Augmented neural networks and problem-structure based heuristics for the bin-packing problem

In this paper, we apply the Augmented-neural-networks (AugNN) approach for solving the classical bin-packing problem (BPP). AugNN is a metaheuristic that combines a priority- rule heuristic with the iterative search approach of neural networks to generate good solutions fast. This is the first time this approach has been applied to the BPP. We also propose a decomposition approach for solving harder BPP, in which sub problems are solved using a combination of AugNN approach and heuristics that exploit the problem structure. We discuss the characteristics of problems on which such problem-structure based heuristics could be applied. We empirically show the effectiveness of the AugNN and the decomposition approach on many benchmark problems in the literature. For the 1210 benchmark problems tested, 917 problems were solved to optimality and the average gap between the obtained solution and the upper bound for all the problems was reduced to under 0.66% and computation time averaged below 33 seconds per problem. We also discuss the computational complexity of our approach

How to pack trapezoids: exact and evolutionary algorithms

The purposes of this paper are twofold. In the first, we describe an exact polynomial-time algorithm for the pair sequencing problem and show how this method can be used to pack fixed-height trapezoids into a single bin such that interitem wastage is minimised. We then go on to examine how this algorithm can be combined with bespoke evolutionary and local search methods for tackling the multiple-bin version of this problem—one that is closely related to one-dimensional bin packing. In the course of doing this, a number of ideas surrounding recombination, diversity, and genetic repair are also introduced and analysed

Vehicle routing with multi-dimensional loading constraints

Zwei der wichtigsten Problemstellungen in der Transportlogistik behandeln einerseits das Verladen von Produkten auf LKWs und andererseits die ressourceneffiziente Belieferung der Kunden auf dem gegebenen Straßennetz. Bis dato wurden diese zwei Probleme mit Hilfe von kombinatorischer Optimierung getrennt von einander behandelt und es existieren zahlreiche Publikationen zu beiden Themen in den einschlägigen Fachzeitschriften. Erst in den letzten drei Jahren wurde einem integrierten Ansatz, der beide Problemstellungen zu einem Optimierungsproblem vereint betrachtet. Somit werden die Bestellungen einzelner Kunden nicht bloß über ihre Gewichte, sondern auch über ihre Abmessungen definiert. Der klare Vorteil dieses Ansatzes liegt darin, dass die einzelnen LKW Routen auch tatsächlich so gefahren werden können, da die tatsächliche Beladung auch berücksichtigt wurde. Andererseits steigt die kombinatorische Komplexität drastisch, weil das kapazitierte Vehicle Routing Problem (CVRP) mit Bin Packing Problemen (BPP) kombiniert wird und beide Probleme für sich alleine NP schwer sind. Diese Dissertation präsentiert drei verschiedene Probleme, die sich neben der Frage welches Fahrzeug beliefert welchen Kunden auch der Frage widmet, wie die bestellten Produkte auf den LKW geladen werden können. - Das Multi-Pile Vehicle Routing Problem (MP-VRP) bindet in das klassische CVRP eine Beladekomponente ein, die zwischen eindimensionalem und zweidimensionalem Bin Packing Problem angesiedelt ist. Die Problemstellungen wurden durch einen österreichischen Holzzulieferer motiviert. - Beim kapazitierten Vehicle Routing Problem mit zweidimensionalen Beladenebenbedingungen (2L-CVRP) bestellt jeder Kunden rechteckige Objekte, welche auf der rechteckigen Beladefläche des LKWs untergebracht werden müssen. - Das allgemeinste Beladeproblem stellt das dreidimensionale Bin Packing Problem dar. Hier bestellt jeder Kunde dreidimensionale Objekte, welche auf dem dreidimensionalen Laderaum des LKWs untergebracht werden müssen. Das klassische dreidimensionale Bin Packing Problem wird durch zusätzliche Beladenebenbedingungen erweitert. Momentan gibt es zu diesen kombinierten Problemen nur wenige Publikationen. Exakte Ansätze gibt es momentan nur zwei, einen für das MP-VRP (hier können Probleme bis zu 50 Kunden gelöst werden) und für das 2L-CVRP (hier können Probleme bis zu 30 Kunden exakt gelöst werden). Für Realweltanwendungen müssen jedoch Heuristiken gefunden werden, welche größere Probleminstanzen lösen können. In dieser Arbeit wird für alle drei Problemstellungen ein Ameisenalgorithmus verwendet und mit bestehenden Lösungsansätzen aus dem Bereich der Tabu-Suche (TS) verglichen. Es wird gezeigt, dass der präsentierte Ameisenansatz für die zur Verfügung stehenden Benchmarkinstanzen die besten Ergebnisse liefert. Darüber hinaus wird der Einfluss verschiedener Beladenebenbedingungen auf die Lösungsgüte untersucht, was eine wichtige Entscheidungsgrundlage für Unternehmen darstellt.Two of the most important problems in distribution logistics concern the loading of the freight into the vehicles, and the successive routing of the vehicles along the road network, with the aim of satisfying the demands of the clients. In the combinatorial optimization field, these two loading and routing problems have been studied intensively but separately yielding a large number of publications either for routing or packing problems. Only in recent years some attention has been brought to their combined optimization. The obvious advantage is that, by considering the information on the freight to be loaded, one can construct more appropriate routes for the vehicles. The counterpart is that the combinatorial difficulty of the problem increases consistently. One must not forget that both the vehicle routing problem and the bin packing problem are NP hard problems! This thesis presents three different problems concerning the combination of routing and loading (packing) problems. - The Multi-Pile Vehicle Routing Problem (MP-VRP) incorporates an interesting loading problem situated between one dimensional and two dimensional bin packing. This problem has been inspired by a real world application of an Austrian wood distributing company. - The Capacitated Vehicle Routing Problem with Two-Dimensional Loading Constraints (2L-CVRP) augments the classical Capacitated Vehicle Routing Problem by requiring the satisfaction of general two dimensional loading constraints. This means that customers order items represented by rectangles that have to be feasibly placed on the rectangular shaped loading surface of the used vehicles. - The most general packing problem to be integrated is the Three Dimensional Bin Packing Problem (3DBPP) resulting in the Capacitated Vehicle Routing Problem with Three-Dimensional Loading Constraints (3L-CVRP). Here the order of each customer consists of cuboid shaped items that have to be feasibly placed on the loading space of the vehicle. A feasible placement is influenced by additional constraints that extend the classical 3DBPP. Concerning the literature solving these problems with exact methods it becomes clear that this is only possible to some very limited extent (e.g.: the MP-VRP can be solved up to 50, the 2L-CVRP can be solved exact up to 30 customers, for the 3L-CVRP no exact approach exists). Nevertheless for real world applications the problem instances are much larger which justifies the use of (meta-)heuristics. The rank-based Ant System was modified and extended to solve the combined problem by integrating different packing routines. The designed methods outperform the existing techniques for the three different problem classes. The influence of different loading constraints on the objective value is investigated/is intensively studied to support the decision makers of companies facing similar problems

Exact and evolutionary algorithms for the score-constrained packing problem

This thesis concerns the Score-Constrained Packing Problem (SCPP), a combinatorial optimisation problem related to the one-dimensional bin packing problem. The aim of the SCPP is to pack a set of rectangular items from left to right into the fewest number of bins such that no bin is overfilled; however, the order and orientation of the items in each bin affects the feasibility of the overall solution. The SCPP has applications in the packaging industry, and obtaining high quality solutions for instances of the SCPP has the ability to reduce the amount of waste material, costs, and time, which motivates the study in this thesis. The minimal existing research on the SCPP leads us to explore a wide range of approaches to the problem in this thesis, implementing ideas from related problems in literature as well as bespoke methods. To begin, we present an exact algorithm that can produce a feasible configuration of a subset of items in a single bin in polynomial-time. We then introduce a range of methods for the SCPP including heuristics, an evolutionary algorithm framework comprising a local search procedure and a choice of three distinct recombination operators, and two algorithms combining metaheuristics with an exact procedure. Each method is investigated to gain more insight into the characteristics that benefit or hinder the improvement of solutions, both theoretically and computationally, using a large number of problem instances with varying parameters. This allows us to determine the specific methods and properties that produce superior solutions depending on the type of problem instance