Constructive procedures to solve 2-dimensional bin packing problems with irregular pieces and guillotine cuts

This paper presents an approach for solving a new real problem in cutting and packing. At its core is an innovative mixed integer programme model that places irregular pieces and defines guillotine cuts. The two-dimensional irregular shape bin packing problem with guillotine constraints arises in the glass cutting industry, for example, the cutting of glass for conservatories. Almost all cutting and packing problems that include guillotine cuts deal with rectangles only, where all cuts are orthogonal to the edges of the stock sheet and a maximum of two angles of rotation are permitted. The literature tackling packing problems with irregular shapes largely focuses on strip packing i.e. minimizing the length of a single fixed width stock sheet, and does not consider guillotine cuts. Hence, this problem combines the challenges of tackling the complexity of packing irregular pieces with free rotation, guaranteeing guillotine cuts that are not always orthogonal to the edges of the stock sheet, and allocating pieces to bins. To our knowledge only one other recent paper tackles this problem. We present a hybrid algorithm that is a constructive heuristic that determines the relative position of pieces in the bin and guillotine constraints via a mixed integer programme model. We investigate two approaches for allocating guillotine cuts at the same time as determining the placement of the piece, and a two phase approach that delays the allocation of cuts to provide flexibility in space usage. Finally we describe an improvement procedure that is applied to each bin before it is closed. This approach improves on the results of the only other publication on this problem, and gives competitive results for the classic rectangle bin packing problem with guillotine constraint

A beam search approach to solve the convex irregular bin packing problem with guillotine cuts

This paper presents a two dimensional convex irregular bin packing problem with guillotine cuts. The problem combines the challenges of tackling the complexity of packing irregular pieces, guaranteeing guillotine cuts that are not always orthogonal to the edges of the bin, and allocating pieces to bins that are not necessarily of the same size. This problem is known as a two-dimensional multi bin size bin packing problem with convex irregular pieces and guillotine cuts. Since pieces are separated by means of guillotine cuts, our study is restricted to convex pieces.A beam search algorithm is described, which is successfully applied to both the multi and single bin size instances. The algorithm is competitive with the results reported in the literature for the single bin size problem and provides the first results for the multi bin size problem

An anytime tree search algorithm for two-dimensional two- and three-staged guillotine packing problems

[libralesso_anytime_2020] proposed an anytime tree search algorithm for the 2018 ROADEF/EURO challenge glass cutting problem (https://www.roadef.org/challenge/2018/en/index.php). The resulting program was ranked first among 64 participants. In this article, we generalize it and show that it is not only effective for the specific problem it was originally designed for, but is also very competitive and even returns state-of-the-art solutions on a large variety of Cutting and Packing problems from the literature. We adapted the algorithm for two-dimensional Bin Packing, Multiple Knapsack, and Strip Packing Problems, with two- or three-staged exact or non-exact guillotine cuts, the orientation of the first cut being imposed or not, and with or without item rotation. The combination of efficiency, ability to provide good solutions fast, simplicity and versatility makes it particularly suited for industrial applications, which require quickly developing algorithms implementing several business-specific constraints. The algorithm is implemented in a new software package called PackingSolver

Two-Dimensional Bin Packing Problem with Guillotine Restrictions

This thesis, after presenting recent advances obtained for the two-dimensional bin packing problem, focuses on the case where guillotine restrictions are imposed. A mathematical characterization of non-guillotine patterns is provided and the relation between the solution value of the two-dimensional problem with guillotine restrictions and the two-dimensional problem unrestricted is being studied from a worst-case perspective. Finally it presents a new heuristic algorithm, for the two-dimensional problem with guillotine restrictions, based on partial enumeration, and computationally evaluates its performance on a large set of instances from the literature. Computational experiments show that the algorithm is able to produce proven optimal solutions for a large number of problems, and gives a tight approximation of the optimum in the remaining cases

Improvement of constructive heuristics for combinatorial optimisation problems in operations management.

Операциони менаџер користи скуп поступака чији је циљ да се послови ураде брже, јефтиније и квалитетније. Научници из области операционог менаџмента имају задатак да ови поступци буду изводљиви и практични. Скоро увек, менаџери покушавају да нешто оптимизују – или је то минимизација трошкова и потрошње енергије, или пак, максимизација профита, резултата, перформанси и ефикасности. Међутим, није увек могуће пронаћи оптимална решења. У пракси, менаџер мора да се задовољи решењима која можда нису оптимална, али су допустива, задовољавајућа, робустна, и достижна у разумном времену. Оваква решења се добијају применама хеуристика, које могу бити конструктивне, побољшавајуће или хибридне. Област истраживања у докторској дисертацији су конструктивне хеуристике за проблеме комбинаторне оптимизације у операционом менаџменту који припадају класи сложености НП. Представљен је нови генерализовани конструктивни алгоритам који омогућава да се разноврсне хеуристике формирају избором његових аргумената. Такође је уведено опште окружење за генерисање пермутација, које формира везу између енумерације пермутација и корака у конструктивним хеуристикама уметања. Предложен је скуп аргумената генерализованог алгоритма који омогућује паралелно праћење више парцијалних решења за време извршавања алгоритма. Могућности и предности генерализованог алгоритма су представљене кроз његову примену на проблем формирања ћелија у производним системима, проблем распореда производних ћелија и проблем редоследа послова у линији. Нови приступ даје решења која на испитиваним примерима надмашују најбоље познате резултате из литературе.Operations manager deals with a collection of methods for getting things done more quickly, more cheaply or to a higher standard of quality. It is the job of the management scientist to make sure that these methods are practical and relevant. Almost always managers try to optimize something - whether to minimize the cost and energy consumption, or to maximize the profit, output, performance and efficiency. Subsequently, it is not always possible to find the optimal solutions. In practice, managers have to settle for suboptimal solutions or even feasible ones that are satisfactory, robust, and practically achievable in a reasonable time scale. These kind of solutions are obtained with heuristics, which can be constructive, improvement heuristics or hybrid. The field of research in the doctoral thesis are constructive heuristics for NP-hard combinatorial optimization problems in operations management. A new generalized constructive algorithm is presented which makes it possible to select a wide variety of heuristics just by the selection of its arguments values. A general framework for generating permutations of integers is presented. This framework forms a link between the numbering of permutations and steps in the insertion-based heuristics. A number of arguments controlling the operation of the generalized algorithm tracking multiple partial solutions, are identified. Features and benefits of the generalized algorithm are presented through the implemetations to the Cell Formation Problem, the Quadratic Assignment Problem and the Permutation Flowshop Problem. The new approach produces solutions that outperform, on the tested instances, the best known results from literature

Un algoritmo FFD-Eficiente para resolver el problema de corte de guillotina con demanda no unitaria de requerimientos sobre stock de tamaño variado

Resuelve el problema Guillotine Cutting Stock Problem with Demand on Varied Stock (GCSP-DVS) a través de un algoritmo FFD-Eficiente variado (FFD-E 2DGV). Además, demuestra la capacidad del algoritmo propuesto para incidir en el ahorro significativo a través del reúso de materia prima reciclable para el proceso industrial de corte bidimensional. Asimismo, compendia los resultados del algoritmo propuesto aplicado al GCSP-DVS y los resultados comparativos entre el FFD y el FFD-E aplicado al GCSP-D; generando un banco inédito para instancias de cortes 2 dimensiones de tipo guillotina sobre stock de tamaño variado y otra de demostraciones numéricas comparativas del FFD-E respecto al FFD, respectivamente. Finalmente, implementa un sistema computacional parametrizable que ejecute el algoritmo propuesto y arroje reportes de solución del citado problema GCSP con demanda sobre stock variado (GCSP-DVS).Tesi

User hints for optimisation processes

Innovative improvements in the area of Human-Computer Interaction and User Interfaces have en-abled intuitive and effective applications for a variety of problems. On the other hand, there has also been the realization that several real-world optimization problems still cannot be totally auto-mated. Very often, user interaction is necessary for refining the optimization problem, managing the computational resources available, or validating or adjusting a computer-generated solution. This thesis investigates how humans can help optimization methods to solve such difficult prob-lems. It presents an interactive framework where users play a dynamic and important role by pro-viding hints. Hints are actions that help to insert domain knowledge, to escape from local minima, to reduce the space of solutions to be explored, or to avoid ambiguity when there is more than one optimal solution. Examples of user hints are adjustments of constraints and of an objective function, focusing automatic methods on a subproblem of higher importance, and manual changes of an ex-isting solution. User hints are given in an intuitive way through a graphical interface. Visualization tools are also included in order to inform about the state of the optimization process. We apply the User Hints framework to three combinatorial optimization problems: Graph Clus-tering, Graph Drawing and Map Labeling. Prototype systems are presented and evaluated for each problem. The results of the study indicate that optimization processes can benefit from human interaction. The main goal of this thesis is to list cases where human interaction is helpful, and provide an ar-chitecture for supporting interactive optimization. Our contributions include the general User Hints framework and particular implementations of it for each optimization problem. We also present a general process, with guidelines, for applying our framework to other optimization problems