Local Search for Integer Linear Programming

Integer linear programming models a wide range of practical combinatorial optimization problems and has significant impacts in industry and management sectors. This work develops the first standalone local search solver for general integer linear programming validated on a large heterogeneous problem dataset. We propose a local search framework that switches in three modes, namely Search, Improve, and Restore modes, and design tailored operators adapted to different modes, thus improve the quality of the current solution according to different situations. For the Search and Restore modes, we propose an operator named tight move, which adaptively modifies variables' values trying to make some constraint tight. For the Improve mode, an efficient operator lift move is proposed to improve the quality of the objective function while maintaining feasibility. Putting these together, we develop a local search solver for integer linear programming called Local-ILP. Experiments conducted on the MIPLIB dataset show the effectiveness of our solver in solving large-scale hard integer linear programming problems within a reasonably short time. Local-ILP is competitive and complementary to the state-of-the-art commercial solver Gurobi and significantly outperforms the state-of-the-art non-commercial solver SCIP. Moreover, our solver establishes new records for 6 MIPLIB open instances.