A mixed integer linear programming formulation for low discrepancy consecutive k-sums permutation problem

Abstract

In this paper, low discrepancy consecutive k-sums permutation problem is considered. A mixed integer linear programing (MILP) formulation with a moderate number of variables and constraints is proposed. The correctness proof shows that the proposed formulation is equivalent to the basic definition of low discrepancy consecutive k-sums permutation problem. Computational results, obtained on standard CPLEX solver, give 88 new exact values, which clearly show the usefulness of the proposed MILP formulation.