Computational Comparison of Exact Solution Methods for 0-1 Quadratic Programs: Recommendations for Practitioners

Table 1

Summary of answers to Questions 1 through 5.

Question	Answer/recommendation
1: When applying the standard linearization to a BQP, should you reduce the size of the formulation based on the sign of the quadratic objective coefficients?	Our recommendation is to use the sign-based formulation STD when using the standard linearization.
2: When applying Glover’s formulation, should you represent the quadratic objective coefficient matrix C in upper triangular or symmetric form?	Our recommendation is to represent the quadratic objective coefficient matrix in upper triangular form when using Glover’s method.
3: With regards to the overall computational effort to formulate and solve problem G1 to optimality using a MILP solver, should we compute the bounds Uj^1, Uj^0, L^1j, and L^0j using (15), (16), or (17)?	In general, we recommend using the bounds of (16) when applying Glover’s method. However, for smaller-sized instances it may be beneficial to use the weaker bounds of (15).
4: How do formulations G1 and G2 compare when submitted to a MILP solver?	In general, formulation G2 is superior to G1.
5: Is it advantageous to perform the substitution of variables to reduce Problem G2 to G2a or G2b when submitting the model to a MILP solver?	While formulations G2, G2a, and G2b are fairly comparable in terms of performance, our general recommendation is to use G2a when applying Glover’s method.