SOP: Parallel surrogate global optimization with Pareto center selection for computationally expensive single objective problems

This paper presents a parallel surrogate-based global optimization method for computationally expensive objective functions that is more effective for larger numbers of processors. To reach this goal, we integrated concepts from multi-objective optimization and tabu search into, single objective, surrogate optimization. Our proposed derivative-free algorithm, called SOP, uses non-dominated sorting of points for which the expensive function has been previously evaluated. The two objectives are the expensive function value of the point and the minimum distance of the point to previously evaluated points. Based on the results of non-dominated sorting, P points from the sorted fronts are selected as centers from which many candidate points are generated by random perturbations. Based on surrogate approximation, the best candidate point is subsequently selected for expensive evaluation for each of the P centers, with simultaneous computation on P processors. Centers that previously did not generate good solutions are tabu with a given tenure. We show almost sure convergence of this algorithm under some conditions. The performance of SOP is compared with two RBF based methods. The test results show that SOP is an efficient method that can reduce time required to find a good near optimal solution. In a number of cases the efficiency of SOP is so good that SOP with 8 processors found an accurate answer in less wall-clock time than the other algorithms did with 32 processors.

Interval-based ranking in noisy evolutionary multiobjective optimization

As one of the most competitive approaches to multi-objective optimization, evolutionary algorithms have been shown to obtain very good results for many realworld multi-objective problems. One of the issues that can affect the performance of these algorithms is the uncertainty in the quality of the solutions which is usually represented with the noise in the objective values. Therefore, handling noisy objectives in evolutionary multi-objective optimization algorithms becomes very important and is gaining more attention in recent years. In this paper we present ?-degree Pareto dominance relation for ordering the solutions in multi-objective optimization when the values of the objective functions are given as intervals. Based on this dominance relation, we propose an adaptation of the non-dominated sorting algorithm for ranking the solutions. This ranking method is then used in a standardmulti-objective evolutionary algorithm and a recently proposed novel multi-objective estimation of distribution algorithm based on joint variable-objective probabilistic modeling, and applied to a set of multi-objective problems with different levels of independent noise. The experimental results show that the use of the proposed method for solution ranking allows to approximate Pareto sets which are considerably better than those obtained when using the dominance probability-based ranking method, which is one of the main methods for noise handling in multi-objective optimization.

Avaliação de incertezas na calibração automática do modelo SWMM

Este trabalho é referente ao desenvolvimento de um calibrador multiobjetivo automático do modelo SWMM (Storm Water Management Model), e avaliação de algumas fontes de incertezas presentes no processo de calibração, visando à representação satisfatória da transformação chuva-vazão. O código foi escrito em linguagem C, e aplica os conceitos do método de otimização multiobjetivo NSGAII (Non Dominated Sorting Genetic Algorithm) com elitismo controlado, além de utilizar o código fonte do modelo SWMM para a determinação das vazões simuladas. Paralelamente, também foi criada uma interface visual, para melhorar a facilidade de utilização do calibrador. Os testes do calibrador foram aplicados a três sistemas diferentes: um sistema hipotético disponibilizado no pacote de instalação do SWMM; um sistema real de pequenas dimensões, denominado La Terraza, localizado no município de Sierra Vista, Arizona (EUA); e um sistema de maiores dimensões, a bacia hidrográfica do Córrego do Gregório, localizada no município de São Carlos (SP). Os resultados indicam que o calibrador construído apresenta, em geral, eficiência satisfatória, porém é bastante dependente da qualidade dos dados observados em campo e dos parâmetros de entrada escolhidos pelo usuário. Foi demonstrada a importância da escolha dos eventos utilizados na calibração, do estabelecimento de limites adequados nos valores das variáveis de decisão, da escolha das funções objetivo e, principalmente, da qualidade e representatividade dos dados de monitoramento pluvio e fluviométrico. Conclui-se que estes testes desenvolvidos contribuem para o entendimento mais aprofundado dos processos envolvidos na modelagem e calibração, possibilitando avanços na confiabilidade dos resultados da modelagem.

Planejamento de sistemas de distribuição de energia elétrica considerando questões de confiabilidade e risco

O problema de Planejamento da Expansão de Sistemas de Distribuição (PESD) visa determinar diretrizes para a expansão da rede considerando a crescente demanda dos consumidores. Nesse contexto, as empresas distribuidoras de energia elétrica têm o papel de propor ações no sistema de distribuição com o intuito de adequar o fornecimento da energia aos padrões exigidos pelos órgãos reguladores. Tradicionalmente considera-se apenas a minimização do custo global de investimento de planos de expansão, negligenciando-se questões de confiabilidade e robustez do sistema. Como consequência, os planos de expansão obtidos levam o sistema de distribuição a configurações que são vulneráveis a elevados cortes de carga na ocorrência de contingências na rede. Este trabalho busca a elaboração de uma metodologia para inserir questões de confiabilidade e risco ao problema PESD tradicional, com o intuito de escolher planos de expansão que maximizem a robustez da rede e, consequentemente, atenuar os danos causados pelas contingências no sistema. Formulou-se um modelo multiobjetivo do problema PESD em que se minimizam dois objetivos: o custo global (que incorpora custo de investimento, custo de manutenção, custo de operação e custo de produção de energia) e o risco de implantação de planos de expansão. Para ambos os objetivos, são formulados modelos lineares inteiros mistos que são resolvidos utilizando o solver CPLEX através do software GAMS. Para administrar a busca por soluções ótimas, optou-se por programar em linguagem C++ dois Algoritmos Evolutivos: Non-dominated Sorting Genetic Algorithm-2 (NSGA2) e Strength Pareto Evolutionary Algorithm-2 (SPEA2). Esses algoritmos mostraram-se eficazes nessa busca, o que foi constatado através de simulações do planejamento da expansão de dois sistemas testes adaptados da literatura. O conjunto de soluções encontradas nas simulações contém planos de expansão com diferentes níveis de custo global e de risco de implantação, destacando a diversidade das soluções propostas. Algumas dessas topologias são ilustradas para se evidenciar suas diferenças.

Intensificação da transferência de calor e otimização de trocadores de calor compactos tipo venezianas com geradores de vórtices tipo delta-winglets.

Esta pesquisa visa a análise da contribuição de cinco variáveis de entrada e a otimização do desempenho termo-hidráulico de trocadores de calor com venezianas combinados com geradores de vórtices delta-winglets. O desempenho termohidráulico de duas geometrias distintas, aqui nomeadas por GEO1 e GEO2, foram avaliadas. Smoothing Spline ANOVA foi usado para avaliar a contribuição dos parâmetros de entrada na transferência de calor e perda de carga. Considerando aplicação automotiva, foram investigados números de Reynolds iguais a 120 e 240, baseados no diâmetro hidráulico. Os resultados indicaram que o ângulo de venezianas é o maior contribuidor para o aumento do fator de atrito para GEO1 e GEO2, para ambos os números de Reynolds. Para o número de Reynolds menor, o parâmetro mais importante em termos de transferência de calor foi o ângulo das venezianas para ambas as geometrias. Para o número de Reynolds maior, o ângulo de ataque dos geradores de vórtices posicionados na primeira fileira é o maior contribuidor para a tranfesferência de calor, no caso da geometria GEO1, enquanto que o ângulo de ataque dos geradores de vórtices na primeira fileira foi tão importante quanto os ângulos das venezianas para a geometria GEO2. Embora as geometrias analisadas possam ser consideradas como técnicas compostas de intensificação da transferência de calor, não foram observadas interações relevantes entre ângulo de venezianas e parâmetros dos geradores de vórtices. O processo de otimização usa NSGA-II (Non-Dominated Sorting Genetic Algorithm) combinado com redes neurais artificiais. Os resultados mostraram que a adição dos geradores de vórtices em GEO1 aumentaram a transferência de calor em 21% e 23% com aumentos na perda de carga iguais a 24,66% e 36,67% para o menor e maior números de Reynolds, respectivamente. Para GEO2, a transferência de calor aumentou 13% e 15% com aumento na perda de carga de 20,33% e 23,70%, para o menor e maior número de Reynolds, respectivamente. As soluções otimizadas para o fator de Colburn mostraram que a transferência de calor atrás da primeira e da segunda fileiras de geradores de vórtices tem a mesma ordem de magnitude para ambos os números de Reynolds. Os padrões de escoamento e as características de transferência de calor das soluções otimizadas apresentaram comportamentos vi particulares, diferentemente daqueles encontrados quando as duas técnicas de intensificação de transferência de calor são aplicadas separadamente.

Application of battery energy storage in the Québec interconnection

Le Système Stockage de l’Énergie par Batterie ou Batterie de Stockage d’Énergie (BSE) offre de formidables atouts dans les domaines de la production, du transport, de la distribution et de la consommation d’énergie électrique. Cette technologie est notamment considérée par plusieurs opérateurs à travers le monde entier, comme un nouveau dispositif permettant d’injecter d’importantes quantités d’énergie renouvelable d’une part et d’autre part, en tant que composante essentielle aux grands réseaux électriques. De plus, d’énormes avantages peuvent être associés au déploiement de la technologie du BSE aussi bien dans les réseaux intelligents que pour la réduction de l’émission des gaz à effet de serre, la réduction des pertes marginales, l’alimentation de certains consommateurs en source d’énergie d’urgence, l’amélioration de la gestion de l’énergie, et l’accroissement de l’efficacité énergétique dans les réseaux. Cette présente thèse comprend trois étapes à savoir : l’Étape 1 - est relative à l’utilisation de la BSE en guise de réduction des pertes électriques ; l’Étape 2 - utilise la BSE comme élément de réserve tournante en vue de l’atténuation de la vulnérabilité du réseau ; et l’Étape 3 - introduit une nouvelle méthode d’amélioration des oscillations de fréquence par modulation de la puissance réactive, et l’utilisation de la BSE pour satisfaire la réserve primaire de fréquence. La première Étape, relative à l’utilisation de la BSE en vue de la réduction des pertes, est elle-même subdivisée en deux sous-étapes dont la première est consacrée à l’allocation optimale et le seconde, à l’utilisation optimale. Dans la première sous-étape, l’Algorithme génétique NSGA-II (Non-dominated Sorting Genetic Algorithm II) a été programmé dans CASIR, le Super-Ordinateur de l’IREQ, en tant qu’algorithme évolutionniste multiobjectifs, permettant d’extraire un ensemble de solutions pour un dimensionnement optimal et un emplacement adéquat des multiple unités de BSE, tout en minimisant les pertes de puissance, et en considérant en même temps la capacité totale des puissances des unités de BSE installées comme des fonctions objectives. La première sous-étape donne une réponse satisfaisante à l’allocation et résout aussi la question de la programmation/scheduling dans l’interconnexion du Québec. Dans le but de réaliser l’objectif de la seconde sous-étape, un certain nombre de solutions ont été retenues et développées/implantées durant un intervalle de temps d’une année, tout en tenant compte des paramètres (heure, capacité, rendement/efficacité, facteur de puissance) associés aux cycles de charge et de décharge de la BSE, alors que la réduction des pertes marginales et l’efficacité énergétique constituent les principaux objectifs. Quant à la seconde Étape, un nouvel indice de vulnérabilité a été introduit, formalisé et étudié ; indice qui est bien adapté aux réseaux modernes équipés de BES. L’algorithme génétique NSGA-II est de nouveau exécuté (ré-exécuté) alors que la minimisation de l’indice de vulnérabilité proposé et l’efficacité énergétique représentent les principaux objectifs. Les résultats obtenus prouvent que l’utilisation de la BSE peut, dans certains cas, éviter des pannes majeures du réseau. La troisième Étape expose un nouveau concept d’ajout d’une inertie virtuelle aux réseaux électriques, par le procédé de modulation de la puissance réactive. Il a ensuite été présenté l’utilisation de la BSE en guise de réserve primaire de fréquence. Un modèle générique de BSE, associé à l’interconnexion du Québec, a enfin été proposé dans un environnement MATLAB. Les résultats de simulations confirment la possibilité de l’utilisation des puissances active et réactive du système de la BSE en vue de la régulation de fréquence.

Multi-objective ant colony optimization for requirements selection

The selection of a set of requirements between all the requirements previously defined by customers is an important process, repeated at the beginning of each development step when an incremental or agile software development approach is adopted. The set of selected requirements will be developed during the actual iteration. This selection problem can be reformulated as a search problem, allowing its treatment with metaheuristic optimization techniques. This paper studies how to apply Ant Colony Optimization algorithms to select requirements. First, we describe this problem formally extending an earlier version of the problem, and introduce a method based on Ant Colony System to find a variety of efficient solutions. The performance achieved by the Ant Colony System is compared with that of Greedy Randomized Adaptive Search Procedure and Non-dominated Sorting Genetic Algorithm, by means of computational experiments carried out on two instances of the problem constructed from data provided by the experts.

Bit-index sort: a fast non-comparison integer sorting algorithm for permutations

This paper describes a fast integer sorting algorithm, herein referred as Bit-index sort, which is a non-comparison sorting algorithm for partial per-mutations, with linear complexity order in execution time. Bit-index sort uses a bit-array to classify input sequences of distinct integers, and exploits built-in bit functions in C compilers supported by machine hardware to retrieve the ordered output sequence. Results show that Bit-index sort outperforms in execution time to quicksort and counting sort algorithms. A parallel approach for Bit-index sort using two simultaneous threads is included, which obtains speedups up to 1.6.

Automated synthesis procedure of RF discrete tuning differential capacitance circuits

The paper presents a RFDSCA automated synthesis procedure. This algorithm determines several RFDSCA circuits from the top-level system specifications all with the same maximum performance. The genetic synthesis tool optimizes a fitness function proportional to the RFDSCA quality factor and uses the epsiv-concept and maximin sorting scheme to achieve a set of solutions well distributed along a non-dominated front. To confirm the results of the algorithm, three RFDSCAs were simulated in SpectreRF and one of them was implemented and tested. The design used a 0.25 mum BiCMOS process. All the results (synthesized, simulated and measured) are very close, which indicate that the genetic synthesis method is a very useful tool to design optimum performance RFDSCAs.

Automated Synthesis Procedure of RF Discrete Tuning Differential Capacitance Circuits

The paper presents a RFDSCA automated synthesis procedure. This algorithm determines several RFDSCA circuits from the top-level system specifications all with the same maximum performance. The genetic synthesis tool optimizes a fitness function proportional to the RFDSCA quality factor and uses the epsiv-concept and maximin sorting scheme to achieve a set of solutions well distributed along a non-dominated front. To confirm the results of the algorithm, three RFDSCAs were simulated in SpectreRF and one of them was implemented and tested. The design used a 0.25 mum BiCMOS process. All the results (synthesized, simulated and measured) are very close, which indicate that the genetic synthesis method is a very useful tool to design optimum performance RFDSCAs.

Combining non-dominance, objective-order and spread metric to extend firefly algorithm to multi-objective optimization

In this paper, we propose an extension of the firefly algorithm (FA) to multi-objective optimization. FA is a swarm intelligence optimization algorithm inspired by the flashing behavior of fireflies at night that is capable of computing global solutions to continuous optimization problems. Our proposal relies on a fitness assignment scheme that gives lower fitness values to the positions of fireflies that correspond to non-dominated points with smaller aggregation of objective function distances to the minimum values. Furthermore, FA randomness is based on the spread metric to reduce the gaps between consecutive non-dominated solutions. The obtained results from the preliminary computational experiments show that our proposal gives a dense and well distributed approximated Pareto front with a large number of points.

Identifying Individual and Group Effects in the Presence of Sorting: A Neighborhood Effects Application

Researchers have long recognized that the non-random sorting of individuals into groups generates correlation between individual and group attributes that is likely to bias naive estimates of both individual and group effects. This paper proposes a non-parametric strategy for identifying these effects in a model that allows for both individual and group unobservables, applying this strategy to the estimation of neighborhood effects on labor market outcomes. The first part of this strategy is guided by a robust feature of the equilibrium in the canonical vertical sorting model of Epple and Platt (1998), that there is a monotonic relationship between neighborhood housing prices and neighborhood quality. This implies that under certain conditions a non- parametric function of neighborhood housing prices serves as a suitable control function for the neighborhood unobservable in the labor market outcome regression. The second part of the proposed strategy uses aggregation to develop suitable instruments for both exogenous and endogenous group attributes. Instrumenting for each individual's observed neighborhood attributes with the average neighborhood attributes of a set of observationally identical individuals eliminates the portion of the variation in neighborhood attributes due to sorting on unobserved individual attributes. The neighborhood effects application is based on confidential microdata from the 1990 Decennial Census for the Boston MSA. The results imply that the direct effects of geographic proximity to jobs, neighborhood poverty rates, and average neighborhood education are substantially larger than the conditional correlations identified using OLS, although the net effect of neighborhood quality on labor market outcomes remains small. These findings are robust across a wide variety of specifications and robustness checks.

Entropy diversity in multi-objective particle swarm optimization

Multi-objective particle swarm optimization (MOPSO) is a search algorithm based on social behavior. Most of the existing multi-objective particle swarm optimization schemes are based on Pareto optimality and aim to obtain a representative non-dominated Pareto front for a given problem. Several approaches have been proposed to study the convergence and performance of the algorithm, particularly by accessing the final results. In the present paper, a different approach is proposed, by using Shannon entropy to analyzethe MOPSO dynamics along the algorithm execution. The results indicate that Shannon entropy can be used as an indicator of diversity and convergence for MOPSO problems.

Multi-criteria optimization manipulator trajectory planning

In the last twenty years genetic algorithms (GAs) were applied in a plethora of fields such as: control, system identification, robotics, planning and scheduling, image processing, and pattern and speech recognition (Bäck et al., 1997). In robotics the problems of trajectory planning, collision avoidance and manipulator structure design considering a single criteria has been solved using several techniques (Alander, 2003). Most engineering applications require the optimization of several criteria simultaneously. Often the problems are complex, include discrete and continuous variables and there is no prior knowledge about the search space. These kind of problems are very more complex, since they consider multiple design criteria simultaneously within the optimization procedure. This is known as a multi-criteria (or multiobjective) optimization, that has been addressed successfully through GAs (Deb, 2001). The overall aim of multi-criteria evolutionary algorithms is to achieve a set of non-dominated optimal solutions known as Pareto front. At the end of the optimization procedure, instead of a single optimal (or near optimal) solution, the decision maker can select a solution from the Pareto front. Some of the key issues in multi-criteria GAs are: i) the number of objectives, ii) to obtain a Pareto front as wide as possible and iii) to achieve a Pareto front uniformly spread. Indeed, multi-objective techniques using GAs have been increasing in relevance as a research area. In 1989, Goldberg suggested the use of a GA to solve multi-objective problems and since then other researchers have been developing new methods, such as the multi-objective genetic algorithm (MOGA) (Fonseca & Fleming, 1995), the non-dominated sorted genetic algorithm (NSGA) (Deb, 2001), and the niched Pareto genetic algorithm (NPGA) (Horn et al., 1994), among several other variants (Coello, 1998). In this work the trajectory planning problem considers: i) robots with 2 and 3 degrees of freedom (dof ), ii) the inclusion of obstacles in the workspace and iii) up to five criteria that are used to qualify the evolving trajectory, namely the: joint traveling distance, joint velocity, end effector / Cartesian distance, end effector / Cartesian velocity and energy involved. These criteria are used to minimize the joint and end effector traveled distance, trajectory ripple and energy required by the manipulator to reach at destination point. Bearing this ideas in mind, the paper addresses the planning of robot trajectories, meaning the development of an algorithm to find a continuous motion that takes the manipulator from a given starting configuration up to a desired end position without colliding with any obstacle in the workspace. The chapter is organized as follows. Section 2 describes the trajectory planning and several approaches proposed in the literature. Section 3 formulates the problem, namely the representation adopted to solve the trajectory planning and the objectives considered in the optimization. Section 4 studies the algorithm convergence. Section 5 studies a 2R manipulator (i.e., a robot with two rotational joints/links) when the optimization trajectory considers two and five objectives. Sections 6 and 7 show the results for the 3R redundant manipulator with five goals and for other complementary experiments are described, respectively. Finally, section 8 draws the main conclusions.

Manipulator trajectory planning using a MOEA

Generating manipulator trajectories considering multiple objectives and obstacle avoidance is a non-trivial optimization problem. In this paper a multi-objective genetic algorithm based technique is proposed to address this problem. Multiple criteria are optimized considering up to five simultaneous objectives. Simulation results are presented for robots with two and three degrees of freedom, considering two and five objectives optimization. A subsequent analysis of the spread and solutions distribution along the converged non-dominated Pareto front is carried out, in terms of the achieved diversity.