José Fernando Oliveira

A GRASP approach to the container-loading problem

The container-loading problem aims to determine the arrangement of items in a container. We present GRMODGRASP, a new algorithm for the CLP based on the GRASP (greedy randomized adaptive search procedure) paradigm. We evaluate GRMODGRASPS performance in terms of volume use and load stability and by comparing it with nine well-known algorithms. Our approach produces solutions that surpass other approaches solutions in terms of volume use and cargo stability.

Solving Irregular Strip Packing problems by hybridising simulated annealing and linear programming

Abstract In this paper a hybrid algorithm to solve Irregular Strip Packing problems is presented. The metaheuristic simulated annealing is used to guide the search over the solution space while linear programming models are solved to generate neighbourhoods during the search process. These linear programming models, which are used to locally optimise the layouts, derive from the application of compaction and separation algorithms. Computational tests were run using instances that are commonly used as benchmarks in the literature. The best results published so far have been improved by this new hybrid packing algorithm.

The geometry of nesting problems: A tutorial

Cutting and packing problems involving irregular shapes is an important problem variant with a wide variety of industrial applications. Despite its relevance to industry, research publications are relatively low when compared to other cutting and packing problems. One explanation offered is the perceived difficulty and substantial time investment of developing a geometric tool box to assess computer generated solutions. In this paper we set out to provide a tutorial covering the core geometric methodologies currently employed by researchers in cutting and packing of irregular shapes. The paper is not designed to be an exhaustive survey of the literature but instead will draw on the literature to illustrate the theory and implementation of the approaches. We aim to provide a sufficiently instructive description to equip new and current researchers in the area to select the most appropriate methodology for their needs.

A 2-exchange heuristic for nesting problems

Abstract This paper describes a new heuristic for the nesting problem based on a 2-exchange neighbourhood generation strategy. This mechanism guides the search through the solution space consisting of the sequences of pieces and relies on a low-level placement heuristic to actually convert one sequence in a feasible layout. The placement heuristic is based on a bottom-left greedy procedure with the ability to fill holes in the middle of the layout at a later stage. Several variants of the 2-exchange nesting heuristic were implemented and tested with different initial solution ranking criteria, different strategies for selecting the next solution, and different neighbourhood sizes. The computational experiments were based on data sets published in the literature. In most of the cases, the 2-exchange nesting algorithm generated better solutions than the best known solutions.

TOPOS – A new constructive algorithm for nesting problems

Abstract. In this paper we present a new constructive algorithm for nesting problems. The layout is built by successively adding a new piece to a partial solution, i.e. to the set of pieces previously nested. Several criteria to choose the next piece to place and its orientation are proposed and tested. Different objective functions are also proposed to evaluate and compare partial solutions. A total of 126 variants of the algorithm, generated by the complete set of combinations of criteria and objective functions, are computationally tested.The computational experiments are based on data sets published in the literature or provided by other authors. In some cases this new algorithm generates better solutions than the best known (published) solutions.Zusammenfassung. In dem vorliegenden Beitrag entwickeln die Autoren ein neues Konstruktionsverfahren für das „Nesting-Problem”, d.h. für ein zweidimensionales Zuschneideproblem mit unregelmäßigen Objekten. Das Schnittmuster wird dadurch gebildet, dass sukzessive zuzuschneidende Objekte (Teile) einer Teillösung angegliedert und damit neue Teillösungen gebildet werden. Verschiedene Kriterien zur Auswahl des jeweils anzuordnenden Teils und seiner Orientierung werden vorgestellt. Außerdem werden verschiedene Zielfunktionen zur Bewertung der Teillösungen herangezogen. Insgesamt ergeben sich so 126 Varianten des Konstruktionsverfahrens, die systematisch anhand von Datensätzen aus der Literatur getestet werden. Für einige Testprobleme stellt das neue Verfahren Lösungen bereit, die besser sind als die besten bisher in der Literatur beschriebenen Lösungen.

A Maximal-Space Algorithm for the Container Loading Problem

In this paper, a greedy randomized adaptive search procedure (GRASP) for the container loading problem is presented. This approach is based on a constructive block heuristic that builds upon the concept of maximal space, a nondisjoint representation of the free space in a container. n nThis new algorithm is extensively tested over the complete set of Bischoff and Ratcliff problems [Bischoff, E. E., M. S. W. Ratcliff. 1995. Issues in the development of approaches to container loading. Omega23 377--390], ranging from weakly heterogeneous to strongly heterogeneous cargo, and outperforms all the known nonparallel approaches that, partially or completely, have used this set of test problems. When comparing against parallel algorithms, it is better on average but not for every class of problem. In terms of efficiency, this approach runs in much less computing time than that required by parallel methods. Thorough computational experiments concerning the evaluation of the impact of algorithm design choices and internal parameters on the overall efficiency of this new approach are also presented.

Single machine multi-product capacitated lot sizing with sequence-dependent setups

In production planning in the glass container industry, machine-dependent setup times and costs are incurred for switch overs from one product to another. The resulting multi-item capacitated lot-sizing problem has sequence-dependent setup times and costs. We present two novel linear mixed-integer programming formulations for this problem, incorporating all the necessary features of setup carryovers. The compact formulation has polynomially many constraints, whereas the stronger formulation uses an exponential number of constraints that can be separated in polynomial time. We also present a five-step heuristic that is effective both in finding a feasible solution (even for tightly capacitated instances) and in producing good solutions to these problems. We report computational experiments.

An integrated approach to the vehicle routing and container loading problems

Real-world distribution problems raise some practical considerations that usually are not considered in a realistic way in more theoretical studies. One of these considerations is related to the vehicle capacity, not only in terms of cubic meters or weight capacity but also in terms of the cargo physical arrangements. In a distribution scene, two combinatorial optimization problems, the vehicle routing problem with time windows and the container loading problem, are inherently related to each other. This work presents a framework to integrate these two problems using two different resolution methods. The first one treats the problem in a sequential approach, while the second uses a hierarchical approach. To test the quality and efficiency of the proposed approaches, some test problems were created based on the well-known Solomon, Bischoff and Ratcliff test problems. The results of the integrated approaches are presented and compared with results of the vehicle routing problem with time windows and the container loading problem applied separately.

Algorithms for Nesting Problems

The Nesting Problem naturally appears in the context of several production processes, as in the textile, wood or steel industries, whenever is necessary to cut pieces with irregular (non-rectangular) shapes from larger plates. This problem belongs to the more generic class of Cutting and Packing problems.

Neighborhood structures for the container loading problem: a VNS implementation

This paper presents a Variable Neighborhood Search (VNS) algorithm for the container loading problem. The algorithm combines a constructive procedure based on the concept of maximal-space, with five new movements defined directly on the physical layout of the packed boxes, which involve insertion and deletion strategies.The new algorithm is tested on the complete set of Bischoff and Ratcliff problems, ranging from weakly to strongly heterogeneous instances, and outperforms all the reported algorithms which have used those test instances.