TSpack: a unified tabu search code for multi-dimensional bin packing problems

We present a computer code that implements a general Tabu Search technique for the solution of two- and three-dimensional bin packing problems, as well as virtually any of their variants requiring the minimization of the number of bins. The user is only requested to provide a procedure that gives an approximate solution to the actual variant to be solve

Алгоритмы для решения двумерной задачи упаковки

В настоящей работе мы предлагаем эффективный Best-Fit (IBF) алгоритм для задачи 2D-BPP, когда предметы и контейнеры имеют фиксированную ориентацию, параллельную координатным осям. Приводится сравнение предлагаемого алгоритма с другими алгоритмами. Эксперименты показывают эффективность и устойчивость предлагаемого подхода

ЭФФЕКТИВНЫЙ BEST-FIT-АЛГОРИТМ ДЛЯ РЕШЕНИЯ ЗАДАЧ ДВУХМЕРНОЙ ОРИЕНТИРОВАННОЙ УПАКОВКИ В КОНТЕЙНЕРЫ

Рассматривается задача двухмерной упаковки в контейнеры (2D-BPP), которая заключаетсяв минимизации числа одинаковых больших прямоугольников, используемых для упаковки конечного набора прямоугольников. Предлагается эффективный Best-Fit-алгоритм (IBF), основанный на методе вогнутого угла, для решения 2D-BPP. Вычислительный эксперимент по оценке эффективности алгоритма в сравнении с четырьмя классическими алгоритмами показывает, что IBF получил лучшие результаты почти для всех тестовых примеров за меньшее время

Un mouvement incrémental pour le problème du strip-packing

Alors qu'il est facile de maintenir la propriété BL lors de l'ajout d'un rectangle, ce maintien est plus coûteux après le retrait d'un rectangle. Cela rend difficile de concevoir des mouvements incrémentaux dans des métaheuristiques ou des algorithmes complets d'optimisation. Cet article explore la possibilité de violer la propriété BL. A la place, nous proposons de maintenir simplement un ensemble de "trous maximaux", ce qui permet l'ajout mais aussi le retrait incrémental de rectangles. Pour valider notre approche alternative, nous avons conçu un mouvement incrémental, qui maintient les trous maximaux, pour le problème du strip-packing, une variante du problème de placement de rectangles. Nous avons également utilisé des heuristiques initiales gloutonnes standard. et la métaheuristique {\tt ID~Walk} pour réaliser une recherche locale basée sur ce mouvement. Les résultats expérimentaux montrent que l'approche est compétitive avec les meilleurs algorithmes incomplets, plus spécialement avec les autres métaheuristiques (dotées de mécanismes pour sortir des mimima locaux)

A Vitual-Force Based Swarm Algorithm for Balanced Circular Bin Packing Problems

Balanced circular bin packing problems consist in positioning a given number of weighted circles in order to minimize the radius of a circular container while satisfying equilibrium constraints. These problems are NP-hard, highly constrained and dimensional. This paper describes a swarm algorithm based on a virtual-force system in order to solve balanced circular bin packing problems. In the proposed approach, a system of forces is applied to each component allowing to take into account the constraints and minimizing the objective function using the fundamental principle of dynamics. The proposed algorithm is experimented and validated on benchmarks of various balanced circular bin packing problems with up to 300 circles. The reported results allow to assess the effectiveness of the proposed approach compared to existing results from the literature.Comment: 23 pages including reference

Logic based Benders' decomposition for orthogonal stock cutting problems

We consider the problem of packing a set of rectangular items into a strip of fixed width, without overlapping, using minimum height. Items must be packed with their edges parallel to those of the strip, but rotation by 90\ub0 is allowed. The problem is usually solved through branch-and-bound algorithms. We propose an alternative method, based on Benders' decomposition. The master problem is solved through a new ILP model based on the arc flow formulation, while constraint programming is used to solve the slave problem. The resulting method is hybridized with a state-of-the-art branch-and-bound algorithm. Computational experiments on classical benchmarks from the literature show the effectiveness of the proposed approach. We additionally show that the algorithm can be successfully used to solve relevant related problems, like rectangle packing and pallet loading

Automating the packing heuristic design process with genetic programming

The literature shows that one-, two-, and three-dimensional bin packing and knapsack packing are difficult problems in operational research. Many techniques, including exact, heuristic, and metaheuristic approaches, have been investigated to solve these problems and it is often not clear which method to use when presented with a new instance. This paper presents an approach which is motivated by the goal of building computer systems which can design heuristic methods. The overall aim is to explore the possibilities for automating the heuristic design process. We present a genetic programming system to automatically generate a good quality heuristic for each instance. It is not necessary to change the methodology depending on the problem type (one-, two-, or three-dimensional knapsack and bin packing problems), and it therefore has a level of generality unmatched by other systems in the literature. We carry out an extensive suite of experiments and compare with the best human designed heuristics in the literature. Note that our heuristic design methodology uses the same parameters for all the experiments. The contribution of this paper is to present a more general packing methodology than those currently available, and to show that, by using this methodology, it is possible for a computer system to design heuristics which are competitive with the human designed heuristics from the literature. This represents the first packing algorithm in the literature able to claim human competitive results in such a wide variety of packing domains

Verbundprojekt PARALOR: Parallele Verfahren zur Wegoptimierung in Flugplanung und Logistik

Die Lösung kombinatorischer Optimierungsprobleme ist in vielen Bereichen von Wirtschaft und Technik der Schlüssel zur Steigerung der Effizienz technischer Abläufen, zur Verbesserung der Produktqualität und zur Veringerung von Produktions-, Material- und Transportkosten. Der Einsatz herkömmlicher sequentieller Verfahren ist für praxisrelevante Probleme aufgrund der enormen Rechenzeiterfordernisse nur sehr eingeschränkt möglich. Parallele Systeme bieten eine Möglichkeit, derartige Probleme in vertretbarer Zeit zu lösen. Im Rahmen des Verbundprojektes PARALOR wird untersucht, wie parallele Algorithmen der kombinatorischen Optimierung in konkreten, industriellen Anwendungen aus der Flugplanung sowie der Speditionslogistik effizient eingesetzt werden können. In diesem Artikel werden wesentliche Ergebnisse des Projekts exemplarisch vorgestellt