmoid->sigmoid( sourceUb );
        double secantSlope = ( y_u - y_l ) / sourceUb;
        terms.append( GurobiWrapper::Term( 1, Stringf( "x%u", targetVariable ) ) );
        terms.append( GurobiWrapper::Term( -secantSlope, Stringf( "x%u", sourceVariable ) ) );
        gurobi.addGeqIndicatorConstraint( binVarName, binVal, terms, y_l );
        terms.clear();

        // lower bound of x_b
        terms.append( GurobiWrapper::Term( 1, Stringf( "x%u", sourceVariable ) ) );
        gurobi.addGeqIndicatorConstraint( binVarName, binVal, terms, 0 );
        terms.clear();

        // lower bound of x_f
        terms.append( GurobiWrapper::Term( 1, Stringf( "x%u", targetVariable ) ) );
        gurobi.addGeqIndicatorConstraint( binVarName, binVal, terms, y_l );
        terms.clear();

        // Constraints where x_b <= 0
        // Upper line is secant and lower line is tangent for an overapproximation with a
        // linearization.

        binVal = 0;