Projective Splitting Algorithms for Integer Linear Programming Part 1:   Pure Integer Programs
  We propose a new exact approach for solving integer linear programming (ILP) problems which we will call projective splitting algorithms (PSAs). Unlike classical methods for solving ILP problems, PSAs conduct the search for the optimal solution by generating candidate solutions tailored to specific values of the objective function. As a consequence of this strategy, the number of variables in the original ILP problem is systematically reduced without adding any additional constraint to the initial formulation. This is the first of a two-part series on PSAs. In this paper we focus on the resolution of pure integer linear programming (PILP) problems, leaving the treatment of mixed integer linear programming (MILP) formulations to the second part of this series. The proposed algorithm was tested against the IBM ILOG CPLEX [2] optimizer on instances of the 0-1 Multidimensional Knapsack Problem (0-1MKP), showing satisfactory results on instances with a large number of variables. 
Federico Rodes, Isabel Mendez-Diaz and Paula Zabala
math.OC