Improved compact linearizations for the unconstrained quadratic 0–1 minimization problem

We present and compare three new compact linearizations for the quadratic 0–1 minimization problem, two of which achieve the same lower bound as does the “standard linearization”. Two of the linearizations require the same number of constraints with respect to Glover’s one, while the last one requires nn additional constraints where nn is the number of variables in the quadratic 0–1 problem. All three linearizations require the same number of additional variables as does Glover’s linearization. This is an improvement on the linearization of Adams, Forrester and Glover (2004) which requires nn additional variables and 2n2n additional constraints to reach the same lower bound as does the standard linearization. Computational results show however that linearizations achieving a weaker lower bound at the root node have better global performances than stronger linearizations when solved by Cplex.