Helsgaun did describe some things in his LKH-3 technical report, although it's quite terse and does not really go into details: http://webhotel4.ruc.dk/~keld/research/LKH-3/LKH-3_REPORT.pd... . You may be better served by just looking at the source code in http://webhotel4.ruc.dk/~keld/research/LKH-3/LKH-3.0.6.tgz if you're interested how some specific constraint is handled.