New variants of variable neighbourhood search for 0-1 mixed integer programming and clustering

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Many real-world optimisation problems are discrete in nature. Although recent rapid developments in computer technologies are steadily increasing the speed of computations, the size of an instance of a hard discrete optimisation problem solvable in prescribed time does not increase linearly with the computer speed. This calls for the development of new solution methodologies for solving larger instances in shorter time. Furthermore, large instances of discrete optimisation problems are normally impossible to solve to optimality within a reasonable computational time/space and can only be tackled with a heuristic approach. In this thesis the development of so called matheuristics, the heuristics which are based on the mathematical formulation of the problem, is studied and employed within the variable neighbourhood search framework. Some new variants of the variable neighbourhood searchmetaheuristic itself are suggested, which naturally emerge from exploiting the information from the mathematical programming formulation of the problem. However, those variants may also be applied to problems described by the combinatorial formulation. A unifying perspective on modern advances in local search-based metaheuristics, a so called hyper-reactive approach, is also proposed. Two NP-hard discrete optimisation problems are considered: 0-1 mixed integer programming and clustering with application to colour image quantisation. Several new heuristics for 0-1 mixed integer programming problem are developed, based on the principle of variable neighbourhood search. One set of proposed heuristics consists of improvement heuristics, which attempt to find high-quality near-optimal solutions starting from a given feasible solution. Another set consists of constructive heuristics, which attempt to find initial feasible solutions for 0-1 mixed integer programs. Finally, some variable neighbourhood search based clustering techniques are applied for solving the colour image quantisation problem. All new methods presented are compared to other algorithms recommended in literature and a comprehensive performance analysis is provided. Computational results show that the methods proposed either outperform the existing state-of-the-art methods for the problems observed, or provide comparable results. The theory and algorithms presented in this thesis indicate that hybridisation of the CPLEX MIP solver and the VNS metaheuristic can be very effective for solving large instances of the 0-1 mixed integer programming problem. More generally, the results presented in this thesis suggest that hybridisation of exact (commercial) integer programming solvers and some metaheuristic methods is of high interest and such combinations deserve further practical and theoretical investigation. Results also show that VNS can be successfully applied to solving a colour image quantisation problem.Support from the Mathematical Institute, Serbian Academy of Sciences and Arts, are acknowledged for this research

New variants of variable neighbourhood search for 0-1 mixed integer programming and clustering

Many real-world optimisation problems are discrete in nature. Although recent rapid developments in computer technologies are steadily increasing the speed of computations, the size of an instance of a hard discrete optimisation problem solvable in prescribed time does not increase linearly with the computer speed. This calls for the development of new solution methodologies for solving larger instances in shorter time. Furthermore, large instances of discrete optimisation problems are normally impossible to solve to optimality within a reasonable computational time/space and can only be tackled with a heuristic approach. In this thesis the development of so called matheuristics, the heuristics which are based on the mathematical formulation of the problem, is studied and employed within the variable neighbourhood search framework. Some new variants of the variable neighbourhood searchmetaheuristic itself are suggested, which naturally emerge from exploiting the information from the mathematical programming formulation of the problem. However, those variants may also be applied to problems described by the combinatorial formulation. A unifying perspective on modern advances in local search-based metaheuristics, a so called hyper-reactive approach, is also proposed. Two NP-hard discrete optimisation problems are considered: 0-1 mixed integer programming and clustering with application to colour image quantisation. Several new heuristics for 0-1 mixed integer programming problem are developed, based on the principle of variable neighbourhood search. One set of proposed heuristics consists of improvement heuristics, which attempt to find high-quality near-optimal solutions starting from a given feasible solution. Another set consists of constructive heuristics, which attempt to find initial feasible solutions for 0-1 mixed integer programs. Finally, some variable neighbourhood search based clustering techniques are applied for solving the colour image quantisation problem. All new methods presented are compared to other algorithms recommended in literature and a comprehensive performance analysis is provided. Computational results show that the methods proposed either outperform the existing state-of-the-art methods for the problems observed, or provide comparable results. The theory and algorithms presented in this thesis indicate that hybridisation of the CPLEX MIP solver and the VNS metaheuristic can be very effective for solving large instances of the 0-1 mixed integer programming problem. More generally, the results presented in this thesis suggest that hybridisation of exact (commercial) integer programming solvers and some metaheuristic methods is of high interest and such combinations deserve further practical and theoretical investigation. Results also show that VNS can be successfully applied to solving a colour image quantisation problem.EThOS - Electronic Theses Online ServiceMathematical Institute, Serbian Academy of Sciences and ArtsGBUnited Kingdo

Algoritmos evolutivos para alguns problemas em telecomunicações

Orientadores: Flavio Keidi Miyazawa, Mauricio Guilherme de Carvalho ResendeTese (doutorado) - Universidade Estadual de Campinas, Instituto de ComputaçãoResumo: Nos últimos anos, as redes de telecomunicação tem experienciado um grande aumento no fluxo de dados. Desde a utilização massiva de vídeo sob demanda até o incontável número de dispositivos móveis trocando texto e vídeo, o tráfego alcançou uma escala capaz de superar a capacidade das redes atuais. Portanto, as companhias de telecomunicação ao redor do mundo tem sido forçadas a aumentar a capacidade de suas redes para servir esta crescente demanda. Como o custo de instalar uma infraestrutura de rede é geralmente muito grande, o projeto de redes usa fortemente ferramentas de otimização para manter os custos tão baixos quanto possível. Nesta tese, nós analisamos vários aspectos do projeto e implementação de redes de telecomunicação. Primeiramente, nós apresentamos um novo problema de projeto de redes usado para servir demandas sem fio de dispositivos móveis e rotear tal tráfego para a rede principal. Tais redes de acesso são baseadas em tecnologias sem fio modernos como Wi-Fi, LTE e HSPA. Este problema consideramos várias restrições reais e é difícil de ser resolvido. Nós estudamos casos reais nas vizinhanças de uma grande cidade nos Estados Unidos. Em seguida, nós apresentamos uma variação do problema de localização de hubs usado para modelar as redes principais (backbones ou laços centrais). Este problema também pode ser utilizado para modelar redes de transporte de cargas e passageiros. Nós também estudamos o problema de clusterização correlacionada com sobreposições usado para modelar o comportamento dos usuários quando utilizam seus equipamentos móveis. Neste problema, nós podemos rotular um objeto usando múltiplos rótulos e analisar a conexão entre eles. Este problema é adequado para análise de mobilidade de equipamentos que pode ser usada para estimar o tráfego em uma dada região. E finalmente, nós analisamos o licenciamento de espectro sobre uma perspectiva governamental. Nestes casos, uma agência do governo deseja vender licenças para companhias de telecomunicação para que operem em uma dada faixa de espectro. Este processo usualmente é conduzido usando leilões combinatoriais. Para todos problemas, nós propomos algoritmos genéticos de chaves aleatórias viciadas e modelos de programação linear inteira mista para resolvê-los (exceto para o problema de clusterização correlacionada com sobreposição, devido sua natureza não-linear). Os algoritmos que propusemos foram capazes de superar algoritmos do estado da arte para todos problemasAbstract: Cutting and packing problems are common problems that occur in many industry and business process. Their optimized resolution leads to great profits in several sectors. A common problem, that occur in textil and paper industries, is to cut a strip of some material to obtain several small items, using the minimum length of material. This problem, known by Two Dimensional Strip Packing Problem (2SP), is a hard combinatorial optimization problem. In this work, we present an exact algorithm to 2SP, restricted to two staged cuts (known by Two Dimensional Level Strip Packing, 2LSP). The algorithm uses the branch-and-price technique, and heuristics based on approximation algorithms to obtain upper bounds. The algorithm obtained optimal or almost optimal for small and moderate sized instancesAbstract: In last twenty years, telecommunication networks have experienced a huge increase in data utilization. From massive on-demand video to uncountable mobile devices exchanging text and video, traffic reached scales that overcame the network capacities. Therefore, telecommunication companies around the world have been forced to increase their capacity to serve this increasing demand. As the cost to deploy network infrastructure is usually very large, the design of a network heavily uses optimization tools to keep costs as low as possible. In this thesis, we analyze several aspects of the design and deployment of communication networks. First, we present a new network design problem used to serve wireless demands from mobile devices and route the traffic to the core network. Such access networks are based on modern wireless access technologies such as Wi-Fi, LTE, and HSPA. This problem has several real world constraints and it is hard to solve. We study real cases of the vicinity of a large city in the United States. Following, we present a variation of the hub-location problem used to model these core networks. Such problem is also suitable to model transportation networks. We also study the overlapping correlation clustering problem used to model the user's behavior when using their mobile devices. In such problem, one can label an object with multiple labels and analyzes the connections between them. Although this problem is very generic, it is suitable to analyze device mobility which can be used to estimate traffic in geographical regions. Finally, we analyze spectrum licensing from a governmental perspective. In these cases, a governmental agency wants to sell rights for telecommunication companies to operate over a given spectrum range. This process usually is conducted using combinatorial auctions. For all problems we propose biased random-key genetic algorithms and mixed integer linear programming models (except in the case of the overlapping correlation clustering problem due its non-linear nature). Our algorithms were able to overcome the state of the art algorithms for all problemsDoutoradoCiência da ComputaçãoDoutor em Ciência da Computaçã

LIPIcs, Volume 244, ESA 2022, Complete Volume

LIPIcs, Volume 244, ESA 2022, Complete Volum