Restart strategies for GRASP with path-relinking heuristics

Abstract. GRASP with path-relinking is a hybrid metaheuristic, or stochastic local search (Monte Carlo) method, for combinatorial optimization. A restart strategy in GRASP with path-relinking heuristics is a set of iterations {i1, i2, . . .} on which the heuristic is restarted from scratch using a new seed for the random number generator. Restart strategies have been shown to speed up stochastic local search algorithms. In this paper, we propose a new restart strategy for GRASP with path-relinking heuristics. We illustrate the speedup obtained with our restart strategy on GRASP with path-relinking heuristics for the maximum cut problem, the maximum weighted satisfiability problem, and the private virtual circuit routing problem

An Iterative Path-Breaking Approach with Mutation and Restart Strategies for the MAX-SAT Problem

Although Path-Relinking is an effective local search method for many combinatorial optimization problems, its application is not straightforward in solving the MAX-SAT, an optimization variant of the satisfiability problem (SAT) that has many real-world applications and has gained more and more attention in academy and industry. Indeed, it was not used in any recent competitive MAX-SAT algorithms in our knowledge. In this paper, we propose a new local search algorithm called IPBMR for the MAX-SAT, that remedies the drawbacks of the Path-Relinking method by using a careful combination of three components: a new strategy named Path-Breaking to avoid unpromising regions of the search space when generating trajectories between two elite solutions; a weak and a strong mutation strategies, together with restarts, to diversify the search; and stochastic path generating steps to avoid premature local optimum solutions. We then present experimental results to show that IPBMR outperforms two of the best state-of-the-art MAX-SAT solvers, and an empirical investigation to identify and explain the effect of the three components in IPBMR

A parallel multi-population biased random-key genetic algorithm for electric distribution network reconfiguration

This work presents a multi-population biased random-key genetic algorithm (BRKGA) for the electric distribution network reconfiguration problem (DNR). DNR belongs to the class of network design problems which include transportation problems, computer network restoration and telecommunication network design and can be used for loss minimization and load balancing, being an important tool for distribution network operators. A BRKGA is a class of genetic algorithms in which solutions are encoded as vectors of random keys, i.e. randomly generated real numbers from a uniform distribution in the interval [0, 1). A vector of random keys is translated into a solution of the optimization problem by a decoder. The decoder used generates only feasible solutions by using an efficient codification based upon the fundamentals of graph theory, restricting the search space. The parallelization is based on the single program multiple data paradigm and is executed on the cores of a multi-core processor. Time to target plots, which characterize the running times of stochastic algorithms for combinatorial optimization, are used to compare the performance of the serial and parallel algorithms. The proposed method has been tested on two standard distribution systems and the results show the effectiveness and performance of the parallel algorithm

A nonmonotone GRASP

A greedy randomized adaptive search procedure (GRASP) is an itera- tive multistart metaheuristic for difficult combinatorial optimization problems. Each GRASP iteration consists of two phases: a construction phase, in which a feasible solution is produced, and a local search phase, in which a local optimum in the neighborhood of the constructed solution is sought. Repeated applications of the con- struction procedure yields different starting solutions for the local search and the best overall solution is kept as the result. The GRASP local search applies iterative improvement until a locally optimal solution is found. During this phase, starting from the current solution an improving neighbor solution is accepted and considered as the new current solution. In this paper, we propose a variant of the GRASP framework that uses a new “nonmonotone” strategy to explore the neighborhood of the current solu- tion. We formally state the convergence of the nonmonotone local search to a locally optimal solution and illustrate the effectiveness of the resulting Nonmonotone GRASP on three classical hard combinatorial optimization problems: the maximum cut prob- lem (MAX-CUT), the weighted maximum satisfiability problem (MAX-SAT), and the quadratic assignment problem (QAP)

Portfolios in Stochastic Local Search: Efficiently Computing Most Probable Explanations in Bayesian Networks

Portfolio methods support the combination of different algorithms and heuristics, including stochastic local search (SLS) heuristics, and have been identified as a promising approach to solve computationally hard problems. While successful in experiments, theoretical foundations and analytical results for portfolio-based SLS heuristics are less developed. This article aims to improve the understanding of the role of portfolios of heuristics in SLS. We emphasize the problem of computing most probable explanations (MPEs) in Bayesian networks (BNs). Algorithmically, we discuss a portfolio-based SLS algorithm for MPE computation, Stochastic Greedy Search (SGS). SGS supports the integration of different initialization operators (or initialization heuristics) and different search operators (greedy and noisy heuristics), thereby enabling new analytical and experimental results. Analytically, we introduce a novel Markov chain model tailored to portfolio-based SLS algorithms including SGS, thereby enabling us to analytically form expected hitting time results that explain empirical run time results. For a specific BN, we show the benefit of using a homogenous initialization portfolio. To further illustrate the portfolio approach, we consider novel additive search heuristics for handling determinism in the form of zero entries in conditional probability tables in BNs. Our additive approach adds rather than multiplies probabilities when computing the utility of an explanation. We motivate the additive measure by studying the dramatic impact of zero entries in conditional probability tables on the number of zero-probability explanations, which again complicates the search process. We consider the relationship between MAXSAT and MPE, and show that additive utility (or gain) is a generalization, to the probabilistic setting, of MAXSAT utility (or gain) used in the celebrated GSAT and WalkSAT algorithms and their descendants. Utilizing our Markov chain framework, we show that expected hitting time is a rational function - i.e. a ratio of two polynomials - of the probability of applying an additive search operator. Experimentally, we report on synthetically generated BNs as well as BNs from applications, and compare SGSs performance to that of Hugin, which performs BN inference by compilation to and propagation in clique trees. On synthetic networks, SGS speeds up computation by approximately two orders of magnitude compared to Hugin. In application networks, our approach is highly competitive in Bayesian networks with a high degree of determinism. In addition to showing that stochastic local search can be competitive with clique tree clustering, our empirical results provide an improved understanding of the circumstances under which portfolio-based SLS outperforms clique tree clustering and vice versa

GRASP with path-relinking for the weighted MAXSAT problem

A GRASP with path relinking for finding good-quality solutions of the weighted maximum satisfiability problem (MAX-SAT) is described in this paper. GRASP, or Greedy Randomized Adaptive Search Procedure, is a randomized multistart metaheuristic, where, at each iteration, locally optimal solutions are constructed, each independent of the others. Previous experimental results indicate its effectiveness for solving weighted MAX-SAT instances. Path relinking is a procedure used to intensify the search around good-quality isolated solutions that have been produced by the GRASP heuristic. Experimental comparison of the pure GRASP (without path relinking) and the GRASP with path relinking illustrates the effectiveness of path relinking in decreasing the average time needed to find a good-quality solution for the weighted maximum satisfiability problem

Implementación de un algoritmo genético para optimizar la distribución del agua en el riego de cultivos

En la actualidad, existen diversas razones que generan un enorme problema de escasez de agua, entre las cuales se encuentra el incremento de su uso en el riego de cultivos debido a una ineficiente distribución; siendo esta una de las más alarmantes. La gestión del agua es un aspecto importante a considerar en las diversas actividades en las que se utiliza este recurso, particularmente, en la agricultura en donde gran parte del recurso hídrico está destinado a la irrigación de cultivos y terrenos. Debido a esto se requiere un uso eficiente del agua, que reduzca pérdidas o costos de producción, con una buena distribución del recurso de modo que reduzca los problemas de drenaje y salinidad, con adecuado requerimiento de agua para los cultivos y así se obtenga una calidad apropiada en los alimentos. De la misma manera, conseguir un buen uso del recurso hídrico con la finalidad de poseer suficiente agua para el riego de cultivos de modo que se eviten problemas de producción de cultivos o vedas por falta de un adecuado manejo de agua. Además, que se manejen aspectos y factores naturales que son importantes en la actividad agrícola en cuanto a la irrigación de cultivos, minimizando el despilfarro del recurso, pérdidas de cultivos y disminución de cosechas. Este manejo de factores naturales inclusive de acuerdo a las diversas y cambiantes temporadas de producción de cultivos. El presente proyecto presenta el desarrollo de un algoritmo genético que permita optimizar la distribución del recurso hídrico en el riego de cultivos en distintas áreas o terrenos tomando en cuenta los diferentes factores que condicionan la fase de crecimiento del sembrío hasta llegar a la etapa de cosecha. Esto de manera que se busque una mejor selección para el regado de plantaciones, logrando así organizar su desarrollo y el ahorro del consumo vital como es el agua. La importancia del desarrollo de este tema recae en el buen uso y manejo del recurso hídrico así como otras condiciones naturales que son importantes también.Tesi

Extração de regras de classificação de bases de dados por meio de procedimentos meta-heurísticos baseados em GRASP

Orientadora : Prof. Dr. Maria Teresinha Arns SteinerTese (doutorado) - Universidade Federal do Paraná, Setor de Tecnologia, Programa de Pós-Graduação em Métodos Numéricos em Engenharia. Defesa: Curitiba, 28/05/2014Inclui referênciasResumo: O processo de gestão do conhecimento nas mais diversas áreas – seja em indústrias, hospitais, escolas, bancos, dentre outros – exige constante atenção à multiplicidade de decisões a serem tomadas acerca de suas atividades. Para a tomada de decisões, faz-se necessária a utilização de técnicas científicas que lhes garantam a máxima acurácia. O presente trabalho faz o uso de ferramentas matemáticas que cumpram a finalidade de extração de conhecimento de base de dados. O objetivo é a proposição de uma nova meta-heurística, baseada no procedimento GRASP (Greedy Randomized Adaptive Search Procedure) como ferramenta de Data Mining (DM), no contexto do processo denominado Knowledge Discovery in Databases (KDD) para a tarefa de extração de regras de classificação em bases de dados. Assim, a metodologia aqui proposta possui três grandes blocos segundo o processo KDD: pré-processamento dos dados, no qual todos os atributos previsores são codificados de maneira a corresponder a uma ou mais coordenadas binárias; aplicação da meta-heurística propriamente dita para extração de regras de classificação; construção do classificador, momento em que as regras extraídas são ordenadas segundo critérios baseados no "fator de suporte" e na "confiança". A fim de validar esta proposta, a metodologia foi implementada e aplicada a sete bases de dados distintas, com um número variável de instâncias, de atributos e de classes. Os resultados obtidos apresentam elevada precisão preditiva, atingindo, por exemplo, 98% de acurácia para a base de dados zoo, 97% para a base íris e 94% para a base wine. Buscando ratificar os resultados obtidos, foram estabelecidas comparações entre a meta-heurística aqui proposta e os algoritmos BFTree, RepTree e J4.8, todos de árvore de decisão. A partir destas comparações, observa-se que em seis das sete bases analisadas a proposta implementada é superior, em termos de acurácia, aos algoritmos de árvore de decisão utilizados. Desta forma, conclui-se que a meta-heurística proposta atende os pré-requisitos para a tarefa de extração de conhecimento de base de dados.Abstract: The process of knowledge management in several areas – existing in industries, hospitals, schools, banks, among others - requires constant attention to the multiplicity of decisions to be made about their activities. In order to make decisions, it is necessary to use scientific techniques that will ensure their maximum accuracy. This study makes use of mathematical tools that meet the purpose of extracting knowledge from a database. The aim is to propose a new metaheuristic based on GRASP (Greedy Randomized Adaptive Search Procedure) procedure as a tool of Data Mining (DM) within the context of the process called Knowledge Discovery in Databases (KDD) for the task of extracting classification rules in databases. Thus, the methodology proposed herein has three large blocks according to the KDD process: data pre-processing, in which all predictor attributes are encoded to correspond to one or more binary coordinates; application of the metaheuristic itself for extracting classification rules; construction of the classifier, when the extracted rules are ordered in accordance with criteria based on "support factor" and "trust." In order to validate this proposal, the methodology has been implemented and applied to seven different databases, with a variable number of instances, attributes and classes. The results show high predictive accuracy, reaching, for example, 98% accuracy in the zoo database, 97% for the iris base and 94% for the wine base. Seeking to ratify the results, comparisons between the metaheuristic proposed herein and BFTree, RepTree and J4.8 decision tree algorithms were established. Based on these comparisons, it is observed that in six out of seven analyzed bases the implemented proposal is superior, in terms of accuracy, to the used decision tree algorithms. In this way, it is concluded that the meta-heuristic proposed meets the prerequisites for the task of extracting knowledge from a database

Compromiso entre Pares e ISPs en el contexto P4P : Optimización en dos niveles.

El diseño de ruteos para redes peer-to-peer (P2P) tiene muchos desafíos. Los usuarios (llamados pares o peers) exigen alta Calidad de Experiencia en las aplicaciones que utilizan (compartir archivos, video streaming, etc.) generando un alto tráfico en la red, el cual por lo general no contempla las limitaciones de la red de Internet subyacente. Los ISPs (Internet Service Providers) mantienen su negocio ofreciendo un buen servicio para los usuarios finales tratando de utilizar de forma eficiente sus recursos (especialmente sus enlaces internacionales que son los recursos más costosos). Una estrategia reciente que considera conjuntamente los objetivos de los pares e ISPs es la llamada P4P [50] (Proactive Provider Participation). Esta estrategia coloca el máximo tráfico total en la red, reduciendo al mismo tiempo el porcentaje de la utilización del enlace internacional más congestionado. En este trabajo el problema multióbjetivo P4P es resuelto de forma aproximada mediante un algoritmo FPTAS (Fully Polynomial Time Approximation Scheme) cuando el objetivo es compartir un sólo contenido en la red. Una metaheurística basada en GRASP (Greedy Randomized Adaptive Search Procedure) es aplicada para resolver el problema general, cuando los pares comparten múltiples contenidos. Utilizando instancias generadas aleatoriamente se obtienen muy buenos resultados contrastando las soluciones obtenidas con cotas conocidas. Finalmente se muestran resultados de emulaciones en una plataforma P2P real llamada GoalBit, contrastando los resultados obtenidos con la metodología P4P versus una metodología de ruteo aleatoria. Los resultados son alentadores, justificando el uso de P4P, ya que se logra reducir la utilización de los enlaces internacionales al mismo tiempo que aumenta la transferencia de flujo neto de los usuarios