Alcuin's Propositiones de Civitatibus: the Earliest Packing Problems

A Comparative Study of Exact Algorithms for the Two Dimensional Strip Packing Problem

In this paper we consider a two dimensional strip packing problem. The problem consists of packing a set of rectangular items in one strip of width W and infinite height. They must be packed without overlapping, parallel to the edge of the strip and we assume that the items are oriented, i.e. they cannot be rotated. To solve this problem, we use three exact methods: a branch and bound method, a...

 Abstract: Packing rectangular shapes into a rectangular space is one of the most important discussions on Cutting & Packing problems (C;P) such as: cutting problem, bin-packing problem and distributor's pallet loading problem, etc. Assume a set of rectangular pieces with specific lengths, widths and utility values. Also assume a rectangular packing space with specific width and length. The obj...

Desarrollo de Indicadores de Casos Aplicables a la Selección de Algoritmos en el Problema 2-Partition

In this work, the problem was approached to transform instances and complexity indicators between the problems Bin-Packing and Partition. Diverse researches have realized reductions and polynomials transformations between NP-complete problems, it mentioned to Garey & Johnson, Karp and Cook. In this thesis a new approach proposes to transform instances and to develop complexity indicators betwee...

Differential evolution methods based on local searches

In this paper we analyze the behavior of a quite standard Differential Evolution (DE) algorithm applied to the objective function transformed by means of local searches. First some surprising results are presented which concern the application of this method to standard test functions. Later we introduce an application to diskand to sphere-packing problems, two well known and particularly hard ...

A semidefinite programming hierarchy for packing problems in discrete geometry

Packing problems in discrete geometry can be modeled as finding independent sets in infinite graphs where one is interested in independent sets which are as large as possible. For finite graphs one popular way to compute upper bounds for the maximal size of an independent set is to use Lasserre’s semidefinite programming hierarchy. We generalize this approach to infinite graphs. For this we int...