1 research outputs found
New Characterizations and Efficient Local Search for General Integer Linear Programming
Integer linear programming (ILP) models a wide range of practical
combinatorial optimization problems and has significant impacts in industry and
management sectors. This work proposes new characterizations of ILP with the
concept of boundary solutions. Motivated by the new characterizations, we
develop an efficient local search solver, which is the first local search
solver for general ILP validated on a large heterogeneous problem dataset. We
propose a new local search framework that switches between three modes, namely
Search, Improve, and Restore modes. We design tailored operators adapted to
different modes, thus improving 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. The theoretical analysis of our algorithm is also
presented, which shows our algorithm could avoid visiting unnecessary regions
and also maintain good connectivity of targeted solutions.Comment: 36 pages, 2 figures, 7 table