A Lagrangian reconstruction of a class of local search methods

Heuristic repair algorithms, a class of local search methods, demonstrate impressive efficiency in solving some large-scale and hard instances of constraint satisfaction problems (CSPs). We draw a surprising connection between heuristic repair techniques and the discrete Lagrange multiplier methods by transforming CSPs into zero-one constrained optimization problems. A Lagrangian-based search scheme LSDL is proposed. We show how GENET, a representative heuristic repair algorithm, can be reconstructed from LSDL. The dual viewpoint of GENET as a heuristic repair method and Lagrange multiplier method allows us to investigate variants of GENET from both perspectives. Benchmarking results confirm that first, our reconstructed GENET has the same fast convergence behavior as other GENET implementations reported in the literature, competing favourably with other state-of-the-art methods on a set of hard graph colouring problems. Second, our best variant, which combines techniques from heuristic repair and Lagrangian methods, is always more efficient than the reconstructed GENET, and can better it by an order of magnitude.