Lifted Cover Inequalities for 0-1 Integer Programs: Computation

We investigate the algorithmic and implementation issues related to the eeective and eecient use of lifted cover inequalities and lifted GUB cover inequalities in a branch-and-cut algorithm for 0-1 integer programming. We have tried various strategies on several test problems and we identify the best ones for use in practice. Branch-and-cut, with lifted cover inequalities as cuts, has been used successfully (CPLEX 4], OSL, see IBM 15], MINTO, see Nemhauser, Savelsbergh, and Sigismondi 18]) to solve general 0-1 integer programs of the form maxfcx : Ax b; x 2 B n g; where A is an integer matrix that contains knapsack rows, i.e., rows with some coeecients not equal to 0,1,-1, and B n is the set of n-dimensional 0-1 vectors. Branch-and-cut, introduced by Grr otschel, J unger, and Reinelt 7] and Padberg and Rinaldi 22], is enhanced branch-and-bound where the LP relaxation is tightened at nodes of the tree by the addition of valid inequalities that are not satissed by the current solution to the LP relaxation (see Hooman and Padberg 13] and Nemhauser and Wolsey 20] for expositions). Lifted cover inequalities (LCIs) are valid inequalities derived from a knapsack constraint. A cover inequality simply states that not all of the variables in a set can equal one and lifting strengthens the cover inequality by including in the inequality variables that are not in the set.