On a New Constraint Reduction Heuristic Using Improved Bisection Method for Mixed Integer Linear Programming

Abstract

In this study, we develop a surrogate relaxation-based procedure to reduce mixed-integer linear programming (MILP) problem sizes. This technique starts with one surrogate constraint which is a nonnegative linear combination of multiple constraints of the problem. At this initial step, we calculate optimal Lagrangian multipliers from LP relaxation of the problem and use them as initial surrogate multipliers. We incorporate the improved bisection method (IBM) (B. Gavish, F. Glover, and H. Pirkul, Surrogate Constraints in Integer Programming, J. Inform. Optim. Sci. 12(2) (1991), 219-228.) into our algorithm. This simple heuristic algorithm is designed to iteratively generate a new surrogate cut that is to guarantee to satisfy the most violated two constraints of the corresponding iteration. The performance of the heuristic is tested using both some problems from the OR libraries and randomly generated ones.