A new mixed-integer programming model for irregular strip packing based on vertical slices with a reproducible survey

The irregular strip-packing problem, also known as nesting or marker making, is defined as the automatic computation of a non-overlapping placement of a set of non-convex polygons onto a rectangular strip of fixed width and unbounded length, such that the strip length is minimized. Nesting methods based on heuristics are a mature technology, and currently, the only practical solution to this problem. However, recent performance gains of the Mixed-Integer Programming (MIP) solvers, together with the known limitations of the heuristics methods, have encouraged the exploration of exact optimization models for nesting during the last decade. Despite the research effort, the current family of exact MIP models for nesting cannot efficiently solve both large problem instances and instances containing polygons with complex geometries. In order to improve the efficiency of the current MIP models, this work introduces a new family of continuous MIP models based on a novel formulation of the NoFit-Polygon Covering Model (NFP-CM), called NFP-CM based on Vertical Slices (NFP-CM-VS). Our new family of MIP models is based on a new convex decomposition of the feasible space of relative placements between pieces into vertical slices, together with a new family of valid inequalities, symmetry breakings, and variable eliminations derived from the former convex decomposition. Our experiments show that our new NFP-CM-VS models outperform the current state-of-the-art MIP models. Finally, we provide a detailed reproducibility protocol and dataset based on our Java software library as supplementary material to allow the exact replication of our models, experiments, and results

Discrete Optimization in Early Vision - Model Tractability Versus Fidelity

Early vision is the process occurring before any semantic interpretation of an image takes place. Motion estimation, object segmentation and detection are all parts of early vision, but recognition is not. Some models in early vision are easy to perform inference with---they are tractable. Others describe the reality well---they have high fidelity. This thesis improves the tractability-fidelity trade-off of the current state of the art by introducing new discrete methods for image segmentation and other problems of early vision. The first part studies pseudo-boolean optimization, both from a theoretical perspective as well as a practical one by introducing new algorithms. The main result is the generalization of the roof duality concept to polynomials of higher degree than two. Another focus is parallelization; discrete optimization methods for multi-core processors, computer clusters, and graphical processing units are presented. Remaining in an image segmentation context, the second part studies parametric problems where a set of model parameters and a segmentation are estimated simultaneously. For a small number of parameters these problems can still be optimally solved. One application is an optimal method for solving the two-phase Mumford-Shah functional. The third part shifts the focus to curvature regularization---where the commonly used length and area penalization is replaced by curvature in two and three dimensions. These problems can be discretized over a mesh and special attention is given to the mesh geometry. Specifically, hexagonal meshes in the plane are compared to square ones and a method for generating adaptive meshes is introduced and evaluated. The framework is then extended to curvature regularization of surfaces. Finally, the thesis is concluded by three applications to early vision problems: cardiac MRI segmentation, image registration, and cell classification

A Polyhedral Study of Mixed 0-1 Set

We consider a variant of the well-known single node fixed charge network flow set with constant capacities. This set arises from the relaxation of more general mixed integer sets such as lot-sizing problems with multiple suppliers. We provide a complete polyhedral characterization of the convex hull of the given set

Proceedings of the 8th Cologne-Twente Workshop on Graphs and Combinatorial Optimization

International audienceThe Cologne-Twente Workshop (CTW) on Graphs and Combinatorial Optimization started off as a series of workshops organized bi-annually by either Köln University or Twente University. As its importance grew over time, it re-centered its geographical focus by including northern Italy (CTW04 in Menaggio, on the lake Como and CTW08 in Gargnano, on the Garda lake). This year, CTW (in its eighth edition) will be staged in France for the first time: more precisely in the heart of Paris, at the Conservatoire National d’Arts et Métiers (CNAM), between 2nd and 4th June 2009, by a mixed organizing committee with members from LIX, Ecole Polytechnique and CEDRIC, CNAM

An Energy-Efficient Distributed Algorithm for k-Coverage Problem in Wireless Sensor Networks

Wireless sensor networks (WSNs) have recently achieved a great deal of attention due to its numerous attractive applications in many different fields. Sensors and WSNs possesses a number of special characteristics that make them very promising in many applications, but also put on them lots of constraints that make issues in sensor network particularly difficult. These issues may include topology control, routing, coverage, security, and data management. In this thesis, we focus our attention on the coverage problem. Firstly, we define the Sensor Energy-efficient Scheduling for k-coverage (SESK) problem. We then solve it by proposing a novel, completely localized and distributed scheduling approach, naming Distributed Energy-efficient Scheduling for k-coverage (DESK) such that the energy consumption among all the sensors is balanced, and the network lifetime is maximized while still satisfying the k-coverage requirement. Finally, in related work section we conduct an extensive survey of the existing work in literature that focuses on with the coverage problem

Aproximación mediante modelos de programación entera a problemas de empaquetamiento.

El cáncer es un padecimiento de carácter global que constituye una de las primeras causas de muerte en el mundo; es el causante de alrededor del 13 % de todas las muertes. Su distribución mundial, su ascendente incidencia, costosos tratamientos y severos efectos secundarios de los mismos nos obligan a buscar nuevas alternativas que coadyuven a las terapias anticancerígenas ya existentes. Entre esas alternativas se ha optado por el uso de extractos naturales ya que son fuente de numerosos productos efectivos contra diversas enfermedades, incluido el cáncer. El objetivo de la presente investigación fue la de evaluar la actividad citotóxica de dos plantas endémicas de México, el cactus Pachycereus marginatus y la cucurbitácea Ibervillea sonorae, contra la línea celular de cáncer murino L51578Y-R, así como de aislar las substancias químicas responsables de dicha actividad. 522 g de material vegetal de P. marginatus y 136 g de I. sonorae fueron utilizados. Ambas plantas fueron sometidas a una extracción Soxhlet consecutiva con solventes de polaridad creciente (n-hexano, cloroformo y metanol) y a una extracción no consecutiva únicamente con metanol. Todos los extractos crudos del cactus demostraron una notable y similar actividad, aproximadamente 90 % desde 3.9 µg/ml. Los extractos de I. sonorae demostraron cierta citotoxicidad, siendo el extracto clorofórmico el más activo, 60 % a 7.8 µg/ml. Producto de un fraccionamiento biodirigido de éstos extractos se lograron aislar e identificar los siguientes compuestos: de Pachycerus marginatus, Lofenol (66 % a 62.5 µg/ml), β-sitosterol (61 % a 62.5 µg/ml) y ácido palmítico (86 % a 62.5 µg/ml); de Ibervillea sonorae, cucurbitacina 1(56 % a 125 µg/ml) y cucurbitacina 2 (90 % a 125 µg/ml). Los resultados de este trabajo revelan el potencial de estas plantas como fuentes de productos anticancerígenos así como también contribuyen al conocimiento fitoquímico de las misma