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.

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.

Hyperspectral unmixing based on mixtures of Dirichlet components

This paper introduces a new unsupervised hyperspectral unmixing method conceived to linear but highly mixed hyperspectral data sets, in which the simplex of minimum volume, usually estimated by the purely geometrically based algorithms, is far way from the true simplex associated with the endmembers. The proposed method, an extension of our previous studies, resorts to the statistical framework. The abundance fraction prior is a mixture of Dirichlet densities, thus automatically enforcing the constraints on the abundance fractions imposed by the acquisition process, namely, nonnegativity and sum-to-one. A cyclic minimization algorithm is developed where the following are observed: 1) The number of Dirichlet modes is inferred based on the minimum description length principle; 2) a generalized expectation maximization algorithm is derived to infer the model parameters; and 3) a sequence of augmented Lagrangian-based optimizations is used to compute the signatures of the endmembers. Experiments on simulated and real data are presented to show the effectiveness of the proposed algorithm in unmixing problems beyond the reach of the geometrically based state-of-the-art competitors.

Sensing Cloud Optimization applied to a non-convex constrained economical dispatch

Conferência: 39th Annual Conference of the IEEE Industrial-Electronics-Society (IECON) - NOV 10-14, 2013

Unit Commitment in a Competitive and Emission Constrained Environment

This paper is on the unit commitment problem, considering not only the economic perspective, but also the environmental perspective. We propose a bi-objective approach to handle the problem with conflicting profit and emission objectives. Numerical results based on the standard IEEE 30-bus test system illustrate the proficiency of the proposed approach.

Sensing Cloud Optimization to Solve ED of Units with Valve-Point Effects and Multi-fuels

In this paper a solution to an highly constrained and non-convex economical dispatch (ED) problem with a meta-heuristic technique named Sensing Cloud Optimization (SCO) is presented. The proposed meta-heuristic is based on a cloud of particles whose central point represents the objective function value and the remaining particles act as sensors "to fill" the search space and "guide" the central particle so it moves into the best direction. To demonstrate its performance, a case study with multi-fuel units and valve- point effects is presented.

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.

CP properties of symmetry-constrained two-Higgs-doublet models

The two-Higgs-doublet model can be constrained by imposing Higgs-family symmetries and/or generalized CP symmetries. It is known that there are only six independent classes of such symmetry-constrained models. We study the CP properties of all cases in the bilinear formalism. An exact symmetry implies CP conservation. We show that soft breaking of the symmetry can lead to spontaneous CP violation (CPV) in three of the classes.

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.

Nonlinear optimization method for short-term hydro scheduling considering head-dependency

This paper is on the problem of short-term hydro scheduling, particularly concerning head-dependent reservoirs under competitive environment. We propose a new nonlinear optimization method to consider hydroelectric power generation as a function of water discharge and also of the head. Head-dependency is considered on short-term hydro scheduling in order to obtain more realistic and feasible results. The proposed method has been applied successfully to solve a case study based on one of the main Portuguese cascaded hydro systems, providing a higher profit at a negligible additional computation time in comparison with a linear optimization method that ignores head-dependency.

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.

From efficiency to optimality in proportional reinsurance under group correlation

Based on our recent discovery of closed form formulae of efficient Mean Variance retentions in variable quota-share proportional reinsurance under group correlation, we analyzed the influence of different combination of correlation and safety loading levels on the efficient frontier, both in a single period stylized problem and in a multiperiod one.

A risk-averse optimization model for trading wind energy in a market environment under uncertainty

In this paper, a stochastic programming approach is proposed for trading wind energy in a market environment under uncertainty. Uncertainty in the energy market prices is the main cause of high volatility of profits achieved by power producers. The volatile and intermittent nature of wind energy represents another source of uncertainty. Hence, each uncertain parameter is modeled by scenarios, where each scenario represents a plausible realization of the uncertain parameters with an associated occurrence probability. Also, an appropriate risk measurement is considered. The proposed approach is applied on a realistic case study, based on a wind farm in Portugal. Finally, conclusions are duly drawn. (C) 2011 Elsevier Ltd. All rights reserved.

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.

Synthesis of optimization of [11C] Pittsburgh compound B by the captive solvent method

Mestrado em Medicina Nuclear.