Efficient reformulation for 0–1 programs — methods and computational results

The Multidimensional 0-1 Knapsack Problem—Bounds and Computational Aspects

“…Because z(L(µ * , s)) depends on µ * , the remaining gap can be reduced by using another optimal multiplier. By considering the LP-problem : It is well-known that coefficient reduction plays a key role in the automatic reformulation of 0-1 programs (See Bradley, Hammer, and Wolsey, 1974 for seminal ideas, Dietrich and Escudero, 1990;Dietrich, Escudero, and Chance, 1993 for new results and an extended bibliography). In addition, coefficient reduction improves the lagrangean, surrogate and LP duality gaps, but it can be noticed that coefficient reduction narrows the surrogate duality gap more than it does the Lagrangean or LP-gap.…”

A Conditional Logic Approach for Strengthening Mixed 0-1 Linear Programs

“…They incorporated SOS-tightened inequalities, as well as inequalities strengthened using plant location constraints (in a manner similar to Dietrich and Escudero (1990)), as part of a preprocessing scheme in a successful branch-and-cut algorithm. A more extensive study of coefficient increasing and coefficient decreasing methods was conducted in a sequence of papers (see Dietrich and Escudero, 1989a, 1989b, 1992Dietrich, Escudero, and Chance, 1993;Toth, 1995, 1998;Escudero and Muñoz, 1998 among others), where special structures such as clique constraints, cover restrictions, and variable upper bounding were effectively exploited. The central theory to this body of research, along with a good overview of the general approach and promising computational results, can be found in Dietrich, Escudero, and Chance (1993).…”

“…A more extensive study of coefficient increasing and coefficient decreasing methods was conducted in a sequence of papers (see Dietrich and Escudero, 1989a, 1989b, 1992Dietrich, Escudero, and Chance, 1993;Toth, 1995, 1998;Escudero and Muñoz, 1998 among others), where special structures such as clique constraints, cover restrictions, and variable upper bounding were effectively exploited. The central theory to this body of research, along with a good overview of the general approach and promising computational results, can be found in Dietrich, Escudero, and Chance (1993). The article by Escudero, Martello, and Toth (1998) shows how additional gains can be achieved by incorporating probing analysis and recent algorithmic advances for variants of the classical knapsack problem (see Martello and Toth, 1995).…”

On using an automatic scheme for obtaining the convex hull defining inequalities of a Weismantel 0–1 knapsack constraint

“…Let us use our coefficient reduction scheme given in Escudero et al (1995), see also Dietrich et al (1993), for deriving the other facet defining inequalities for the original 0-1 knapsack constraint (3.1). To begin with let us drop the variable xl from (3.1).…”

“…Our methods, see Dietrich et al (1993), Escudero et al (1997), and Escudero et al (1995) (appropriately embedded in branch-and-cut procedures, see Hoffman and Padberg (1991)) may produce reductions of the LP feasible set that are not generally detected by other (so-called myopic) procedures, where only information from the same constraint to replace is exploited, aside the integrality of the variables.…”