Algoritmos e formulações matemáticas para problemas de roteamento em arcos

Orientador: Fábio Luiz UsbertiTese (doutorado) - Universidade Estadual de Campinas, Instituto de ComputaçãoResumo: Problemas de roteamento em arcos têm por objetivo determinar rotas de custo mínimo que visitam um subconjunto de arcos de um grafo, com uma ou mais restrições adicionais. Esta tese estuda três problemas NP-difíceis de roteamento em arcos: (1) o problema de roteamento em arcos capacitado (CARP); (2) o problema de roteamento em arcos capacitado e aberto (OCARP); e (3) o problema do carteiro chinês com cobertura (CCPP). Apresentamos formulações matemáticas e métodos exatos e heurísticos para tratar computacionalmente esses problemas: (i) uma heurística construtiva gulosa e randomizada é proposta para o CARP; (ii) uma metaheurística de algoritmos genéticos híbrido e dois métodos de limitantes inferiores por programação linear inteira, um branch-and-cut e um baseado em redes de fluxos, são propostos para o OCARP; e (iii) um método exato branch-and-cut com desigualdades válidas e uma heurística construtiva são propostos para o CCPP. Extensivos experimentos computacionais utilizando instâncias de benchmark foram executados para demonstrar o desempenho dos métodos propostos em relação aos métodos da literatura, considerando tanto a qualidade das soluções obtidas quanto o tempo de processamento. Nossos resultados mostram que os métodos propostos são estado da arte. Os problemas estudados apresentam aplicações práticas relevantes: o CARP tem aplicações em coleta de lixo urbano e remoção de neve de estradas; o OCARP tem aplicações em roteamento de leituristas e na definição de caminhos de corte em chapas metálicas; e o CCPP tem aplicações em roteamento de leituristas com o uso de tecnologia wireless. A solução desses problemas remete à diminuição de custos logísticos, melhorando a competitividade das empresasAbstract: Arc routing problems aim to find minimum cost routes that visit a subset of arcs of a graph, with one or more side constraints. This thesis studies three NP-hard arc routing problems: (1) the capacitated arc routing problem (CARP); (2) the open capacitated arc routing problem (OCARP); and (3) the covering Chinese postman problem (CCPP). We present mathematical formulations and heuristic and exact methods to computationally solve these problems: (i) a greedy and randomized constructive heuristic is proposed for the CARP; (ii) a hybrid genetic algorithm metaheuristic and two linear integer programming lower bound methods, one based on branch-and-cut and one based on flow networks, are proposed for the OCARP; and (iii) an exact branch-and-cut method with valid inequalities and a constructive heuristic are proposed for the CCPP. Extensive computational experiments using benchmark instances were performed to demonstrate the performance of the proposed methods in comparison to the previous methods, regarding both quality of solutions and processing time. Our results show that the proposed methods are state-of-the-art. The studied problems have many relevant practical applications: the CARP has applications on urban waste collection and snow removal; the OCARP has applications on the routing of meter readers and the cutting of metal sheets; and last, the CCPP has applications on automated meter readers routing. The solution of these problems leads to the reduction of logistics costs, improving businesses competitivenessDoutoradoCiência da ComputaçãoDoutor em Ciência da Computação2016/00315-0FAPES

Logic learning and optimized drawing: two hard combinatorial problems

Nowadays, information extraction from large datasets is a recurring operation in countless fields of applications. The purpose leading this thesis is to ideally follow the data flow along its journey, describing some hard combinatorial problems that arise from two key processes, one consecutive to the other: information extraction and representation. The approaches here considered will focus mainly on metaheuristic algorithms, to address the need for fast and effective optimization methods. The problems studied include data extraction instances, as Supervised Learning in Logic Domains and the Max Cut-Clique Problem, as well as two different Graph Drawing Problems. Moreover, stemming from these main topics, other additional themes will be discussed, namely two different approaches to handle Information Variability in Combinatorial Optimization Problems (COPs), and Topology Optimization of lightweight concrete structures

The Complexity of Planning Revisited - A Parameterized Analysis

The early classifications of the computational complexity of planning under various restrictions in STRIPS (Bylander) and SAS+ (Baeckstroem and Nebel) have influenced following research in planning in many ways. We go back and reanalyse their subclasses, but this time using the more modern tool of parameterized complexity analysis. This provides new results that together with the old results give a more detailed picture of the complexity landscape. We demonstrate separation results not possible with standard complexity theory, which contributes to explaining why certain cases of planning have seemed simpler in practice than theory has predicted. In particular, we show that certain restrictions of practical interest are tractable in the parameterized sense of the term, and that a simple heuristic is sufficient to make a well-known partial-order planner exploit this fact.Comment: (author's self-archived copy

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

A Polyhedral Study of Mixed 0-1 Set

We consider a variant of the well-known single node fixed charge network flow set with constant capacities. This set arises from the relaxation of more general mixed integer sets such as lot-sizing problems with multiple suppliers. We provide a complete polyhedral characterization of the convex hull of the given set

Sequenciamento de movimentos terrestres nos aeroportos

Mestrado em Matemática e AplicaçõesO tráfego aéreo no mundo está em crescimento e para a maioria dos aeroportos não e uma opção expandir os terminais ou as pistas, fazendo com que estes tentem maximizar a eficiência operacional. Muitos aeroportos estão a operar perto da sua capacidade m áxima. Horas de ponta implicam engarrafamentos e causam simultâneos atrasos ao longo de toda a cadeia de operações com consequências para passageiros, companhias aéreas e aeroportos. Por estes motivos há uma necessidade de otimização dos movimentos no solo que ocorrem nos aeroportos. Existem três grandes problemas no que diz respeito as operações dos aeroportos: o sequenciamento das partidas e chegadas; a gestão das operações que precedem a "luz verde" para que o avião possa sair do stand; e os movimentos no solo entre o stand e a pista (e o oposto). O âmbito deste trabalho enquadra-se nos movimentos no solo que interagem com os dois outros problemas de sequenciamento mencionados e fornece decisões em tempo real. O problema dos movimentos terrestres consiste em estabelecer o roteamento dos aviões desde o stand até a pista para levantarem voo, ou no caminho inverso, e sequenciar os seus movimentos. A nossa abordagem consiste numa otimização rápida que considera um conjunto de aviões a moverem-se de, e para, a pista, e uma rede condicionada pela planta do aeroporto. Considera, ainda, restrições tais como: de rota; separações entre aviões devido ao jet blast; velocidade de cada avião; de tempo para chegadas e partidas, num ambiente em constante mudança. O objetivo e minimizar o consumo de combustível enquanto os aviões estão no solo (da perspetiva das companhias aéreas) e minimizar o tempo despendido em cada slot de janela temporal na ocupação do espaço terrestre do aeroporto, garantindo todas as regras de segurança. Também os passageiros e o ambiente beneficiam de um conjunto de movimentações em terra otimizadas. A otimização proposta fornece uma solução heuristica rápida para cada evento em tempo real respeitando todas as regras estabelecidas no Ad- vanced Surface Movement, Guidance and Control Systems (A-SMGCS) da Organização Internacional de Aviação Civil (ICAO).Worldwide air tra c tends to increase and for many airports it's no longer an option to expand terminals and runways, so airports are trying to maximize their operational e ciency. Many airports already operate near their maximum capacity. Peak hours imply operational bottlenecks and cause chained delays across ights impacting passenger, airlines and airports. Therefore there is a need for the optimization of the ground movements at the airports. There are three major problems concerning airport operations: the departures and arrivals sequencing on the runways; the sta management operations preceding the green light for aircraft to leave the gate; and the ground movement between the gate and the runway (and reverse). The scope of this work is the ground movement problem that interacts with the other two scheduling problems mentioned and provides decisions in real-time. The ground movement problem consists of routing the planes from the gate to the runway for takeo or on reverse path, and to schedule their movements. Our approach proposes a fast optimization system that considers a set of planes moving to and from a set of runways along a given road network conditioned by the airport ground layout. It considers constraints such as the route constraints, separation between aircrafts due to jet blast, aircraft movement speeds, timing constraints for arrivals and departures in a constantly changing environment. The objective is to minimize fuel consumptions on the ground (from the airline perspective) and to minimize the time spent on the time window slot for occupying the airport ground (from the airports perspective) while granting all safety regulations at all times. Also passengers and the environment bene t from an optimized ground movement. The optimization approach proposed provides a fast heuristic solution for each real-time event generated respecting all the rules established by Advanced Surface Movement, Guidance and Control Systems (ASMGCS) of the International Civil Aviation Organization (ICAO)

SCIP-Jack—a solver for STP and variants with parallelization extensions

This is the author accepted manuscript. The final version is available from Springer Verlag via the DOI in this record The Steiner tree problem in graphs is a classical problem that commonly arises in practical applications as one of many variants. While often a strong relationship between different Steiner tree problem variants can be observed, solution approaches employed so far have been prevalently problemspecific. In contrast, this paper introduces a general-purpose solver that can be used to solve both the classical Steiner tree problem and many of its variants without modification. This versatility is achieved by transforming various problem variants into a general form and solving them by using a state-ofthe-art MIP-framework. The result is a high-performance solver that can be employed in massively parallel environments and is capable of solving previously unsolved instances.German Federal Ministry of Education and Researc

NetGAP: A Graph-Grammar approach for concept design of networked platforms with extra-functional requirements

During the concept design of complex networked systems, concept developers have to assure that the choice of hardware modules and the topology of the target platform will provide adequate resources to support the needs of the application. For example, future-generation aerospace systems need to consider multiple requirements, with many trade-offs, foreseeing rapid technological change and a long time span for realization and service. For that purpose, we introduce NetGAP, an automated 3-phase approach to synthesize network topologies and support the exploration and concept design of networked systems with multiple requirements including dependability, security, and performance. NetGAP represents the possible interconnections between hardware modules using a graph grammar and uses a Monte Carlo Tree Search optimization to generate candidate topologies from the grammar while aiming to satisfy the requirements. We apply the proposed approach to the synthetic version of a realistic avionics application use case and show the merits of the solution to support the early-stage exploration of alternative candidate topologies. The method is shown to vividly characterize the topology-related trade-offs between requirements stemming from security, fault tolerance, timeliness, and the "cost" of adding new modules or links. Finally, we discuss the flexibility of using the approach when changes in the application and its requirements occur

A New Spatial Approach for Efficient Transformation of Equality - Generalized TSP to TSP

The Equality - Generalized Travelling Salesman Problem (E-GTSP) asks to find a Hamiltonian cycle visiting each group exactly once, where each group represents a type of visiting node. This can represent a range of combinatorial optimization problem of NP-hard type like planning, logistics, etc. Its solution requires transformation of E-GTSP to TSP before solving it using a given TSP solver. This paper presents 5 different search-algorithms for optimal transformation which considers spatial spread of nodes of each group. Algorithms are tested over 15 cities with different street-network’s fractal-dimension for 5 instances of group-counts each. It’s observed that the R-Search algorithm, which selects nodes from each group depending upon their radial separation with respect to the start-end point, is the optimal search criterion among all other algorithms with a mean length error of 8.8%. This study will help developers and researchers to answer complex routing problems from a spatial perspective