RÉSUMÉ : We consider two variants of knapsack problems with setups arising as subproblems in a DantzigWolfe decomposition approach to more complex combinatorial optimization problems. In the multiple-class binary knapsack problem with setups, items are partitioned into classes whose use implies a setup cost and associated capacity consumption. Item weights are assumed to be a multiple of their ...

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 ...

We consider the distributed version of the Multiple Knapsack Problem (MKP), wherem items are to be distributed amongst n processors, each with a knapsack. We propose different distributed approximation algorithms with a tradeoff between time and message complexities. The algorithms are based on the greedy approach of assigning the best item to the knapsack with the largest capacity. These algor...

The Three-Dimensional Knapsack Packing Problem consists of finding the maximum profit for packing a subset of boxes in a larger box (packing box). The boxes to pack are rectangular but of different sizes. This problem is a variant of the Knapsack Problem and therefore its computational complexity is NP-Complete. This article shows a parallel genetic algorithm based on the Island Model and the N...

It is well known that the standard (linear) knapsack problem can be solved exactly by dynamic programming in O(nc) time, where n is the number of items and c is the capacity of the knapsack. The quadratic knapsack problem, on the other hand, is NP-hard in the strong sense, which makes it unlikely that it can be solved in pseudo-polynomial time. We show however that the dynamic programming appro...

In this paper, we solve 0-1 knapsack problem using genetic algorithm. The knapsack problem is also called the NP (non deterministic polynomial) problem. We have to maximize the profit value that can be put in to a knapsack under the confinement of its weight. Solve the knapsack problem and also show its possible and effectiveness crowd an example. The Genetic Algorithm uses corrupted renewal an...