Heuristics with a worst-case bound for unconstrained quadratic 0–1 programming

In this paper, we present two heuristics for solving the unconstrained quadratic 0–1 programming problem. First heuristic realizes the steepest ascent from the centre of the hypercube, while the second constructs a series of solutions and chooses the best of them. In order to evaluate their worst-case behaviour We define the performance ratio K which uses the objective function value at the reference point x=1/2. We show for both heuristics that K is bounded by 1 from above and this bound is sharp. Finally, we report on the results of a computational study with proposed and local improvement heuristics.