GLODS: Global and Local Optimization using Direct Search

Locating and identifying points as global minimizers is, in general, a hard and time-consuming task. Difficulties increase in the impossibility of using the derivatives of the functions defining the problem. In this work, we propose a new class of methods suited for global derivative-free constrained optimization. Using direct search of directional type, the algorithm alternates between a search step, where potentially good regions are located, and a poll step where the previously located promising regions are explored. This exploitation is made through the launching of several instances of directional direct searches, one in each of the regions of interest. Differently from a simple multistart strategy, direct searches will merge when sufficiently close. The goal is to end with as many direct searches as the number of local minimizers, which would easily allow locating the global extreme value. We describe the algorithmic structure considered, present the corresponding convergence analysis and report numerical results, showing that the proposed method is competitive with currently commonly used global derivative-free optimization solvers.

Optimal design of piezolaminated structures using B-spline strip finite element models

A package of B-spline finite strip models is developed for the linear analysis of piezolaminated plates and shells. This package is associated to a global optimization technique in order to enhance the performance of these types of structures, subjected to various types of objective functions and/or constraints, with discrete and continuous design variables. The models considered are based on a higher-order displacement field and one can apply them to the static, free vibration and buckling analyses of laminated adaptive structures with arbitrary lay-ups, loading and boundary conditions. Genetic algorithms, with either binary or floating point encoding of design variables, were considered to find optimal locations of piezoelectric actuators as well as to determine the best voltages applied to them in order to obtain a desired structure shape. These models provide an overall economy of computing effort for static and vibration problems.

Optimização da lista de células vizinhas em redes LTE

Trabalho Final de Mestrado para obtenção do grau de Mestre em Engenharia de Electrónica e Telecomunicações

Otimização de placas compósitas laminadas utilizando redes neuronais e enxames de partículas

Trabalho Final de mestrado para obtenção do grau de Mestre em engenharia Mecância

Node adaptation for global collocation with radial basis functions using direct multisearch for multiobjective optimization

Meshless methods are used for their capability of producing excellent solutions without requiring a mesh, avoiding mesh related problems encountered in other numerical methods, such as finite elements. However, node placement is still an open question, specially in strong form collocation meshless methods. The number of used nodes can have a big influence on matrix size and therefore produce ill-conditioned matrices. In order to optimize node position and number, a direct multisearch technique for multiobjective optimization is used to optimize node distribution in the global collocation method using radial basis functions. The optimization method is applied to the bending of isotropic simply supported plates. Using as a starting condition a uniformly distributed grid, results show that the method is capable of reducing the number of nodes in the grid without compromising the accuracy of the solution. (C) 2013 Elsevier Ltd. All rights reserved.

Surgical correction of scoliosis: Numerical analysis and optimization of the procedure

A previously developed model is used to numerically simulate real clinical cases of the surgical correction of scoliosis. This model consists of one-dimensional finite elements with spatial deformation in which (i) the column is represented by its axis; (ii) the vertebrae are assumed to be rigid; and (iii) the deformability of the column is concentrated in springs that connect the successive rigid elements. The metallic rods used for the surgical correction are modeled by beam elements with linear elastic behavior. To obtain the forces at the connections between the metallic rods and the vertebrae geometrically, non-linear finite element analyses are performed. The tightening sequence determines the magnitude of the forces applied to the patient column, and it is desirable to keep those forces as small as possible. In this study, a Genetic Algorithm optimization is applied to this model in order to determine the sequence that minimizes the corrective forces applied during the surgery. This amounts to find the optimal permutation of integers 1, ... , n, n being the number of vertebrae involved. As such, we are faced with a combinatorial optimization problem isomorph to the Traveling Salesman Problem. The fitness evaluation requires one computing intensive Finite Element Analysis per candidate solution and, thus, a parallel implementation of the Genetic Algorithm is developed.

GA topology optimization using random keys for tree encoding of structures

Topology optimization consists in finding the spatial distribution of a given total volume of material for the resulting structure to have some optimal property, for instance, maximization of structural stiffness or maximization of the fundamental eigenfrequency. In this paper a Genetic Algorithm (GA) employing a representation method based on trees is developed to generate initial feasible individuals that remain feasible upon crossover and mutation and as such do not require any repairing operator to ensure feasibility. Several application examples are studied involving the topology optimization of structures where the objective functions is the maximization of the stiffness and the maximization of the first and the second eigenfrequencies of a plate, all cases having a prescribed material volume constraint.

Direct multisearch for multiobjective optimization

In practical applications of optimization it is common to have several conflicting objective functions to optimize. Frequently, these functions are subject to noise or can be of black-box type, preventing the use of derivative-based techniques. We propose a novel multiobjective derivative-free methodology, calling it direct multisearch (DMS), which does not aggregate any of the objective functions. Our framework is inspired by the search/poll paradigm of direct-search methods of directional type and uses the concept of Pareto dominance to maintain a list of nondominated points (from which the new iterates or poll centers are chosen). The aim of our method is to generate as many points in the Pareto front as possible from the polling procedure itself, while keeping the whole framework general enough to accommodate other disseminating strategies, in particular, when using the (here also) optional search step. DMS generalizes to multiobjective optimization (MOO) all direct-search methods of directional type. We prove under the common assumptions used in direct search for single objective optimization that at least one limit point of the sequence of iterates generated by DMS lies in (a stationary form of) the Pareto front. However, extensive computational experience has shown that our methodology has an impressive capability of generating the whole Pareto front, even without using a search step. Two by-products of this paper are (i) the development of a collection of test problems for MOO and (ii) the extension of performance and data profiles to MOO, allowing a comparison of several solvers on a large set of test problems, in terms of their efficiency and robustness to determine Pareto fronts.

Enabling Global Experiments With Interactive Reconfiguration And Steering By Multiple Users

In global scientific experiments with collaborative scenarios involving multinational teams there are big challenges related to data access, namely data movements are precluded to other regions or Clouds due to the constraints on latency costs, data privacy and data ownership. Furthermore, each site is processing local data sets using specialized algorithms and producing intermediate results that are helpful as inputs to applications running on remote sites. This paper shows how to model such collaborative scenarios as a scientific workflow implemented with AWARD (Autonomic Workflow Activities Reconfigurable and Dynamic), a decentralized framework offering a feasible solution to run the workflow activities on distributed data centers in different regions without the need of large data movements. The AWARD workflow activities are independently monitored and dynamically reconfigured and steering by different users, namely by hot-swapping the algorithms to enhance the computation results or by changing the workflow structure to support feedback dependencies where an activity receives feedback output from a successor activity. A real implementation of one practical scenario and its execution on multiple data centers of the Amazon Cloud is presented including experimental results with steering by multiple users.

Neighbour list optimization for real LTE radio network

With the increasing complexity of current networks, it became evident the need for Self-Organizing Networks (SON), which aims to automate most of the associated radio planning and optimization tasks. Within SON, this paper aims to optimize the Neighbour Cell List (NCL) for Long Term Evolution (LTE) evolved NodeBs (eNBs). An algorithm composed by three decisions were were developed: distance-based, Radio Frequency (RF) measurement-based and Handover (HO) stats-based. The distance-based decision, proposes a new NCL taking account the eNB location and interference tiers, based in the quadrants method. The last two algorithms consider signal strength measurements and HO statistics, respectively; they also define a ranking to each eNB and neighbour relation addition/removal based on user defined constraints. The algorithms were developed and implemented over an already existent radio network optimization professional tool. Several case studies were produced using real data from a Portuguese LTE mobile operator. © 2014 IEEE.

Optimal location of supports in beam structures using genetic algorithms

Real structures can be thought as an assembly of components, as for instances plates, shells and beams. This later type of component is very commonly found in structures like frames which can involve a significant degree of complexity or as a reinforcement element of plates or shells. To obtain the desired mechanical behavior of these components or to improve their operating conditions when rehabilitating structures, one of the eventual parameters to consider for that purpose, when possible, is the location of the supports. In the present work, a beam-type structure is considered, and for a set of cases concerning different number and types of supports, as well as different load cases, the authors optimize the location of the supports in order to obtain minimum values of the maximum transverse deflection. The optimization processes are carried out using genetic algorithms. The results obtained, clearly show a good performance of the approach proposed. © 2014 IEEE.

Materials selection for a set of multiple parts considering manufacturing costs and weight reduction with structural isoperformance using direct multisearch optimization

Materials selection is a matter of great importance to engineering design and software tools are valuable to inform decisions in the early stages of product development. However, when a set of alternative materials is available for the different parts a product is made of, the question of what optimal material mix to choose for a group of parts is not trivial. The engineer/designer therefore goes about this in a part-by-part procedure. Optimizing each part per se can lead to a global sub-optimal solution from the product point of view. An optimization procedure to deal with products with multiple parts, each with discrete design variables, and able to determine the optimal solution assuming different objectives is therefore needed. To solve this multiobjective optimization problem, a new routine based on Direct MultiSearch (DMS) algorithm is created. Results from the Pareto front can help the designer to align his/hers materials selection for a complete set of materials with product attribute objectives, depending on the relative importance of each objective.

Multiobjective optimization of cold-formed steel columns

The optimal design of cold-formed steel columns is addressed in this paper, with two objectives: maximize the local-global buckling strength and maximize the distortional buckling strength. The design variables of the problem are the angles of orientation of cross-section wall elements the thickness and width of the steel sheet that forms the cross-section are fixed. The elastic local, distortional and global buckling loads are determined using Finite Strip Method (CUFSM) and the strength of cold-formed steel columns (with given length) is calculated using the Direct Strength Method (DSM). The bi-objective optimization problem is solved using the Direct MultiSearch (DMS) method, which does not use any derivatives of the objective functions. Trade-off Pareto optimal fronts are obtained separately for symmetric and anti-symmetric cross-section shapes. The results are analyzed and further discussed, and some interesting conclusions about the individual strengths (local-global and distortional) are found.

Multiobjective optimization of viscoelastic laminated sandwich structures using the Direct MultiSearch method

A multiobjective approach for optimization of passive damping for vibration reduction in sandwich structures is presented in this paper. Constrained optimization is conducted for maximization of modal loss factors and minimization of weight of sandwich beams and plates with elastic laminated constraining layers and a viscoelastic core, with layer thickness and material and laminate layer ply orientation angles as design variables. The problem is solved using the Direct MultiSearch (DMS) solver for derivative-free multiobjective optimization and solutions are compared with alternative ones obtained using genetic algorithms.

Development of fire-resistant (B1 & B2) winter 1 KPU foams applied by gun or straw adapter and optimization of a gun applied winter 1 KPU foam

A realização do presente trabalho teve como principais objectivos o desenvolvimento de espumas de poliuretano de um componente com propriedades de resistência à chama superiores (B1 & B2), aplicadas por pistola ou por adaptador/tubo e a optimização de uma espuma de poliuretano de um componente de inverno aplicada por pistola. Todo o trabalho desenvolvido está dividido em dois projectos distintos: i. O primeiro projecto consistiu em desenvolver espumas de um componente com propriedades de resistência à chama (classificadas como B1 e B2 de acordo com a norma alemã DIN 4102), aplicadas por pistola (GWB1 e GWB2) ou por adaptador/tubo (AWB), utilizando polióis poliésteres aromáticos modificados e aditivos retardantes de chama halogenados. Estas espumas deveriam apresentar também propriedades aceitáveis a baixas temperaturas. Após realizar várias formulações foi possível desenvolver uma espuma AWB2 com apenas 3,3% de poliol poliéster no pré-polímero e com propriedades equivalentes às da melhor espuma comercial mesmo a 5/-10 (temperatura da lata/cura da espuma em °C) e também com uma altura de chama de apenas 11 cm. A partir de duas formulações (AWB2) que passaram o Teste B2, foram obtidas também, uma espuma GWB2 e outra GWB1 com propriedades equivalentes às da melhor espuma da concorrência a -10/-10 e a 23/5, respectivamente, embora não tenham sido submetidas ao teste B2 e B1 após as modificações efectuadas. ii. O segundo projecto consistiu em optimizar uma espuma de poliuretano de um componente de inverno aplicada por pistola (GWB3). A espuma inicial tinha problemas de glass bubbles quando esta era dispensada a partir de uma lata cheia, sendo necessário ultrapassar este problema. Este problema foi resolvido diminuindo a razão de GPL/DME através do aumento da percentagem em volume de DME no pré-polímero para 14% no entanto, a estabilidade dimensional piorou um pouco. O reagente FCA 400 foi removido da formulação anterior (6925) numa tentativa de diminuir o custo da espuma, obtendo-se uma espuma aceitável a 23/23 e a 5/5, com uma redução de 4% no custo da produção e com uma redução de 5,5% no custo por litro de espuma dispensada, quando comparada com a sua antecessora. Por último, foi avaliada a influência da concentração de diferentes surfactantes na formulação 6925, verificando-se o melhoramento da estrutura celular da espuma para concentrções mais elevadas de surfactante, sendo este efeito mais notório a temperaturas mais baixas (5/5). Dos surfactantes estudados, o B 8871 mostrou o melhor desempenho a 5/5 com a concentração mais baixa, sendo portanto o melhor surfactante, enquanto o Struksilon 8003 demonstrou ser o menos adequado para esta formulação específica, apresentando piores resultados globais. Pode-se ainda acrescentar que os surfactantes L-5351, L-5352 e B 8526 também não são adequados para esta formulação uma vez que as espumas resultantes apresentam cell collapse, especialmente a 5/5. No caso dos surfactantes L-5351 e L-5352, esta propriedade piora com concentrações mais elevadas. Em cada projecto foram também efectuados testes de benchmark em determinadas espumas comerciais com o principal objectivo de comparar todos os resultados das espumas desenvolvidas, em ambos os projectos, com espumas da concorrência.