Lagrangian techniques for solving a class of zero-one integer linear programs

We consider a class of zero-one integer programming feasibility problems (0-1 ILPF problems) in which the coefficients of variables can be integers, and the objective is to find an assignment of binary variables so that all constraints are satisfied. We propose a Lagrangian formulation in the continuous space and develop a gradient search in this space. By using two counteracting forces, one performing gradient search in the primal space (of the original variables) and the other in the dual space (of the Lagrangian variables), we show that our search algorithm does not get trapped in local minima and reaches equilibrium only when a feasible assignment to the original problem is found. We present experimental results comparing our method with backtracking and local search (based on random restarts). Our results show that 0-1 ILPF problems of reasonable sizes can be solved by an order of magnitude faster than existing methods.