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.

Optimal design for active damping in sandwich structures using the Direct MultiSearch method

This paper addresses the problem of optimal positioning of surface bonded piezoelectric patches in sandwich plates with viscoelastic core and laminated face layers. The objective is to maximize a set of modal loss factors for a given frequency range using multiobjective topology optimization. Active damping is introduced through co-located negative velocity feedback control. The multiobjective topology optimization problem is solved using the Direct MultiSearch Method. An application to a simply supported sandwich plate is presented with results for the maximization of the first six modal loss factors. The influence of the finite element mesh is analyzed and the results are, to some extent, compared with those obtained using alternative single objective optimization. (C) 2013 Elsevier Ltd. All rights reserved.

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.

Optimal design for active damping in sandwich structures using the Direct MultiSearch method

This paper addresses the problem of optimal positioning of surface bonded piezoelectric patches in sandwich plates with viscoelastic core and laminated face layers. The objective is to maximize a set of modal loss factors for a given frequency range using multiobjective topology optimization. Active damping is introduced through co-located negative velocity feedback control. The multiobjective topology optimization problem is solved using the Direct MultiSearch Method. An application to a simply supported sandwich plate is presented with results for the maximization of the first six modal loss factors. The influence of the finite element mesh is analyzed and the results are, to some extent, compared with those obtained using alternative single objective optimization.

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 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.

Optimization of cruciform specimens for biaxial fatigue loading with direct multi search

In order to correctly assess the biaxial fatigue material properties one must experimentally test different load conditions and stress levels. With the rise of new in-plane biaxial fatigue testing machines, using smaller and more efficient electrical motors, instead of the conventional hydraulic machines, it is necessary to reduce the specimen size and to ensure that the specimen geometry is appropriate for the load capacity installed. At the present time there are no standard specimen's geometries and the indications on literature how to design an efficient test specimen are insufficient. The main goal of this paper is to present the methodology on how to obtain an optimal cruciform specimen geometry, with thickness reduction in the gauge area, appropriate for fatigue crack initiation, as a function of the base material sheet thickness used to build the specimen. The geometry is optimized for maximum stress using several parameters, ensuring that in the gauge area the stress distributions on the loading directions are uniform and maximum with two limit phase shift loading conditions (delta = 0 degrees and (delta = 180 degrees). Therefore the fatigue damage will always initiate on the center of the specimen, avoiding failure outside this region. Using the Renard Series of preferred numbers for the base material sheet thickness as a reference, the reaming geometry parameters are optimized using a derivative-free methodology, called direct multi search (DMS) method. The final optimal geometry as a function of the base material sheet thickness is proposed, as a guide line for cruciform specimens design, and as a possible contribution for a future standard on in-plane biaxial fatigue tests

Design optimization of cruciform specimens for biaxial fatigue loading

In order to correctly assess the biaxial fatigue material properties one must experimentally test different load conditions and stress levels. With the rise of new in-plane biaxial fatigue testing machines, using smaller and more efficient electrical motors, instead of the conventional hydraulic machines, it is necessary to reduce the specimen size and to ensure that the specimen geometry is appropriated for the load capacity installed. At the present time there are no standard specimen’s geometries and the indications on literature how to design an efficient test specimen are insufficient. The main goal of this paper is to present the methodology on how to obtain an optimal cruciform specimen geometry, with thickness reduction in the gauge area, appropriated for fatigue crack initiation, as a function of the base material sheet thickness used to build the specimen. The geometry is optimized for maximum stress using several parameters, ensuring that in the gauge area the stress is uniform and maximum with two limit phase shift loading conditions. Therefore the fatigue damage will always initiate on the center of the specimen, avoiding failure outside this region. Using the Renard Series of preferred numbers for the base material sheet thickness as a reference, the reaming geometry parameters are optimized using a derivative-free methodology, called direct multi search (DMS) method. The final optimal geometry as a function of the base material sheet thickness is proposed, as a guide line for cruciform specimens design, and as a possible contribution for a future standard on in-plane biaxial fatigue tests. © 2014, Gruppo Italiano Frattura. All rights reserved.

Multiobjective design of viscoelastic laminated composite sandwich panels

The optimal design of laminated sandwich panels with viscoelastic core is addressed in this paper, with the objective of simultaneously minimizing weight and material cost and maximizing modal damping. The design variables are the number of layers in the laminated sandwich panel, the layer constituent materials and orientation angles and the viscoelastic layer thickness. The problem is solved using the Direct MultiSearch (DMS) solver for multiobjective optimization problems which does not use any derivatives of the objective functions. A finite element model for sandwich plates with transversely compressible viscoelastic core and anisotropic laminated face layers is used. Trade-off Pareto optimal fronts are obtained and the results are analyzed and discussed.

Multiobjective optimization for node adaptation in the analysis of composite plates using a meshless collocation method

The bending of simply supported composite plates is analyzed using a direct collocation meshless numerical method. In order to optimize node distribution the Direct MultiSearch (DMS) for multi-objective optimization method is applied. In addition, the method optimizes the shape parameter in radial basis functions. The optimization algorithm was able to find good solutions for a large variety of nodes distribution.

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.

Direct Visualization Of The Action Of Triton X-100 On Giant Vesicles Of Erythrocyte Membrane Lipids.

The raft hypothesis proposes that microdomains enriched in sphingolipids, cholesterol, and specific proteins are transiently formed to accomplish important cellular tasks. Equivocally, detergent-resistant membranes were initially assumed to be identical to membrane rafts, because of similarities between their compositions. In fact, the impact of detergents in membrane organization is still controversial. Here, we use phase contrast and fluorescence microscopy to observe giant unilamellar vesicles (GUVs) made of erythrocyte membrane lipids (erythro-GUVs) when exposed to the detergent Triton X-100 (TX-100). We clearly show that TX-100 has a restructuring action on biomembranes. Contact with TX-100 readily induces domain formation on the previously homogeneous membrane of erythro-GUVs at physiological and room temperatures. The shape and dynamics of the formed domains point to liquid-ordered/liquid-disordered (Lo/Ld) phase separation, typically found in raft-like ternary lipid mixtures. The Ld domains are then separated from the original vesicle and completely solubilized by TX-100. The insoluble vesicle left, in the Lo phase, represents around 2/3 of the original vesicle surface at room temperature and decreases to almost 1/2 at physiological temperature. This chain of events could be entirely reproduced with biomimetic GUVs of a simple ternary lipid mixture, 2:1:2 POPC/SM/chol (phosphatidylcholine/sphyngomyelin/cholesterol), showing that this behavior will arise because of fundamental physicochemical properties of simple lipid mixtures. This work provides direct visualization of TX-100-induced domain formation followed by selective (Ld phase) solubilization in a model system with a complex biological lipid composition.

Direct Adhesive Pin-retained Restorations For Severely Worn Dentition Treatment: A 1.5-year Follow-up Report.

Excessive occlusal surface wear can result in occlusal disharmony, functional and esthetic impairment. As a therapeutic approach, conventional single crowns have been proposed, but this kind of treatment is complex, highly invasive and expensive. This case report describes the clinical outcomes of an alternative minimally invasive treatment based on direct adhesive-pin retained restorations. A 64-year-old woman with severely worn dentition, eating problems related to missing teeth and generalized tooth hypersensitivity was referred for treatment. Proper treatment planning based on the diagnostic wax-up simulation was used to guide the reconstruction of maxillary anterior teeth with direct composite resin over self-threading dentin pins. As the mandibular remaining teeth were extremely worn, a tooth-supported overdenture was installed. A stabilization splint was also used to protect the restorations. This treatment was a less expensive alternative to full-mouth rehabilitation with positive esthetic and functional outcomes after 1.5 years of follow-up.

Direct And Non-destructive Proof Of Authenticity For The 2nd Generation Of Brazilian Real Banknotes Via Easy Ambient Sonic Spray Ionization Mass Spectrometry.

Using a desorption/ionization technique, easy ambient sonic-spray ionization coupled to mass spectrometry (EASI-MS), documents related to the 2nd generation of Brazilian Real currency (R$) were screened in the positive ion mode for authenticity based on chemical profiles obtained directly from the banknote surface. Characteristic profiles were observed for authentic, seized suspect counterfeit and counterfeited homemade banknotes from inkjet and laserjet printers. The chemicals in the authentic banknotes' surface were detected via a few minor sets of ions, namely from the plasticizers bis(2-ethylhexyl)phthalate (DEHP) and dibutyl phthalate (DBP), most likely related to the official offset printing process, and other common quaternary ammonium cations, presenting a similar chemical profile to 1st-generation R$. The seized suspect counterfeit banknotes, however, displayed abundant diagnostic ions in the m/z 400-800 range due to the presence of oligomers. High-accuracy FT-ICR MS analysis enabled molecular formula assignment for each ion. The ions were separated by 44 m/z, which enabled their characterization as Surfynol® 4XX (S4XX, XX=40, 65, and 85), wherein increasing XX values indicate increasing amounts of ethoxylation on a backbone of 2,4,7,9-tetramethyl-5-decyne-4,7-diol (Surfynol® 104). Sodiated triethylene glycol monobutyl ether (TBG) of m/z 229 (C10H22O4Na) was also identified in the seized counterfeit banknotes via EASI(+) FT-ICR MS. Surfynol® and TBG are constituents of inks used for inkjet printing.

Fast And Direct Na And K Determination In Table, Marine, And Low-sodium Salts By X-ray Fluorescence And Chemometrics.

X-ray fluorescence (XRF) is a fast, low-cost, nondestructive, and truly multielement analytical technique. The objectives of this study are to quantify the amount of Na(+) and K(+) in samples of table salt (refined, marine, and light) and to compare three different methodologies of quantification using XRF. A fundamental parameter method revealed difficulties in quantifying accurately lighter elements (Z < 22). A univariate methodology based on peak area calibration is an attractive alternative, even though additional steps of data manipulation might consume some time. Quantifications were performed with good correlations for both Na (r = 0.974) and K (r = 0.992). A partial least-squares (PLS) regression method with five latent variables was very fast. Na(+) quantifications provided calibration errors lower than 16% and a correlation of 0.995. Of great concern was the observation of high Na(+) levels in low-sodium salts. The presented application may be performed in a fast and multielement fashion, in accordance with Green Chemistry specifications.