An integer linear programming approach for a class of bilinear integer programs

Abstract

We propose an Integer Linear Programming (ILP) approach for solving integer programming problems with bilinear objectives and linear constraints. Our approach is based on finding upper and lower bounds for the optimal bilinear objective function, and using the upper bound to produce a tight binary decomposition of an ensemble in the bilinear objective function. This allows us to transform the original problem into an equivalent ILP that can be solved efficiently. Numerical experiments suggest that the proposed approach outperforms a latest iterative ILP approach, with notable reductions in the average solution time.