We study the two-dimensional geometric knapsack problem, in which we are given a set of n axis-aligned rectangular items, each one with an associated profit, and square knapsack. The goal is to find (non-overlapping) packing maximum profit subset items inside (without rotating items). best-known polynomial-time approximation factor for this problem (even just cardinality case) 2+ε [Jansen Zhang...

line and oo-line approximation algorithms for vector covering problems. analysis of algorithms for dual bin packing problems. packing can be solved within 1 + in linear time.gorithms for the m-dimensional 0-1 knapsack problem: worst-case and probabilistic analyses.schatz. Resource scheduling in enhanced pay-per-view continuous media databases. An eecient approximation scheme for the one-dimensi...

A special class of the knapsack problem is called the separable nonlinear knapsack problem. This problem has received considerable attention recently because of its numerous applications. Dynamic programming is one of the basic approaches for solving this problem. Unfortunately, the size of state-pace will dramatically increase and cause the dimensionality problem. In this paper, an efficient a...

In this paper we introduce the knapsack problem for perishable inventories concerning the optimal dynamic allocation of a collection of products to a limited knapsack. The motivation for designing such a problem comes from retail revenue management, where different products often have an associated lifetime during which they can only be sold, and the managers can regularly select some products ...

Dimensional analysis, for multi-criteria decision making, is a mathematical method that includes diverse heterogeneous criteria into a single dimensionless index. Dimensional Analysis, in its current definition, presents the drawback to manipulate fuzzy information commonly presented in a multi-criteria decision making problem. To overcome such limitation, we propose two dimensional analysis ba...

Since 1985 various evolutionary approaches to multiobjec-tive optimization have been developed, capable of searching for multiple solutions concurrently in a single run. But the few comparative studies of diierent methods available to date are mostly qualitative and restricted to two approaches. In this paper an extensive, quantitative comparison is presented, applying four multiobjective evolu...

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.

We consider a Two-Dimensional Cutting Stock Problem where stock of different sizes is available, and a set of rectangular items has to be obtained through two-staged guillotine cuts. We propose a heuristic algorithm, based on column generation, which requires as subproblem the solution of a Two-Dimensional Knapsack Problem with two-staged guillotines cuts. A further contribution of the paper co...

Rollout algorithms have enjoyed success across a variety of domains as heuristic solution procedures for stochastic dynamic programs (SDPs). However, because most rollout implementations are closely tied to specific problems, the visibility of advances in rollout methods is limited, thereby making it difficult for researchers in other fields to extract general procedures and apply them to diffe...