3D packing of balls in different containers by VNS

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel UniversityIn real world applications such as the transporting of goods products, packing is a major issue. Goods products need to be packed such that the smallest space is wasted to achieve the maximum transportation efficiency. Packing becomes more challenging and complex when the product is circular/spherical. This thesis focuses on the best way to pack three-dimensional unit spheres into the smallest spherical and cubical space. Unit spheres are considered in lieu of non-identical spheres because the search mechanisms are more difficult in the latter set up and any improvements will be due to the search mechanism not to the ordering of the spheres. The two-unit sphere packing problems are solved by approximately using a variable neighborhood search (VNS) hybrid heuristic. A general search framework belonging to the Artificial Intelligence domain, the VNS offers a diversification of the search space by changing neighborhood structures and intensification by thoroughly investigating each neighborhood. It is exible, easy to implement, adaptable to both continuous and discrete optimization problems and has been use to solve a variety of problems including large-sized real-life problems. Its runtime is usually lower than other meta heuristic techniques. A tutorial on the VNS and its variants along with recent applications and areas of applicability of each variant. Subsequently, this thesis considers several variations of VNS heuristics for the two problems at hand, discusses their individual efficiencies and effectiveness, their convergence rates and studies their robustness. It highlights the importance of the hybridization which yields near global optima with high precision and accuracy, improving many best- known solutions indicate matching some, and improving the precision and accuracy of others. Keywords: variable neighborhood search, sphere packing, three-dimensional packing, meta heuristic, hybrid heuristics, multiple start heuristics

Heuristiken im Service Operations Management

This doctoral thesis deals with the application of operation research methods in practice. With two cooperation companies from the service sector (retailing and healthcare), three practice-relevant decision problems are jointly elicited and defined. Subsequently, the planning problems are transferred into mathematical problems and solved with the help of optimal and/or heuristic methods. The status quo of the companies could be significantly improved for all the problems dealt with.Diese Doktorarbeit beschäftigt sich mit der Anwendung von Operation Research Methoden in der Praxis. Mit zwei Kooperationsunternehmen aus dem Dienstleistungssektor (Einzelhandel und Gesundheitswesen) werden drei praxisrelevante Planungsprobleme gemeinsam eruiert und definiert. In weiterer Folge werden die Entscheidungsmodelle in mathematische Probleme transferiert und mit Hilfe von optimalen und/oder heuristischen Verfahren gelöst. Bei allen behandelten Problemstellungen konnte der bei den Unternehmen angetroffene Status Quo signifikant verbessert werden

Models and algorithms for hard optimization problems

This thesis is devoted to exact solution methods for NP-hard integer programming models. We consider two of these problems, the cutting stock problem and the vehicle routing problem. Both problems have been studied for several decades by researchers and practitioners of the Operations Research eld. Their interest and contribution to real-world applications in business, industry and several kinds of organizations are irrefutable. Our solution approaches are always exact. We contribute with new lower bounds, families of valid inequalities, integer programming models and exact algorithms for the problems we explore. More precisely, we address two variants of each of the referred problems. In what concerns cutting stock problems, we analyze the one-dimensional pattern minimization problem and the two-dimensional cutting stock problem with the guillotine constraint. The one-dimensional pattern minimization problem is a cutting and packing problem that becomes relevant in situations where changing from one pattern to another involves, for example, a cost for setting up the cutting machine. It is the problem of minimizing the number of di erent patterns of a given cutting stock solution. For this problem, we contribute with new lower bounds. The two-dimensional cutting stock problem with the guillotine constraint and two stages is also addressed. We propose a pseudo-polynomial network ow model, along with some reduction criteria to reduce its symmetry. We strengthen the model with a new family of cutting planes and propose a new lower bound. For this variant, we also consider some variations of the problem.Regarding vehicle routing problems, we address the vehicle routing problem with time windows and multiple use of vehicles and the location routing problem, with capacitated vehicles and depots and multiple use of vehicles. The rst of these problems considers the well know case of vehicle routing with time windows with the additional consideration that vehicles can be assigned to several routes within the same planning period. The second variant considers the combination of the rst problem, without time windows, with a location problem. This means that the depots to be used must be selected from a set of available ones. For both of these variants, we propose a network ow model whose nodes of the underlying graph correspond to time instants of the planning period and whose arcs correspond to vehicle routes. We reduce their symmetry by deriving several reduction criteria. For the vehicle routing problem with time windows and multiple use of vehicles, we propose an iterative algorithm to solve the problem exactly. Our proposed procedures are tested and compared with other methods from the literature. All the computational results produced by the series of experiments are presented and discussed.Esta tese e dedicada a métodos de resolução exata para problemas de programação inteira NP-difíceis. São considerados dois desses problemas, nomeadamente o problema de corte e empacotamento e o problema de encaminhamento de veículos. Ambos os problemas têm vindo a ser abordados por investigadores e profissionais da área da Investigação Operacional há já várias décadas. O seu interesse e contribuição para aplicações reais do mundo dos negócios e industria, assim como para inúmeros outros tipos de organizações são, hoje em dia, inegáveis. A nossa abordagem para a resolução dos problemas descritos e exata. Contribuímos com novos limites inferiores, novas famílias de desigualdades validas, novos modelos de programação inteira e algoritmos de resolução exata para os problemas que nos propomos explorar. Em particular, abordamos duas variantes de cada um dos referidos problemas. Em relação ao problema de corte e empacotamento, analisamos o problema de minimização de padrões a uma dimensão e o problema de corte e empacotamento a duas dimensões, com restrição de guilhotina. O problema de minimização de padrões a uma dimensão e pertinente em situações em que a mudança de padrão envolve, por exemplo, custos de reconfiguração nas máquinas de corte. E o problema de minimização do numero de padrões diferentes de uma dada solução de um problema de corte. Para este problema contribuímos com novos limites inferiores. O problema de corte e empacotamento a duas dimensões com restrição de guilhotina e dois estágios e também abordado. Propomos um modelo pseudopolinomial de rede de fluxos, assim como critérios de redução que eliminam parte da sua simetria. Reforçamos o modelo com uma nova família de planos de corte e propomos novos limites inferiores. Para esta variante, consideramos também outras variações do problema original. No que se refere ao problema de encaminhamento de veículos, abordamos um problema de encaminhamento de veículos com janelas temporais e múltiplas viagens, e também um problema de localização e encaminhamento de veículos com capacidades nos veículos e depósitos e múltiplo uso dos veículos. O primeiro destes problemas considera o conhecido caso de encaminhamento de veículos com janelas temporais, com a consideração adicional de que os veículos podem ser alocados a v arias rotas no decurso do mesmo período de planeamento. A segunda variante considera a combinação do primeiro problema, embora sem janelas temporais, com um problema de localização. Isto significa que os depósitos a usar são selecionados de um conjunto de localizações disponíveis. Para ambas as variantes, propomos um modelo pseudo-polinomial de rede de fluxos cujos nodos do grafo correspondente representam instantes de tempo do período de planeamento, e cujos arcos representam rotas. Derivamos critérios de redução com o intuito de reduzir a simetria. Para o problema com janelas temporais e múltiplas viagens, propomos um algoritmo iterativo que o resolve de forma exata. Os procedimentos propostos são testados e comparados com outros métodos da literatura. Todos os resultados obtidos pelas experiencias computacionais são apresentados e discutidos

Shadow Price Guided Genetic Algorithms

The Genetic Algorithm (GA) is a popular global search algorithm. Although it has been used successfully in many fields, there are still performance challenges that prevent GA’s further success. The performance challenges include: difficult to reach optimal solutions for complex problems and take a very long time to solve difficult problems. This dissertation is to research new ways to improve GA’s performance on solution quality and convergence speed. The main focus is to present the concept of shadow price and propose a two-measurement GA. The new algorithm uses the fitness value to measure solutions and shadow price to evaluate components. New shadow price Guided operators are used to achieve good measurable evolutions. Simulation results have shown that the new shadow price Guided genetic algorithm (SGA) is effective in terms of performance and efficient in terms of speed

Learning to compare nodes in branch and bound with graph neural networks

En informatique, la résolution de problèmes NP-difficiles en un temps raisonnable est d’une grande importance : optimisation de la chaîne d’approvisionnement, planification, routage, alignement de séquences biologiques multiples, inference dans les modèles graphiques pro- babilistes, et même certains problèmes de cryptographie sont tous des examples de la classe NP-complet. En pratique, nous modélisons beaucoup d’entre eux comme un problème d’op- timisation en nombre entier, que nous résolvons à l’aide de la méthodologie séparation et évaluation. Un algorithme de ce style divise un espace de recherche pour l’explorer récursi- vement (séparation), et obtient des bornes d’optimalité en résolvant des relaxations linéaires sur les sous-espaces (évaluation). Pour spécifier un algorithme, il faut définir plusieurs pa- ramètres, tel que la manière d’explorer les espaces de recherche, de diviser une recherche l’espace une fois exploré, ou de renforcer les relaxations linéaires. Ces politiques peuvent influencer considérablement la performance de résolution. Ce travail se concentre sur une nouvelle manière de dériver politique de recherche, c’est à dire le choix du prochain sous-espace à séparer étant donné une partition en cours, en nous servant de l’apprentissage automatique profond. Premièrement, nous collectons des données résumant, sur une collection de problèmes donnés, quels sous-espaces contiennent l’optimum et quels ne le contiennent pas. En représentant ces sous-espaces sous forme de graphes bipartis qui capturent leurs caractéristiques, nous entraînons un réseau de neurones graphiques à déterminer la probabilité qu’un sous-espace contienne la solution optimale par apprentissage supervisé. Le choix d’un tel modèle est particulièrement utile car il peut s’adapter à des problèmes de différente taille sans modifications. Nous montrons que notre approche bat celle de nos concurrents, consistant à des modèles d’apprentissage automatique plus simples entraînés à partir des statistiques du solveur, ainsi que la politique par défaut de SCIP, un solveur open-source compétitif, sur trois familles NP-dures: des problèmes de recherche de stables de taille maximum, de flots de réseau multicommodité à charge fixe, et de satisfiabilité maximum.In computer science, solving NP-hard problems in a reasonable time is of great importance, such as in supply chain optimization, scheduling, routing, multiple biological sequence align- ment, inference in probabilistic graphical models, and even some problems in cryptography. In practice, we model many of them as a mixed integer linear optimization problem, which we solve using the branch and bound framework. An algorithm of this style divides a search space to explore it recursively (branch) and obtains optimality bounds by solving linear relaxations in such sub-spaces (bound). To specify an algorithm, one must set several pa- rameters, such as how to explore search spaces, how to divide a search space once it has been explored, or how to tighten these linear relaxations. These policies can significantly influence resolution performance. This work focuses on a novel method for deriving a search policy, that is, a rule for select- ing the next sub-space to explore given a current partitioning, using deep machine learning. First, we collect data summarizing which subspaces contain the optimum, and which do not. By representing these sub-spaces as bipartite graphs encoding their characteristics, we train a graph neural network to determine the probability that a subspace contains the optimal so- lution by supervised learning. The choice of such design is particularly useful as the machine learning model can automatically adapt to problems of different sizes without modifications. We show that our approach beats the one of our competitors, consisting of simpler machine learning models trained from solver statistics, as well as the default policy of SCIP, a state- of-the-art open-source solver, on three NP-hard benchmarks: generalized independent set, fixed-charge multicommodity network flow, and maximum satisfiability problems

Structural optimization in steel structures, algorithms and applications

L'abstract è presente nell'allegato / the abstract is in the attachmen

Determination of Cost-Effective Range in Surface Finish for Single Pass Turning

Surface finish is considered a critical characteristic for manufacturing components when manufacturers strive to produce components with high-quality characteristics predefined by design engineers. The objective of this research is to provide a cost-effective range in surface finish for single pass turning that enables the design engineers to explore a wider spectrum of alternative solutions without significantly affecting the functionality of the part. Apart from the one optimal solution, the proposed methodology, which is based on Geometric Programming, would provide a range of cutting conditions solutions that satisfy the economic and functional needs for the designer. This can be achieved by switching cost reduction focus from tooling to labor cost, particularly by adjusting variables values such as spindle speed and feed. An algorithm has been developed to find the new variables values. In addition, a sensitivity analysis model, based on metaheuristic techniques, will also be developed to further give a set of possible solutions that are practically preferable to the practitioners. In addition, the developed methodology can be applied to other engineering applications. The proposed methodology will provide a tool that enhances the design for manufacturability for companies to become more competitive