New extesions of the scalarizations techiques in the multiobjective one-dimensional cutting stock problem

Orientador: Antonio Carlos MorettiTese (doutorado) - Universidade Estadual de Campinas, Instituto de Matemática Estatística e Computação CientíficaResumo: O presente trabalho trata do Problema de Corte Unidimensional Inteiro Multiobjetivo (PCUIM). Este problema possui uma importância prática enorme e a sua abordagem multiobjetiva foi pouco reportada na literatura. O modelo biobjetivo considerado visa minimizar a soma das frequências dos padrões de corte para atender à mínima demanda e ao número de diferentes padrões a serem usados (\textit{setup}), sendo estas metas conflitantes entre si. Neste caso, o PCUIM possui um conjunto não unitário de soluções, ditas de \textit{soluções eficientes}, todas igualmente importantes para o problema. A geração de cada solução eficiente necessita a otimização de um Problema de Programação Linear Inteiro e a obtenção de todas estas soluções pode ser uma tarefa relativamente cara, principalmente quando os padrões de corte não são fornecidos pelo usuário a priori. Nesta tese, foram utilizados sete métodos distintos que transformam o PCUIM em problemas de otimização escalares, que por sua vez, geram as soluções eficientes. Seis métodos foram adaptados da literatura e um foi originalmente desenvolvido. A fim de acelerar a obtenção do conjunto de soluções eficientes, no caso com os padrões fornecidos pelo usuário, foi adotada uma estratégia que relaxa as condições de integralidade das variáveis do problema e, posteriormente, cada solução eficiente produzida é integralizada por meio de uma heurística ineditamente desenvolvida. Os extensos testes computacionais presentes no Capítulo 8, comprovaram que esta ideia foi adequada e eficaz. Além disso, a nova técnica de escalarização se mostrou muito competitiva com as demais consagradas na literatura, possibilitando um crescimento e um avanço na área de Problemas de Corte bem como na Otimização Combinatória MultiobjetivoAbstract: The present work deals with the Multiobjective One-Dimensional Cutting Stock Problem (MODCSP). This problem has an enormous practical importance, and the multiobjective approach has been little reported in the literature. The bi-objective model considered aims to minimize the sum of the frequency of cutting patterns to meet minimal demand and the number of different cutting patterns to be used (setup), being these objectives conflicting. In this case, the MODCSP has a non-unitary set of solutions, said \textit{efficient solutions}, equally important for the problem. The generation of each efficient solution requires the optimization of an Integer Linear Problem. So, the complete enumeration of these solutions can be an expensive task, especially when cutting patterns are not provided by the user. In this thesis, we applied seven different methods that transform the MODCSP on scalar optimization problems, where each problem provide an efficient solution. Six scalarization methods were adapted from literature and one was unprecedentedly developed. In the case of the cutting patterns be provided a priori, we used a relaxation strategy (heuristic) to accelerate obtaining of the set efficient solutions. In this approach, we relaxed the integrality condition of the variables and each efficient solution was rounded by a specially developed heuristic. The extensive results in Chapter 8 validated that this idea was adequate and effective. Furthermore, the new scalarization technique proved to be very competitive with other established in the literature, enabling growth and advancement in the area of the Cutting Problems and in Multiobjective Combinatorial OptimizationDoutoradoMatematica AplicadaDoutor em Matemática Aplicada2013/06035-0FAPESPCAPE

Metaheurísticas em um problema de rotação de culturas

Um dos focos centrais na produção vegetal, discutidos ultimamente, e a utilização de medidas que visam um planejamento sustentável e ecológico, tendo em vista a degradação ambiental ocorrida nos ultimos anos. Por este motivo, a Rotação de Culturas tem ganhado destaque na literatura, pois e um meio de produção cujos princípios práticos viabilizam uma agricultura ecológica e produtiva. Esta prática, uma vez bem conduzida pelos agricultores rurais, traz inúmeros benefícios, visto que o controle de pragas, patógenos e de plantas daninhas e realizado biologicamente, diminuindo a ação de pesticidas prejudiciais ao meio ambiente e medidas de recuperação do solo, tornando-o sempre fértil. Nesta dissertação, e apresentado um modelo de otimização 0-1 para o problema de Rotação de Culturas, cujo objetivo foi encontrar uma programação de plantio de hortaliças que maximize o lucro da produção, levando-se em consideração restrições de epoca de semeadura para cada cultura considerada, o não cultivo de plantas de mesma família em lotes vizinhos, proibição de plantio consecutivo de plantas de mesma família botânica em um mesmo lote, a necessidade de adubação verde, período de descanso do solo e de demanda. Nesta modelagem, foi considerada uma area de plantio genérica, cujos lotes são irregularmente distribuídos e de diferentes tamanhos. Para resolução do problema, foram desenvolvidas e implementadas a seguintes metaheurísticas: (a) Algoritmo Gen etico, (b) Simulated Annealing, e as abordagens mistas (c) Algoritmo Gen etico com Simulated Annealing e (d) Algoritmo Genético com Busca Local (Memético). Para avaliar os comportamentos computacionais das heurísticas, considerou-se instâncias de diferentes formas com variações nas geometrias e area de plantio. Adicionalmente, uma aplicação destes métodos para um...The environmental degradation that has occurred throughout the world claims for sustainable and ecological plant production. In this context, agricultural planning based on crop rotation has been addressed in many studies. Once appropriately applied by farmers, this practice brings many bene ts. In fact, it enables biological control of pests, pathogens and weeds, thus reducing the action of pesticides which are harmful to the environment. Planting according to crop rotation also restores the soil, making it always fertile. This thesis presents a binary linear optimization model to the problem of crop rotation aiming to nd a planting schedule for vegetables that maximizes the pro ts of production. The problem constraints include a speci c period for planting each crop, a prede ned demand per crop, the need for green manure and rest period. Other restraints prevent planting of vegetables of the same family consecutively in the same lot, as well as in neighboring lots. A general planting area with irregularly distributed and di erent sized lots is considered. Four metaheuristics were speci cally developed for the above crop rotation problem and the respective algorithms were implemented: (a) a Genetic Algorithm, (b) a Simulated Annealing, and two hybrid approaches - (c) a Genetic Algorithm with Simulated Annealing and (d) a Genetic Algorithm with Local Search, that is, a Memetic algorithm. To evaluate the computing behavior of these algorithms, we considered a crop rotation instance from literature and also an instance built with real data from a Brazilian agricultural company. The computational results showed that the algorithms, specially the hybrid... (Complete abstract click electronic access below)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES

A genetic algorithm for crop rotation

In the last few years, crop rotation has gained attention due to its economic, environmental and social importance which explains why it can be highly beneficial for farmers. This paper presents a mathematical model for the Crop Rotation Problem (CRP) that was adapted from literature for this highly complex combinatorial problem. The CRP is devised to find a vegetable planting program that takes into account green fertilization restrictions, the set-aside period, planting restrictions for neighboring lots and for crop sequencing, demand constraints, while, at the same time, maximizing the profitability of the planted area. The main aim of this study is to develop a genetic algorithm and test it in a real context. The genetic algorithm involves a constructive heuristic to build the initial population and the operators of crossover, mutation, migration and elitism. The computational experiment was performed for a medium dimension real planting area with 16 lots, considering 29 crops of 10 different botanical families and a two-year planting rotation. Results showed that the algorithm determined feasible solutions in a reasonable computational time, thus proving its efficacy for dealing with this practical application

An exact scalarization method with multiple reference points for bi-objective integer linear optimization problems

This paper presents an exact scalarization method to solve bi-objective integer linear optimization problems. This method uses diverse reference points in the iterations, and it is free from any kind of a priori chosen weighting factors. In addition, two new adapted scalarization methods from literature and the modified Tchebycheff method are studied. Each one of them results in different ways to obtain the Pareto frontier. Computational experiments were performed with random real size instances of two special problems related to the manufacturing industry, which involve lot sizing and cutting stock problems. Extensive tests confirmed the very good performance of the new scalarization method with respect to the computational effort, the number of achieved solutions, the ability to achieve different solutions, and the spreading and spacing of solutions at the Pareto frontier2961356

Metaheuristics for a crop rotation problem

This paper presents a mathematical model adapted from literature for the crop rotation problem with demand constraints (CRP-D). The main aim of the present work is to study metaheuristics and their performance in a real context. The proposed algorithms for solution of the CRP-D are a genetic algorithm, a simulated annealing and hybrid approaches: a genetic algorithm with simulated annealing and a genetic algorithm with local search algorithm. A new constructive heuristic was also developed to provide initial solutions for the metaheuristics. Computational experiments were performed using a real planting area and semi-randomly generated instances created by varying the number, positions and dimensions of the lots. The computational results showed that these algorithms determined good feasible solutions in a short computing time as compared with the time spent to get optimal solutions, thus proving their efficacy for dealing with this practical application of the CRP-D

Trusses Nonlinear Problems Solution with Numerical Methods of Cubic Convergence Order

<div><p>ABSTRACT A large part of the numerical procedures for obtaining the equilibrium path or load-displacement curve of structural problems with nonlinear behavior is based on the Newton-Raphson iterative scheme, to which is coupled the path-following methods. This paper presents new algorithms based on Potra-Pták, Chebyshev and super-Halley methods combined with the Linear Arc-Length path-following method. The main motivation for using these methods is the cubic order convergence. To elucidate the potential of our approach, we present an analysis of space and plane trusses problems with geometric nonlinearity found in the literature. In this direction, we will make use of the Positional Finite Element Method, which considers the nodal coordinates as variables of the nonlinear system instead of displacements. The numerical results of the simulations show the capacity of the computational algorithm developed to obtain the equilibrium path with force and displacement limits points. The implemented iterative methods exhibit better efficiency as the number of time steps and necessary accumulated iterations until convergence and processing time, in comparison with classic methods of Newton-Raphson and Modified Newton-Raphson.</p></div