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

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

Accelerating coordination in temporal networks by engineering the link order

Social dynamics on a network may be accelerated or decelerated depending on which pairs of individuals in the network communicate early and which pairs do later. The order with which the links in a given network are sequentially used, which we call the link order, may be a strong determinant of dynamical behaviour on networks, potentially adding a new dimension to effects of temporal networks relative to static networks. Here we study the effect of the link order on linear coordination (i.e., synchronisation) dynamics. We show that the coordination speed considerably depends on specific orders of links. In addition, applying each single link for a long time to ensure strong pairwise coordination before moving to a next pair of individuals does not often enhance coordination of the entire network. We also implement a simple greedy algorithm to optimise the link order in favour of fast coordination.Comment: 5 figure

An estimation of distribution algorithm for combinatorial optimization problems

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

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

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

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

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