Solving the two dimensional cutting problem using evolutionary algorithms with penalty functions

In this work a solution using evolutionary algorithms with penalty function for the non-guillotine cutting problem is presented. In this particular problem, the rectangular pieces have to be cut from an unique large object, being the goal to maximize the total value of cut pieces. Some chromosomes can hold pieces to be cut, but some pieces cannot be arranged into the object, generating infeasible solutions. A way to deal with this kind of solutions is to use a penalizing strategy. The used penalty functions have been originally developed for the knapsack problem and they are adapted for the cutting problem in this paper. Moreover, the effect on the algorithm performance to combine penalty functions with two different selection methods (binary tournament and roulette wheel) is studied. The algorithm uses a binary representation, one-point crossover, big-creep mutation and in order to evaluated the quality of solutions a placement routine is considered (Heuristic with Efficient Management of Holes). Experimental comparisons of the performance of the resulting algorithms are carried out using publicly available benchmarks to the non-guillotine cutting problem. We report on the high performance of the proposed models at similar (or better) accuracy with respect to existing algorithms.VI Workshop de Agentes y Sistemas Inteligentes (WASI)Red de Universidades con Carreras en Informática (RedUNCI

Container Loading Problems: A State-of-the-Art Review

Container loading is a pivotal function for operating supply chains efficiently. Underperformance results in unnecessary costs (e.g. cost of additional containers to be shipped) and in an unsatisfactory customer service (e.g. violation of deadlines agreed to or set by clients). Thus, it is not surprising that container loading problems have been dealt with frequently in the operations research literature. It has been claimed though that the proposed approaches are of limited practical value since they do not pay enough attention to constraints encountered in practice.In this paper, a review of the state-of-the-art in the field of container loading will be given. We will identify factors which - from a practical point of view - need to be considered when dealing with container loading problems and we will analyze whether and how these factors are represented in methods for the solution of such problems. Modeling approaches, as well as exact and heuristic algorithms will be reviewed. This will allow for assessing the practical relevance of the research which has been carried out in the field. We will also mention several issues which have not been dealt with satisfactorily so far and give an outlook on future research opportunities

Solving the two dimensional cutting problem using evolutionary algorithms with penalty functions

In this work a solution using evolutionary algorithms with penalty function for the non-guillotine cutting problem is presented. In this particular problem, the rectangular pieces have to be cut from an unique large object, being the goal to maximize the total value of cut pieces. Some chromosomes can hold pieces to be cut, but some pieces cannot be arranged into the object, generating infeasible solutions. A way to deal with this kind of solutions is to use a penalizing strategy. The used penalty functions have been originally developed for the knapsack problem and they are adapted for the cutting problem in this paper. Moreover, the effect on the algorithm performance to combine penalty functions with two different selection methods (binary tournament and roulette wheel) is studied. The algorithm uses a binary representation, one-point crossover, big-creep mutation and in order to evaluated the quality of solutions a placement routine is considered (Heuristic with Efficient Management of Holes). Experimental comparisons of the performance of the resulting algorithms are carried out using publicly available benchmarks to the non-guillotine cutting problem. We report on the high performance of the proposed models at similar (or better) accuracy with respect to existing algorithms.VI Workshop de Agentes y Sistemas Inteligentes (WASI)Red de Universidades con Carreras en Informática (RedUNCI

Novel approaches to container loading: from heuristics to hybrid tabu search

A thesis submitted for the degree of Doctor of Philosophy of the University ofBedford shireThis work investigates new approaches to the container loading problem which address the issue of how to load three-dimensional, rectangular items (e.g. boxes) into the container in such a way that maximum utilisation is made of the container space. This problem occurs in several industry sectors where the loading approach places cargo effectively into aeroplanes, ships, trailers or trucks in order to save considerable cost. In carrying out this work, the investigation starts by developing a new heuristic approach to the two-dimensional bin packing problem, which has lower complexity than container loading in the aspects of constraints and geometry. A novel approach, including the heuristic strategies and handling method for remaining areas, is developed that can produce good results when testing with benchmark and real world data. Based on the research for two-dimensional bin packing, a novel heuristic approach is developed to deal with the container loading problem with some practical constraints. The heuristic approach to container loading also includes heuristic strategies and the handling of remaining spaces. The heuristic strategies construct effective loading arrangements where combinations of identical or different box types are loaded in blocks. The handling method for remaining spaces further improves the loading arrangements through the representation, partitioning and merging of remaining spaces. The heuristic approach obtains better volume utilisation and the highest stability compared with other published heuristic approaches. However, it does not achieve as high a volume utilisation as metaheuristic approaches, e.g. genetic algorithms and tabu search.To improve volume utilisation, a new hybrid heuristic approach to the container loading problem is further developed based on the tabu search technique which covers the encoding, evaluation criterion and configuration of neighbourhood and candidate solutions. The heuristic strategies as well as the handling method for remaining spaces developed in the heuristic approach are used in this new hybrid tabu search approach. It is shown that the hybrid approach has better volume utilisation than the published approaches under the condition that all loaded boxes with one hundred per cent support from below. In addition, the experimental results show that both the heuristic and hybrid tabu search approaches can also be applied to the multiple container loading problem

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

제재 시뮬레이션을 통한 소나무 원목의 제재 수익성 분석

학위논문 (석사)-- 서울대학교 대학원 농업생명과학대학 산림과학부, 2017. 8. 정주상.This study conducted a profitability analysis on sawing Pinus densiflora logs by comparing the profitability of lumber and pulp-chip productions. In order to estimate the maximum value recovery from log sawing, a log sawing simulation model was developed based on dynamic programming algorithm proposed by Reinders and Hendriks (1989). Through the log sawing simulation, Pinus densiflora logs in lengths of 3.6 m and 2.7 m were optimally sawn for maximized lumber value in regards with the dimensions and prices of lumber products in Korea. On the other hand, 1.8 m Pinus densiflora logs were applied for pulp-chip production considering the current timber harvesting and log allocation in Korea. Net profits generated from the two productions were estimated using the data obtained from the actual sawmills and pulp-chip manufacture facilities. According to the result, sawing Pinus densiflora logs for 3.6 m and 2.7 m lumber products generated 861% and 723% higher net profits, respectively than pulp-chip production with 1.8 m logs. Between the two lumber productions, the average net profit generated from sawing 3.6 m logs was 24% higher than sawing 2.7 m logs. In addition to the comparative analysis on sawing profitability, the sawing potential of short (1.8 m) Pinus densiflora logs was also evaluated for wooden cutting board and wooden tray manufacture using the log sawing simulation model. The lumber for wooden cutting board manufacture could be sawn from the log with 18 cm of diameter and the lumber for wooden tray manufacture from the log with 22 cm of diameter. The results of this study reconfirm that sawlog harvesting would lead to higher timber sale profits and support the bucking decisions in terms of value recovery and increased stumpage value of Pinus densiflora stands in Korea. Additionally, the study also suggests that thorough considerations of various end-uses of harvested timber would increase the timber sale profits.I. INTRODUCTION 1 II. OBEJCTIVES 4 III. LITERATURE REVIEW 5 IV. RESEARCH FRAMEWORK 9 V. MATERIALS AND METHODS 10 1. A log sawing simulation model 10 1) Model assumptions 10 2) Structure of the model 12 3) Mathematical algorithm 13 2. Comparative analysis on sawing and chipping profitability of Pinus densiflora 17 1) Sawing profitability of Pinus densiflora 17 (1) Process of profitability analysis using the log sawing simulation model 17 (2) Data collection 19 (3) Profitability analysis 22 2) Profitability analysis on pulp-chip production with Pinus densiflora 23 (1) Process of profitability analysis on pulp-chip production 23 (2) Data collection 24 (3) Profitability analysis 25 3. Analysis on sawing potential of short Pinus densiflora logs for wood product manufacture 27 1) Research process 27 2) Data collection 28 (1) Log type 28 (2) Production process 28 3) Analysis on sawing potential 29 (1) Log sawing simulation 29 (2) Estimation of lumber production 29 VI. RESULTS AND DISCUSSION 30 1. Optimal sawing pattern for 3.6m Pinus densiflora logs 30 2. Optimal sawing pattern for 2.7m Pinus densiflora logs 32 3. Lumber yield and recovery rate of sawing 3.6m and 2.7m Pinus densiflora logs 34 4. Pulp-chip yield from chipping 1.8m Pinus densiflora logs 36 5. Net profit comparison between lumber and pulp-chip production 37 6. Production estimation of lumber for wooden cutting board. 40 7. Production estimation of lumber for wooden tray 41 VII. CONCLUSION 42Maste

Algorithms for cutting and packing problems

Orientador: Flávio Keidi MiyazawaTese (doutorado) - Universidade Estadual de Campinas, Instituto de ComputaçãoResumo: Problemas de Corte e Empacotamento são, em sua maioria, NP-difíceis e não existem algoritmos exatos de tempo polinomial para tais se for considerado P ¿ NP. Aplicações práticas envolvendo estes problemas incluem a alocação de recursos para computadores; o corte de chapas de ferro, de madeira, de vidro, de alumínio, peças em couro, etc.; a estocagem de objetos; e, o carregamento de objetos dentro de contêineres ou caminhões-baú. Nesta tese investigamos problemas de Corte e Empacotamento NP-difíceis, nas suas versões bi- e tridimensionais, considerando diversas restrições práticas impostas a tais, a saber: que permitem a rotação ortogonal dos itens; cujos cortes sejam feitos por uma guilhotina; cujos cortes sejam feitos por uma guilhotina respeitando um número máximo de estágios de corte; cujos cortes sejam não-guilhotinados; cujos itens tenham demanda (não) unitária; cujos recipientes tenham tamanhos diferentes; cujos itens sejam representados por polígonos convexos e não-convexos (formas irregulares); cujo empacotamento respeite critérios de estabilidade para corpos rígidos; cujo empacotamento satisfaça uma dada ordem de descarregamento; e, cujos empacotamentos intermediários e final tenham seu centro de gravidade dentro de uma região considerada "segura". Para estes problemas foram propostos algoritmos baseados em programação dinâmica; modelos de programação inteira; técnicas do tipo branch-and-cut; heurísticas, incluindo as baseadas na técnica de geração de colunas; e, meta-heurísticas como o GRASP. Resultados teóricos também foram obtidos. Provamos uma questão em aberto levantada na literatura sobre cortes não-guilhotinados restritos a um conjunto de pontos. Uma extensiva série de testes computacionais considerando instâncias reais e várias outras geradas de forma aleatória foram realizados com os algoritmos desenvolvidos. Os resultados computacionais, sendo alguns deles comparados com a literatura, comprovam a validade dos algoritmos propostos e a sua aplicabilidade prática para resolver os problemas investigadosAbstract: Several versions of Cutting and Packing problems are considered NP-hard and, if we consider that P ¿ NP, we do not have any exact polynomial algorithm for solve them. Practical applications arises for such problems and include: resources allocation for computers; cut of steel, wood, glass, aluminum, etc.; packing of objects; and, loading objects into containers and trucks. In this thesis we investigate Cutting and Packing problems that are NP-hard considering theirs two- and three-dimensional versions, and subject to several practical constraints, that are: that allows the items to be orthogonally rotated; whose cuts are guillotine type; whose cuts are guillotine type and performed in at most k stages; whose cuts are non-guillotine type; whose items have varying and unit demand; whose bins are of variable sizes; whose items are represented by convex and non-convex polygons (irregular shapes); whose packing must satisfy the conditions for static equilibrium of rigid bodies; whose packing must satisfy an order to unloading; and, whose intermediaries and resultant packing have theirs center of gravity inside a safety region; Such cutting and packing problems were solved by dynamic programming algorithms; integer linear programming models; branch-and-cut algorithms; several heuristics, including those ones based on column generation approaches, and metaheuristics like GRASP. Theoretical results were also provided, so a recent open question arised by literature about non-guillotine patterns restricted to a set of points was demonstrated. We performed an extensive series of computational experiments for algorithms developed considering several instances presented in literature and others generated at random. These results, some of them compared with the literature, validate the approaches proposed and suggest their applicability to deal with practical situations involving the problems here investigatedDoutoradoDoutor em Ciência da Computaçã

Influence of cutting process on magnetic properties of electrical steel

La tesi fornisce un'analisi quantitativa del degrado delle proprietà magnetiche a seguito di tranciatura e taglio al laser su lamierini in acciaio magnetico M270-50A. Le misure sui campioni sono state ottenute con un'Apparecchio di Epstein grazie al quale sono state misurate la riduzione della permeabilità magnetica e l'aumento delle perdite specifiche nei campioni. Le misure sono state utilizzate per valutare gli effetti su una macchina asincrona tramite simulazione agli elementi finit

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