Abstract In this paper, a new upper bound for the Multiple Knapsack Problem (MKP) is proposed, based on idea of relaxing MKP to Bounded Sequential Problem, i.e., multiple knapsack problem in which item sizes are divisible. Such relaxation, called sequential obtained by suitably replacing items instance with divisible sizes. Experimental results benchmark instances show that effective, terms qua...

Abstract We consider the product knapsack problem, which is variant of classical 0-1 problem where objective consists maximizing profits selected items. These are allowed to be positive or negative. present first fully polynomial-time approximation scheme for known weakly -hard. Moreover, we analyze quality achieved by a natural extension greedy procedure problem.

presented here is a generalization of the implicit enumeration algorithm that can be applied when the objec-tive function is being maximized and can be rewritten as the difference of two non-decreasing functions. also developed is a computational algorithm, named linear speedup, to use whatever explicit linear constraints are present to speedup the search for a solution. the method is easy to u...

In this paper, we discuss the adjacency structures of some classes of 0-1 polytopes including knapsack polytopes, set covering polytopes and 0-1 polytopes represented by complete sets of implicants. We show that for each class of 0-1 polytope, non-adjacency test problems are NP-complete. For equality constrained knapsack polytopes, we can solve adjacency test problems in pseudo polynomial time.

Chvv atal (1980) describes a class of zero-one knapsack problems provably diicult for branch and bound and dynamic programming algorithms. Chung et al. (1988) identiies a class of integer knapsack problems hard for branch and bound algorithms. We show that for both classes of problems local search provides optimal solutions quickly.

In this paper we discuss the generation of strong valid inequalities for (mixed) integer knapsack sets based on lifting of valid inequalities for basic knapsack sets with two integer variables (and one continuous variable). The description of the basic polyhedra can be made in polynomial time. We use superadditive valid functions in order to obtain sequence independent lifting.

A mathematical programming approach to deal with the global configuration of resource constraints is presented. A specialized parametric programming algorithm to obtain the pareto set for the biobjective problem that appears to deal with the global configuration for 0-1-Integer Linear Programing problems is presented and implemented. Computational results for Multiconstrained Knapsack problems ...

In this paper, we show that lattice reduction is a very powerful tool to nd collision in knapsack based compression-functions and hash-functions. In particular, it can be used to break the knapsack based hash-function that was introduced by Damgard 3]