24 research outputs found

    Vehicle routing and location routing with intermediate stops:A review

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    Bio-inspired Algorithms for TSP and Generalized TSP

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    Technological Innovations and Advances in Hydropower Engineering

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    It has been more than 140 years since water was used to generate electricity. Especially since the 1970s, with the advancement of science and technology, new technologies, new processes, and new materials have been widely used in hydropower construction. Engineering equipment and technology, as well as cascade development, have become increasingly mature, making possible the construction of many high dams and large reservoirs in the world. However, with the passage of time, hydropower infrastructure such as reservoirs, dams, and power stations built in large numbers in the past are aging. This, coupled with singular use of hydropower, limits the development of hydropower in the future. This book reports the achievements in hydropower construction and the efforts of sustainable hydropower development made by various countries around the globe. These existing innovative studies and applications stimulate new ideas for the renewal of hydropower infrastructure and the further improvement of hydropower development and utilization efficiency

    Modelo Matemático e Meta-Heurística Simulated Annealing para Elaboração de Roteiros Turísticos com base no Tourist Trip Design Problem

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    Muito embora existam diversos pacotes de viagens com destinos predefinidos contemplando locais mais populares, nos últimos anos tem crescido a procura por soluções que criem roteiros personalizados voltados às necessidades de cada turista. Para suprir essa nova demanda surge o Problema de Elaboração de Rotas Turísticas (PERT) ou TouristTrip Design Problem (TTDP) o qual Van Oudheusden e Vansteenwegen (2007) sugerem o uso do OrienteeringProblem (OP) e suas extensões para resolução desta classe de problemas. Esta dissertação tem por objetivo o desenvolvimento de um modelo matemático e de uma meta-heurística SimulatedAnnealing (SA) para resolução do TouristTrip Design Problem (TTDP)

    Algorithms for Large Orienteering Problems

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    In this thesis, we have developed algorithms to solve large-scale Orienteering Problems. The Orienteering Problem is a combinatorial optimization problem were given a weighted complete graph with vertex profits and a maximum distance constraint, the goal is to find the simple cycle which maximizes the sum of the profits of the visited vertices. To solve the Orienteering Problem, we have developed an evolutionary algorithm and an Branch-and-Cut algorithm. One of the key characteristics of the evolutionary algorithm is to work with unfeasible solutions. From the point of view of genetic operators, the main contribution has been the development of the Edge Recombination Crossover for the Orienteering Problem, which in a wider context it is also valid for any cycle problem. Another contribution has been the developed local search to handle large problems. The Branch-and-Cut algorithm includes new contributions in the separation algorithms of inequalities stemming from the cycle problem, in the separation loop, in the variables pricing, and in the calculation of the lower and upper bounds of the problem. At the same time, we have generalized for cycle problems the support graph shrinking techniques and procedures to speed up the exact separation algorithms for subcycle elimination constraints. The experiments carried out in large-sized instances, up to 7393 nodes, show that both algorithms achieve outstanding results, both in terms of the quality of solutions and in terms of the execution time.BERC.2014-2017 SEV-2013-0323 PID2019-104933GB-I00 MTM2015-65317-

    Algorithms for large orienteering problems

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    185 p.Tesi lan honetan, tamaina handiko Orientazio Problemak ebazteko algoritmoak garatu ditugu. Orientazio Problema optimizazio konbinatorioko problema bat da: herri multzo bat eta hauen arteko distantzia emanik, herri bakoitzak bere saria duelarik, eta ibilbidearen distantzia osoaren murrizketa bat ezarririk, problemaren helburua sarien batura maximizatzen duen ibilbidea aurkitzean datza. Orientazio Problema ebazteko, algoritmo ebolutibo bat eta Branch-and-Cut algoritmo bat garatu ditugu. Algoritmo ebolutiboaren ezaugarri nagusienetako bat, soluzio ez bideragarriekin lan egitea da. Eragile genetikoen ikuspuntutik algoritmo honen ekarpen nagusia Orientazio Problemarentzako proposatutako Ertzen Birkonbinazio Gurutzaketa da. Beste ekarpen bat problema handiak ebazteko aproposa den bilaketa lokala da. Branch-and-Cut algoritmoak berriz, ziklo problementzako banantze algoritmoetan, banantze begiztan, aldagaien baloratzean, eta problemaren goi eta behe-mugen kalkuluan ditu ekarpen nagusiak. Aldi berean, ziklo problementzako algoritmo zehatzaren parte diren euskarri grafoen sinplifikazio teknika eta azpizikloak identifikatzeko separazio algoritmoak aztertu ditugu. Tamaina handiko problemekin, 7393 herrirainokoak, egindako esperimentuek erakusten dute bi algoritmoek primerako emaitzak lortzen dituztela, bai soluzioen kalitatearen aldetik eta bai algoritmoen azkartasunaren aldetik ere.En esta tesis, hemos desarrollado algoritmos para resolver instancias de gran tamaño para el Problema de Orientación. El Problema de Orientación es un problema de optimización combinatoria en el cual, dado un grafo, con distancias asociadas en las aristas y premios en los vértices, y la restricción de longitud máxima de la ruta, el objetivo es maximizar la suma de recompensas de las ciudades visitadas.Para resolver el Problema de Orientación, hemos desarrollado un algoritmo evolutivo y un algoritmo Branch-and-Cut. La principal característica del algoritmo evolutivo es el uso de soluciones infactibles durante de la búsqueda. Desde el punto de vista de los operadores genéticos, la contribución más notable es el desarrollo del Cruce de Recombinación de Aristas para el Problema de Orientación. Otra contribución ha sido el desarrollo de una búsqueda local que permite abarcar problemas de gran tamaño. El algoritmo Branch-and-Cut incluye contribuciones en los algoritmos de separación para problemas de ciclos, en el bucle de separación, en la estimación de precios de las variables, y en el cálculo de las cotas inferiores y superiores del problema. Al mismo tiempo, generalizamos para problemas de ciclos, la contracción de grafos soporte y procedimientos para acelerar la separación exacta de las restricciones de eliminación de subciclos. Los experimentos llevados a cabo en problemas de gran tamaño, problemas de hasta 7393 nodos, muestran que ambos algoritmos obtienen resultados excelentes, en términos de la calidad de la solución y en términos del tiempo de ejecución.-In this thesis, we have developed algorithms to solve large-scale Orienteering Problems. The Orienteering Problem is a combinatorial optimization problem were given a weighted complete graph with vertex profits and a maximum distance constraint, the goal is to find the simple cycle which maximizes the sum of the profits of the visited vertices. To solve the Orienteering Problem, we have developed an evolutionary algorithm and a Branch-and-Cut algorithm. One of the key characteristics of the evolutionary algorithm is to work with unfeasible solutions. From the point of view of genetic operators, the main contribution has been the development of the Edge Recombination Crossover for the Orienteering Problem, which in a wider context it is also valid for any cycle problem. Another contribution has been the developed local search to handle large problems. The Branch-and-Cut algorithm includes new contributions in the separation algorithms of inequalities stemming from the cycle problem, in the separation loop, in the variables pricing, and in the calculation of the lower and upper bounds of the problem. At the same time, we have generalized for cycle problems the support graph shrinking techniques and procedures to speed up the exact separation algorithms for subcycle elimination constraints. The experiments carried out in large-sized instances, up to 7393 nodes, show that both algorithms achieve outstanding results, both in terms of the quality of solutions and in terms of the execution time.bcam:basque center for applied mathematic

    Determinação de rotas para um navio de investigação utilizado em campanhas de pesca

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    Tese de mestrado em Estatística e Investigação Operacional, apresentada à Universidade de Lisboa, através da Faculdade de Ciências, em 2018O problema de determinação de rotas para navios de investigação para campanhas de pesca, designado como Ship Routing Optimization Problem (SROP), é um problema que até agora não foi muito estudado e explorado. No problema são conhecidos o conjunto de estações de pesca a ser visitadas, o número de circuitos a determinar e o número de dias que no máximo deve durar cada circuito. Também são conhecidas as janelas temporais associadas às visitas às estações que determinam as horas de visita para cada dia e as janelas temporais associadas às visitas aos portos, que garantem que estes sejam visitados com a periodicidade previamente definida. Cada circuito deve começar e terminar no porto origem. Dadas as localizações geográficas das estações de pesca e dos portos, o objetivo do problema é minimizar a distância total percorrida e a duração total de cada circuito, garantindo que todas as estações são visitadas e respeitando as restrições das janelas temporais. Nesta dissertação, apresentam-se três modelos matemáticos em programação linear inteira mista (PLIM) para resolver o problema. Para além dos modelos, sugerem-se também heurísticas que têm como objetivo obter soluções inteiras admissíveis utilizando os modelos propostos e um solver genérico. Pretende-se comparar as três formulações a nível da qualidade dos limites inferiores para o valor ótimo, fornecidos por relaxações lineares totais e parciais e do tempo computacional gasto para obter os mesmos. Através das heurísticas pretende-se obter soluções admissíveis para todas as instâncias e os limites superiores para o valor ótimo associados aos respetivos valores. As instâncias utilizadas são baseadas em campanhas realizadas pelo IPMA (Instituto Português do Mar e da Atmosfera) para estimar a abundância e observar a distribuição geográfica de várias espécies marinhas da costa portuguesa e instâncias disponibilizadas na literatura para o Problema do Caixeiro Viajante com Seleção de Hotéis. Os resultados obtidos confirmam a complexidade do problema e a dificuldade em resolve-lo usando um solver genérico, tendo existido instâncias para as quais não foi possível encontrar uma solução admissível.The problem of determining routes for vessels in fisheries research, called the Ship Routing Optimization Problem (SROP), has not been much studied and explored. The set of fishing stations to be visited, the number of circuits to establish and the maximum number of days that each circuit should last are known, as well as the time windows associated with station visits which determine the visiting hours for each day and the windows associated with visits to the seaports assuring a predefined periodicity. Each circuit must start and end at the home seaport. Given the geographical locations of the fishing stations and seaports, the objective is to minimize the total traveled distance and the total duration of each circuit, ensuring that all stations are visited and time windows constraints are satisfied. In this dissertation, three mixed integer linear programming mathematical models are presented for the problem. Furthermore, heuristics that aim to obtain feasible integer solutions using the proposed models and a generic solver are suggested . It is intended to compare the three models in what concerns the quality of the lower bounds for the optimal value provided by partial or total linear programming relaxations and the computational time spent to obtain them. By using the heuristics, it is intended to obtain feasible solutions that provide upper bounds for all instances. The instances used are based in the campaigns realized by IPMA (Portuguese Sea and Atmosphere Institute) to estimate the abundance and observe the geographical distribution of several demersal fish species from the Portuguese continental coast and instances available in literature for the Traveling Salesman Problem with Hotel Selection. The results obtained confirm the complexity of the problem and the difficulty to solve it using a generic solver. There have been instances for which it was not possible to obtain a feasible solution

    Meta-heurísticas para o problema do caixeiro viajante com seleção de hotéis

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    Tese de mestrado em Estatística e Investigação Operacional, apresentada à Universidade de Lisboa, através da Faculdade de Ciências, 2016O problema do caixeiro viajante (TSP) é um problema com diversas aplicações na medida em que muitas das situações da vida real podem ser modeladas como um problema do caixeiro viajante. Deste modo, ao longo dos anos, o TSP tem sido dos mais estudados em Investigação Operacional. Nesta dissertação é estudada uma variante do TSP, nomeadamente o problema do caixeiro viajante com selecção de hotéis (TSPHS), o qual tem igualmente diversas aplicações práticas. Dados um conjunto de clientes a visitar e um conjunto de potenciais hotéis para pernoitar, sendo conhecidas as distâncias entre clientes e entre clientes e hotéis, o TSPHS consiste em determinar uma rota que visite todos os clientes começando e acabando num mesmo hotel pré-definido. A rota deverá ser tal que possa ser dividida em percursos com duração não superior a um dado limite de tempo inferior a um dia. Por outro lado, cada percurso deverá ter início e fim em algum dos hotéis disponíveis, não tendo necessariamente que ser o mesmo. O objetivo é minimizar o número de percursos e simultaneamente a distância total percorrida. Sendo o TSPHS uma extensão do TSP, ele é também um problema NP-difícil, pelo que a existência de métodos heurísticos como auxílio à resolução destes problemas é fundamental. Nesta dissertação são apresentadas duas meta-heurísticas baseadas em algoritmos genéticos combinados com um procedimento de pesquisa local, que considera oito operadores de vizinhança, e um algoritmo de perturbação de soluções. Foram testados vários parâmetros por forma a obter os melhores resultados para as instâncias de referência utilizadas. Os resultados obtidos foram comparados com os resultados de outros autores. Para uns casos são obtidas melhores soluções para outros não.The traveling salesman problem (TSP) has many applications since there are many reallife situations which can be modeled as a traveling salesman problem. Thus, over the years, TSP has been one of the most studied problems in Operational Research. This thesis addresses a variant of TSP, namely the traveling salesman problem with hotel selection (TSPHS). The TSPHS has also many practical applications. Given a set of customers to be visited and a set of potential hotels to spend the night, the TSPHS consists in determining one route starting and ending in one given hotel that visits all customers. The route is divided into trips lasting no more than a given limit of time. Moreover, each trip must begin and end at any of the available hotels, not necessarily the same. The goal is minimize the number of trips and simultaneously the total traveled distance. Being the TSPHS an extension of the TSP, it is also an NP-hard problem, so the development of heuristic methods as an aiding tool to solve these problems is crucial. This thesis proposes two meta-heuristics based on genetic algorithms combined with a local search procedure which uses eight neighborhood operators and a solution perturbation algorithm. Various parameters were tested in order to obtain the best results for the used benchmark instances. The results obtained were compared with results of other authors. For some cases are obtained better solutions for others not

    Dynamic multi-objective optimization using evolutionary algorithms

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    Dynamic Multi-objective Optimization Problems (DMOPs) offer an opportunity to examine and solve challenging real world scenarios where trade-off solutions between conflicting objectives change over time. Definition of benchmark problems allows modelling of industry scenarios across transport, power and communications networks, manufacturing and logistics. Recently, significant progress has been made in the variety and complexity of DMOP benchmarks and the incorporation of realistic dynamic characteristics. However, significant gaps still exist in standardised methodology for DMOPs, specific problem domain examples and in the understanding of the impacts and explanations of dynamic characteristics. This thesis provides major contributions on these three topics within evolutionary dynamic multi-objective optimization. Firstly, experimental protocols for DMOPs are varied. This limits the applicability and relevance of results produced and conclusions made in the field. A major source of the inconsistency lies in the parameters used to define specific problem instances being examined. The uninformed selection of these has historically held back understanding of their impacts and standardisation in experimental approach to these parameters in the multi-objective problem domain. Using the frequency and severity (or magnitude) of change events, a more informed approach to DMOP experimentation is conceptualized, implemented and evaluated. Establishment of a baseline performance expectation across a comprehensive range of dynamic instances for well-studied DMOP benchmarks is analyzed. To maximize relevance, these profiles are composed from the performance of evolutionary algorithms commonly used for baseline comparisons and those with simple dynamic responses. Comparison and contrast with the coverage of parameter combinations in the sampled literature highlights the importance of these contributions. Secondly, the provision of useful and realistic DMOPs in the combinatorial domain is limited in previous literature. A novel dynamic benchmark problem is presented by the extension of the Travelling Thief Problem (TTP) to include a variety of realistic and contextually justified dynamic changes. Investigation of problem information exploitation and it's potential application as a dynamic response is a key output of these results and context is provided through comparison to results obtained by adapting existing TTP heuristics. Observation driven iterative development prompted the investigation of multi-population island model strategies, together with improvements in the approaches to accurately describe and compare the performance of algorithm models for DMOPs, a contribution which is applicable beyond the dynamic TTP. Thirdly, the purpose of DMOPs is to reconstruct realistic scenarios, or features from them, to allow for experimentation and development of better optimization algorithms. However, numerous important characteristics from real systems still require implementation and will drive research and development of algorithms and mechanisms to handle these industrially relevant problem classes. The novel challenges associated with these implementations are significant and diverse, even for a simple development such as consideration of DMOPs with multiple time dependencies. Real world systems with dynamics are likely to contain multiple temporally changing aspects, particularly in energy and transport domains. Problems with more than one dynamic problem component allow for asynchronous changes and a differing severity between components that leads to an explosion in the size of the possible dynamic instance space. Both continuous and combinatorial problem domains require structured investigation into the best practices for experimental design, algorithm application and performance measurement, comparison and visualization. Highlighting the challenges, the key requirements for effective progress and recommendations on experimentation are explored here
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