94 research outputs found

    Kernels of Mallows Models under the Hamming Distance for solving the Quadratic Assignment Problem

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    The Quadratic Assignment Problem (QAP) is a well-known permutation-based combinatorial optimization problem with real applications in industrial and logistics environments. Motivated by the challenge that this NP-hard problem represents, it has captured the attention of the optimization community for decades. As a result, a large number of algorithms have been proposed to tackle this problem. Among these, exact methods are only able to solve instances of size n<40n<40. To overcome this limitation, many metaheuristic methods have been applied to the QAP. In this work, we follow this direction by approaching the QAP through Estimation of Distribution Algorithms (EDAs). Particularly, a non-parametric distance-based exponential probabilistic model is used. Based on the analysis of the characteristics of the QAP, and previous work in the area, we introduce Kernels of Mallows Model under the Hamming distance to the context of EDAs. Conducted experiments point out that the performance of the proposed algorithm in the QAP is superior to (i) the classical EDAs adapted to deal with the QAP, and also (ii) to the specific EDAs proposed in the literature to deal with permutation problems.Severo Ochoa SEV-2013-0323 TIN2016-78365-R PID2019-106453GAI00 SVP-2014-068574 TIN2017-82626-

    Extending Distance-based Ranking Models In Estimation of Distribution Algorithms

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    Recently, probability models on rankings have been proposed in the field of estimation of distribution algorithms in order to solve permutation-based combinatorial optimisation problems. Particularly, distance-based ranking models, such as Mallows and Generalized Mallows under the Kendall’s-t distance, have demonstrated their validity when solving this type of problems. Nevertheless, there are still many trends that deserve further study. In this paper, we extend the use of distance-based ranking models in the framework of EDAs by introducing new distance metrics such as Cayley and Ulam. In order to analyse the performance of the Mallows and Generalized Mallows EDAs under the Kendall, Cayley and Ulam distances, we run them on a benchmark of 120 instances from four well known permutation problems. The conducted experiments showed that there is not just one metric that performs the best in all the problems. However, the statistical test pointed out that Mallows-Ulam EDA is the most stable algorithm among the studied proposals

    An estimation of distribution algorithm for combinatorial optimization problems

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    This paper considers solving more than one combinatorial problem considered some of the most difficult to solve in the combinatorial optimization field, such as the job shop scheduling problem (JSSP), the vehicle routing problem with time windows (VRPTW), and the quay crane scheduling problem (QCSP). A hybrid metaheuristic algorithm that integrates the Mallows model and the Moth-flame algorithm solves these problems. Through an exponential function, the Mallows model emulates the solution space distribution for the problems; meanwhile, the Moth-flame algorithm is in charge of determining how to produce the offspring by a geometric function that helps identify the new solutions. The proposed metaheuristic, called HEDAMMF (Hybrid Estimation of Distribution Algorithm with Mallows model and Moth-Flame algorithm), improves the performance of recent algorithms. Although knowing the algebra of permutations is required to understand the proposed metaheuristic, utilizing the HEDAMMF is justified because certain problems are fixed differently under different circumstances. These problems do not share the same objective function (fitness) and/or the same constraints. Therefore, it is not possible to use a single model problem. The aforementioned approach is able to outperform recent algorithms under different metrics for these three combinatorial problems. Finally, it is possible to conclude that the hybrid metaheuristics have a better performance, or equal in effectiveness than recent algorithms

    Mallows and generalized Mallows model for matchings

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    The Mallows and Generalized Mallows Models are two of the most popular probability models for distribu- tions on permutations. In this paper, we consider both models under the Hamming distance. This models can be seen as models for matchings instead of models for rankings. These models cannot be factorized, which contrasts with the popular MM and GMM under Kendall’s-τ and Cayley distances. In order to overcome the computational issues that the models involve, we introduce a novel method for computing the partition function. By adapting this method we can compute the expectation, joint and conditional probabilities. All these methods are the basis for three sampling algorithms, which we propose and analyze. Moreover, we also propose a learning algorithm. All the algorithms are analyzed both theoretically and empirically, using synthetic and real data from the context of e-learning and Massive Open Online Courses (MOOC)

    Instances of combinatorial optimization problems: complexity and generation

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    138 p.La optimización combinatoria considera problemas donde el objetivo es hallar el punto que maximiza o minimiza una función y donde el espacio de búsqueda es nito o innito numerable. La resolución de estos problemas es de gran importancia, ya que aparecen de forma natural en diferentes ámbitos como el mundo de la ciencia y de la ingeniería, la industria o la gestión

    A review on Estimation of Distribution Algorithms in Permutation-based Combinatorial Optimization Problems

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    Estimation of Distribution Algorithms (EDAs) are a set of algorithms that belong to the field of Evolutionary Computation. Characterized by the use of probabilistic models to represent the solutions and the dependencies between the variables of the problem, these algorithms have been applied to a wide set of academic and real-world optimization problems, achieving competitive results in most scenarios. Nevertheless, there are some optimization problems, whose solutions can be naturally represented as permutations, for which EDAs have not been extensively developed. Although some work has been carried out in this direction, most of the approaches are adaptations of EDAs designed for problems based on integer or real domains, and only a few algorithms have been specifically designed to deal with permutation-based problems. In order to set the basis for a development of EDAs in permutation-based problems similar to that which occurred in other optimization fields (integer and real-value problems), in this paper we carry out a thorough review of state-of-the-art EDAs applied to permutation-based problems. Furthermore, we provide some ideas on probabilistic modeling over permutation spaces that could inspire the researchers of EDAs to design new approaches for these kinds of problems

    Alternative Representations for Codifying Solutions in Permutation-Based Problems

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    Since their introduction, Estimation of Distribution Algorithms (EDAs) have proved to be very competitive algorithms to solve many optimization problems. However, despite recent developments, in the case of permutation-based combinatorial optimization problems, there are still many aspects that deserve further research. One of them is the influence of the codification employed to represent the solutions on the overall performance of the algorithm. When considering classical EDAs, optimizing permutation problems is challenging, and specific mechanisms are needed to hold the restrictions associated with the permutation nature of solutions.In this paper, in addition to the permutation-vector codification, we investigate alternative representations to describe solutions of permutation problems in the context of EDAs. In order to evaluate their influence, we adopted a classical EDA and conducted an experimental study on two different permutation problems and representations for codifying solutions. The results revealed a narrow relationship between the type of combinatorial problem optimized and the selected representation used to codify its solutions. Moreover, the results point out that choosing the appropriate representation to codify solutions of the given permutation problem is critical for the performance of the algorithm

    Contributions to the mathematical modeling of estimation of distribution algorithms and pseudo-boolean functions

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    134 p.Maximice o minimice una función objetivo definida sobre un espacio discreto. Dado que la mayoría de dichos problemas no pueden ser resueltos mediante una búsqueda exhaustiva, su resolución se aproxima frecuentemente mediante algoritmos heurísticos. Sin embargo, no existe ningún algoritmo que se comporte mejor que el resto de algoritmos para resolver todas las instancias de cualquier problema. Por ello, el objetivo ideal es, dado una instancia de un problema, saber cuál es el algoritmo cuya resoluciones más eficiente. Las dos líneas principales de investigación para lograr dicho objetivo son estudiar las definiciones de los problemas y las posibles instancias que cada problema puede generar y el estudio delos diseños y características de los algoritmos. En esta tesis, se han tratado ambas lineas. Por un lado,hemos estudiado las funciones pseudo-Booleanas y varios problemas binarios específicos. Por otro lado,se ha presentado un modelado matemático para estudiar Algoritmos de Estimación de Distribuciones diseñados para resolver problemas basados en permutaciones. La principal motivación ha sido seguir progresando en este campo para comprender mejor las relaciones entre los Problemas de Optimización Combinatoria y los algoritmos de optimización

    Innovative hybrid MOEA/AD variants for solving multi-objective combinatorial optimization problems

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    Orientador : Aurora Trinidad Ramirez PozoCoorientador : Roberto SantanaTese (doutorado) - Universidade Federal do Paraná, Setor de Ciências Exatas, Programa de Pós-Graduação em Informática. Defesa: Curitiba, 16/12/2016Inclui referências : f. 103-116Resumo: Muitos problemas do mundo real podem ser representados como um problema de otimização combinatória. Muitas vezes, estes problemas são caracterizados pelo grande número de variáveis e pela presença de múltiplos objetivos a serem otimizados ao mesmo tempo. Muitas vezes estes problemas são difíceis de serem resolvidos de forma ótima. Suas resoluções tem sido considerada um desafio nas últimas décadas. Os algoritimos metaheurísticos visam encontrar uma aproximação aceitável do ótimo em um tempo computacional razoável. Os algoritmos metaheurísticos continuam sendo um foco de pesquisa científica, recebendo uma atenção crescente pela comunidade. Uma das têndencias neste cenário é a arbordagem híbrida, na qual diferentes métodos e conceitos são combinados objetivando propor metaheurísticas mais eficientes. Nesta tese, nós propomos algoritmos metaheurísticos híbridos para a solução de problemas combinatoriais multiobjetivo. Os principais ingredientes das nossas propostas são: (i) o algoritmo evolutivo multiobjetivo baseado em decomposição (MOEA/D framework), (ii) a otimização por colônias de formigas e (iii) e os algoritmos de estimação de distribuição. Em nossos frameworks, além dos operadores genéticos tradicionais, podemos instanciar diferentes modelos como mecanismo de reprodução dos algoritmos. Além disso, nós introduzimos alguns componentes nos frameworks objetivando balancear a convergência e a diversidade durante a busca. Nossos esforços foram direcionados para a resolução de problemas considerados difíceis na literatura. São eles: a programação quadrática binária sem restrições multiobjetivo, o problema de programação flow-shop permutacional multiobjetivo, e também os problemas caracterizados como deceptivos. Por meio de estudos experimentais, mostramos que as abordagens propostas são capazes de superar os resultados do estado-da-arte em grande parte dos casos considerados. Mostramos que as diretrizes do MOEA/D hibridizadas com outras metaheurísticas é uma estratégia promissora para a solução de problemas combinatoriais multiobjetivo. Palavras-chave: metaheuristicas, otimização multiobjetivo, problemas combinatoriais, MOEA/D, otimização por colônia de formigas, algoritmos de estimação de distribuição, programação quadrática binária sem restrições multiobjetivo, problema de programação flow-shop permutacional multiobjetivo, abordagens híbridas.Abstract: Several real-world problems can be stated as a combinatorial optimization problem. Very often, they are characterized by the large number of variables and the presence of multiple conflicting objectives to be optimized at the same time. These kind of problems are, usually, hard to be solved optimally, and their solutions have been considered a challenge for a long time. Metaheuristic algorithms aim at finding an acceptable approximation to the optimal solution in a reasonable computational time. The research on metaheuristics remains an attractive area and receives growing attention. One of the trends in this scenario are the hybrid approaches, in which different methods and concepts are combined aiming to propose more efficient approaches. In this thesis, we have proposed hybrid metaheuristic algorithms for solving multi-objective combinatorial optimization problems. Our proposals are based on (i) the multi-objective evolutionary algorithm based on decomposition (MOEA/D framework), (ii) the bio-inspired metaheuristic ant colony optimization, and (iii) the probabilistic models from the estimation of distribution algorithms. Our algorithms are considered MOEA/D variants. In our MOEA/D variants, besides the traditional genetic operators, we can instantiate different models as the variation step (reproduction). Moreover, we include some design modifications into the frameworks to control the convergence and the diversity during their search (evolution). We have addressed some important problems from the literature, e.g., the multi-objective unconstrained binary quadratic programming, the multiobjective permutation flowshop scheduling problem, and the problems characterized by deception. As a result, we show that our proposed frameworks are able to solve these problems efficiently by outperforming the state-of-the-art approaches in most of the cases considered. We show that the MOEA/D guidelines hybridized to other metaheuristic components and concepts is a powerful strategy for solving multi-objective combinatorial optimization problems. Keywords: meta-heuristics, multi-objective optimization, combinatorial problems, MOEA/D, ant colony optimization, estimation of distribution algorithms, unconstrained binary quadratic programming, permutation flowshop scheduling problem, hybrid approaches

    Approaching the Rank Aggregation Problem by Local Search-based Metaheuristics

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    Encouraged by the success of applying metaheuristics algorithms to other ranking-based problems (Kemeny ranking problem and pa rameter estimation for Mallows distributions), in this paper we deal with the rank aggregation problem (RAP), which can be viewed as a generalization of the Kemeny problem to arbitrary rankings. While in the Kemeny problem the input is a set of permutations, the RAP con sists in obtaining the consensus permutation for a sample of arbitrary rankings.This is an NP-hard problem which can be approached by using greedy heuristic algorithms (e.g. Borda). Such algorithms are fast but the solutions so obtained are far to be optimal. In this paper we propose the use of more complex search processes to deal with the RAP. In particular, we perform a comparative study among some local-based search metaheuristics: hill climbing (HC), iterated local search (ILS), variable neighborhood search (VNS) and greedy ran domized adaptive search procedure (GRASP). We provide a complete analysis of the experimental study regard ing accuracy and number of iterations required to reach the best solu tion. From the results we can conclude that the selection of a suitable neighborhood plays a key role, and that depending on the available re sources (cpu time) a different algorithm (VNS, ILS or GRASP) could be the proper choice
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