Application of 2D packing algorithms to the woodwork industry

Esta pesquisa investiga a aplicação de metodologias computacionais na indústria madeireira, com foco no Problema do Corte de Material (PCE) com duas iterações: guilhotinável e não guilhotinável. O estudo aplica um algoritmo evolucionário baseado no Non-dominated Sorting Genetic Algorithm II (NSGA-II) adaptado às complexidades do problema para otimizar o processo de corte. A metodologia tem como objetivo melhorar a eficiência da utilização de material em tarefas de trabalho em madeira, empregando este algoritmo utilizando sobras de peças ao invés de uma nova placa. O relatório fornece dados empíricos e métricas de desempenho do algoritmo, demonstrando a sua eficácia na redução do desperdício e na otimização do trabalho na indústria. Esta abordagem melhora a eficiência operacional e sublinha os benefícios ambientais da utilização mais sustentável dos recursos de madeira, exemplificando o potencial da integração de técnicas computacionais em indústrias tradicionais para atingir este objetivo.This research investigates the application of computational methodologies in the woodworking industry, focusing on the Cutting Stock Problem (CSP) with two iterations: guillotinable and non-guillotinable iterations. The study applies an Evolutionary Algorithm (EA) based on Non-dominated Sorting Genetic Algorithm II (NSGA-II) customized to fit the intricacies of the problem to optimize the cutting process. The methodology aims to enhance material usage efficiency in woodworking tasks by employing this algorithm using leftover parts instead of a new board. The report provides empirical data and performance metrics of the algorithm, demonstrating its effectiveness in reducing waste and optimizing labor in the industry. This approach improves operational efficiency and underscores the environmental benefits of using timber resources more sustainably, exemplifying the potential of integrating computational techniques in traditional industries to achieve this objective

Two-dimensional placement compaction using an evolutionary approach: a study

The placement problem of two-dimensional objects over planar surfaces optimizing given utility functions is a combinatorial optimization problem. Our main drive is that of surveying genetic algorithms and hybrid metaheuristics in terms of final positioning area compaction of the solution. Furthermore, a new hybrid evolutionary approach, combining a genetic algorithm merged with a non-linear compaction method is introduced and compared with referenced literature heuristics using both randomly generated instances and benchmark problems. A wide variety of experiments is made, and the respective results and discussions are presented. Finally, conclusions are drawn, and future research is defined

On three soft rectangle packing problems with guillotine constraints

We investigate how to partition a rectangular region of length $L_1$ and height $L_2$ into $n$ rectangles of given areas $(a_1, \dots, a_n)$ using two-stage guillotine cuts, so as to minimize either (i) the sum of the perimeters, (ii) the largest perimeter, or (iii) the maximum aspect ratio of the rectangles. These problems play an important role in the ongoing Vietnamese land-allocation reform, as well as in the optimization of matrix multiplication algorithms. We show that the first problem can be solved to optimality in $\mathcal{O}(n \log n)$, while the two others are NP-hard. We propose mixed integer programming (MIP) formulations and a binary search-based approach for solving the NP-hard problems. Experimental analyses are conducted to compare the solution approaches in terms of computational efficiency and solution quality, for different objectives

Shaper-GA: automatic shape generation for modular housing

This work presents an automatic system that, from the specification of an architectural language of design, generates several alternative floor plants for the construction of modular homes. The system uses Genetic Algorithms and is capable of efficiently producing various plant solutions. The rules of architecture are implemented in the fitness function translating the rules of a Shape Grammar created by the architect. Different solutions of feasible plants are generated, that is, solutions that obey the rules of Shape Grammar and do not have overlays between the rooms. The system can be integrated with a user-friendly interface in the future, to allow for the house owners customization of their own house. Such a tool can also be delivered to construction companies for them to manage the design of modular houses that meet specific clients requirements.Este trabalho apresenta um sistema automático que, a partir da especificação de uma linguagem arquitetural de design, gera plantas alternativas para residências de construção modular. O sistema usa Algoritmos Genéticos e é capaz de produzir várias soluções de plantas de modo eficiente. As regras de arquitetura são implementadas na função de fitness a partir de uma Gramática de Forma criada pelo arquiteto. São geradas diferentes soluções de plantas exequíveis, isto é, soluções que obedecem à Gramática de Forma e não têm sobreposições entre as suas divisões. Pode ser futuramente integrado com uma interface amigável para o utilizador de forma a que este personalize e crie a sua futura casa. Tal ferramenta pode também ser entregue às companhias de construção de forma a que estas gerem uma planta para uma casa modular personalizada

Moldable Items Packing Optimization

This research has led to the development of two mathematical models to optimize the problem of packing a hybrid mix of rigid and moldable items within a three-dimensional volume. These two developed packing models characterize moldable items from two perspectives: (1) when limited discrete configurations represent the moldable items and (2) when all continuous configurations are available to the model. This optimization scheme is a component of a lean effort that attempts to reduce the lead-time associated with the implementation of dynamic product modifications that imply packing changes. To test the developed models, they are applied to the dynamic packing changes of Meals, Ready-to-Eat (MREs) at two different levels: packing MRE food items in the menu bags and packing menu bags in the boxes. These models optimize the packing volume utilization and provide information for MRE assemblers, enabling them to preplan for packing changes in a short lead-time. The optimization results are validated by running the solutions multiple times to access the consistency of solutions. Autodesk Inventor helps visualize the solutions to communicate the optimized packing solutions with the MRE assemblers for training purposes

Simple and practical optimization approach based to solve a truck load and delivery problem at long haul distances with heterogenous products

This paper proposes an optimization based approach for solving the logistic processes of deliveries scheduling and product accommodation during loading with a heterogeneous fleet of vehicles. The approach focuses on the case of products with “low density values” and high heterogeneous volume and weight, and with traveling large distances to different zones, in which transportation costs constitute a important proportion of total logistic costs. The proposed approach consists of a two-phase strategy: The first uses a “Cutting Stock Problem” formulation to define utilization areas inside trucks assigned to each product family. This task is achieved by minimizing the long-haul transportation costs as a function of the vehicle size, considering a set of predefined solutions for feasible and efficient loading obtained as a result of the accumulated experience. The second phase consists of Bin Packing Problem version with a known number of bins, which were previously determined in the first phase of the approach. In this phase, different orders from a set of customers are assigned to each truck by obeying the predefined utilization areas per product category obtained in the first phase while minimizing the number of visits of each truck. The results show that the model addresses the analyzed problem in an efficient manner, which is reflected in reasonable resolution times and costs from a practical implementation perspective. Additionally, it is observed that long-haul delivery costs and vehicle utilization tend to improve with the increase of the utilized number of patterns even when the execution time is incremented.MaestríaMagister en Ingeniería Civi