The 0-1 bidimensional knapsack problem: Toward an efficient high-level primitive tool
ABSTRACT Efficient codes exist for exactly solving the 0-1 knapsack problem, which is a common primitive structure in relaxation and decomposition techniques for the solution of general models. We suggest moving to a higher primitive level by using the bidimensional knapsack, which can be used to enhance linear programming or Lagrangean type classical relaxations.With the ultimate aim of providing an exact and efficient solution to the bidimensional knapsack problem, we describe here a heuristic approach based on surrogate duality. In particular, we consider the usefulness of a specific preprocessing phase before a possible enumerative phase.Extensive numerical experiments, based on test problems from the literature as well as randomly generated instances, show that our code compares favorably with the GP procedure developed by Gavish and Pirkul for the multidimensional case.
- SourceAvailable from: George L. Nemhauser
Article: MINTO, a mixed INTeger optimizer[show abstract] [hide abstract]
ABSTRACT: MINTO is a software system that solves mixed-integer linear programs by a branch-and-bound algorithm with linear programming relaxations. It also provides automatic constraint classification, preprocessing, primal heuristics and constraint generation. Moreover, the user can enrich the basic algorithm by providing a variety of specialized application routines that can customize MINTO to achieve maximum efficiency for a problem class.Operations Research Letters. 11/1997;
- INFOR Information Systems and Operational Research 12/1994; 32. · 0.40 Impact Factor
- [show abstract] [hide abstract]
ABSTRACT: An exact algorithm is proposed for the 0–1 collapsing knapsack problem as defined by Guignard and Posner. Bounding of the number of variables equal to 1 in an optimal solution is extensively used, as well as inner- and outer-linearization of the nonlinear right-hand side of the constraint. This allows generally a drastic reduction of the feasible domain. An implicit enumeration scheme solves the problem reduced by the preprocessing phase. Computational experiments are reported on.Discrete Applied Mathematics. 01/1994; 49:175-187.