Derivative-free optimization and filter methods to solve nonlinear constrained problems

In real optimization problems, usually the analytical expression of the objective function is not known, nor its derivatives, or they are complex. In these cases it becomes essential to use optimization methods where the calculation of the derivatives, or the verification of their existence, is not necessary: the Direct Search Methods or Derivative-free Methods are one solution. When the problem has constraints, penalty functions are often used. Unfortunately the choice of the penalty parameters is, frequently, very difficult, because most strategies for choosing it are heuristics strategies. As an alternative to penalty function appeared the filter methods. A filter algorithm introduces a function that aggregates the constrained violations and constructs a biobjective problem. In this problem the step is accepted if it either reduces the objective function or the constrained violation. This implies that the filter methods are less parameter dependent than a penalty function. In this work, we present a new direct search method, based on simplex methods, for general constrained optimization that combines the features of the simplex method and filter methods. This method does not compute or approximate any derivatives, penalty constants or Lagrange multipliers. The basic idea of simplex filter algorithm is to construct an initial simplex and use the simplex to drive the search. We illustrate the behavior of our algorithm through some examples. The proposed methods were implemented in Java.

Fast screening procedure for antibiotics in wastewaters by direct HPLC-DAD analysis

Growing concern about the contamination of wastewaters by antibiotics demands fast but sensitive analytical methodologies, for the screening of a large number of samples. The purpose of this work was to develop a simple methodology, using direct injection of the samples, by HPLC with diode array detection (DAD), for a multiresidue analysis of five antibiotics of different classes. Wastewater from an urban water treatment plant was selected as a model to study possible coelution of interfering compounds. The linearity interval ranged from 40 to 400 µg/L for amoxicillin (Amox), metronidazole (Metro), cefazolin (Cefa), and chloramphenicol (Chloram) and from 20 to 200 µg/L for sulfamethoxazole (Sulfa), with LODs lower than 14 µg/L. Repeatability, expressed by the CV of six repeated injections, ranged from 1 to 8%, while the intermediate precision varied between 2 and 11%. The recovery ranged from 90 to 109%. This method enables the fast screening of a large number of samples, with an expanded uncertainty in the 1–22% range. The advantage of the proposed method is to significantly reduce the number of samples to be analyzed by more complex methods.

Direct electroanalytical determination of fluvastatin in a pharmaceutical dosage form: batch and flow analysis

The reduction of luvastatin (FLV) at a hanging mercury-drop electrode (HMDE) was studied by square-wave adsorptive-stripping voltammetry (SWAdSV). FLV can be accumulated and reduced at the electrode, with a maximum peak current intensity at a potential of approximately 1.26V vs. AgCl=Ag, in an aqueous electrolyte solution of pH 5.25. The method shows linearity between peak current intensity and FLV concentration between 1.0 10 8 and 2.7 10 6 mol L 1. Limits of detection (LOD) and quantification (LOQ) were found to be 9.9 10 9 mol L 1 and 3.3 10 8 mol L 1, respectively. Furthermore, FLV oxidation at a glassy carbon electrode surface was used for its hydrodynamic monitoring by amperometric detection in a flow-injection system. The amperometric signal was linear with FLV concentration over the range 1.0 10 6 to 1.0 10 5 mol L 1, with an LOD of 2.4 10 7 mol L 1 and an LOQ of 8.0 10 7 mol L 1. A sample rate of 50 injections per hour was achieved. Both methods were validated and showed to be precise and accurate, being satisfactorily applied to the determination of FLV in a commercial pharmaceutical.

Direct medical costs associated with schizophrenia relapses in health care services in the city of São Paulo

OBJECTIVE: To assess direct medical costs associated with schizophrenia relapses in mental health services. METHODS: The study was conducted in three health facilities in the city of São Paulo: a public state hospital; a Brazilian National Health System (SUS)-contracted hospital; and a community mental health center. Medical records of 90 patients with schizophrenia who received care in 2006 were reviewed. Information on inpatient expenditures was collected and used for cost estimates. RESULTS: Mean direct medical cost of schizophrenia relapses per patient was US$ 4,083.50 (R$ 8,167.58) in the public state hospital; US$ 2,302.76 (R$ 4,605.46) in the community mental health center; and US$ 1,198.50 (R$ 2,397.74) in the SUS-affiliated hospital. The main component was daily inpatient room rates (87% - 98%). Medication costs varied depending on the use of typical or atypical antipsychotic drugs. Atypical antipsychotic drugs were more often used in the community mental health center. CONCLUSIONS: Costs associated with schizophrenia relapses support investments in antipsychotic drugs and strategies to reduce disease relapse and the need for mental health inpatient services. Treating patients in a community mental health center was associated with medium costs and added the benefit of not depriving these patients from family life.

Direct treatment costs of HIV/AIDS in Portugal

OBJECTIVE To analyze the direct medical costs of HIV/AIDS in Portugal from the perspective of the National Health Service. METHODS A retrospective analysis of medical records was conducted for 150 patients from five specialized centers in Portugal in 2008. Data on utilization of medical resources during 12 months and patients’ characteristics were collected. A unit cost was applied to each care component using official sources and accounting data from National Health Service hospitals. RESULTS The average cost of treatment was 14,277 €/patient/year. The main cost-driver was antiretroviral treatment (€ 9,598), followed by hospitalization costs (€ 1,323). Treatment costs increased with the severity of disease from € 11,901 (> 500 CD4 cells/µl) to € 23,351 (CD4 count ≤ 50 cells/ µl). Cost progression was mainly due to the increase in hospitalization costs, while antiretroviral treatment costs remained stable over disease stages. CONCLUSIONS The high burden related to antiretroviral treatment is counterbalanced by relatively low hospitalization costs, which, however, increase with severity of disease. The relatively modest progression of total costs highlights that alternative public health strategies that do not affect transmission of disease may only have a limited impact on expenditure, since treatment costs are largely dominated by constant antiretroviral treatment costs.

Classification of some penalty methods

Optimization problems arise in science, engineering, economy, etc. and we need to find the best solutions for each reality. The methods used to solve these problems depend on several factors, including the amount and type of accessible information, the available algorithms for solving them, and, obviously, the intrinsic characteristics of the problem. There are many kinds of optimization problems and, consequently, many kinds of methods to solve them. When the involved functions are nonlinear and their derivatives are not known or are very difficult to calculate, these methods are more rare. These kinds of functions are frequently called black box functions. To solve such problems without constraints (unconstrained optimization), we can use direct search methods. These methods do not require any derivatives or approximations of them. But when the problem has constraints (nonlinear programming problems) and, additionally, the constraint functions are black box functions, it is much more difficult to find the most appropriate method. Penalty methods can then be used. They transform the original problem into a sequence of other problems, derived from the initial, all without constraints. Then this sequence of problems (without constraints) can be solved using the methods available for unconstrained optimization. In this chapter, we present a classification of some of the existing penalty methods and describe some of their assumptions and limitations. These methods allow the solving of optimization problems with continuous, discrete, and mixing constraints, without requiring continuity, differentiability, or convexity. Thus, penalty methods can be used as the first step in the resolution of constrained problems, by means of methods that typically are used by unconstrained problems. We also discuss a new class of penalty methods for nonlinear optimization, which adjust the penalty parameter dynamically.

Direct search optimization application programming interface with remote access

Search Optimization methods are needed to solve optimization problems where the objective function and/or constraints functions might be non differentiable, non convex or might not be possible to determine its analytical expressions either due to its complexity or its cost (monetary, computational, time,...). Many optimization problems in engineering and other fields have these characteristics, because functions values can result from experimental or simulation processes, can be modelled by functions with complex expressions or by noise functions and it is impossible or very difficult to calculate their derivatives. Direct Search Optimization methods only use function values and do not need any derivatives or approximations of them. In this work we present a Java API that including several methods and algorithms, that do not use derivatives, to solve constrained and unconstrained optimization problems. Traditional API access, by installing it on the developer and/or user computer, and remote API access to it, using Web Services, are also presented. Remote access to the API has the advantage of always allow the access to the latest version of the API. For users that simply want to have a tool to solve Nonlinear Optimization Problems and do not want to integrate these methods in applications, also two applications were developed. One is a standalone Java application and the other a Web-based application, both using the developed API.

Filters method in direct search optimization, new measures to admissibility

Constrained nonlinear optimization problems are usually solved using penalty or barrier methods combined with unconstrained optimization methods. Another alternative used to solve constrained nonlinear optimization problems is the lters method. Filters method, introduced by Fletcher and Ley er in 2002, have been widely used in several areas of constrained nonlinear optimization. These methods treat optimization problem as bi-objective attempts to minimize the objective function and a continuous function that aggregates the constraint violation functions. Audet and Dennis have presented the rst lters method for derivative-free nonlinear programming, based on pattern search methods. Motivated by this work we have de- veloped a new direct search method, based on simplex methods, for general constrained optimization, that combines the features of the simplex method and lters method. This work presents a new variant of these methods which combines the lters method with other direct search methods and are proposed some alternatives to aggregate the constraint violation functions.

Lifestyle factors, direct and indirect costs for a Brazilian airline company

OBJECTIVE To analyze lifestyle risk factors related to direct healthcare costs and the indirect costs due to sick leave among workers of an airline company in Brazil. METHODS In this longitudinal 12-month study of 2,201 employees of a Brazilian airline company, the costs of sick leave and healthcare were the primary outcomes of interest. Information on the independent variables, such as gender, age, educational level, type of work, stress, and lifestyle-related factors (body mass index, physical activity, and smoking), was collected using a questionnaire on enrolment in the study. Data on sick leave days were available from the company register, and data on healthcare costs were obtained from insurance records. Multivariate linear regression analysis was used to investigate the association between direct and indirect healthcare costs with sociodemographic, work, and lifestyle-related factors. RESULTS Over the 12-month study period, the average direct healthcare expenditure per worker was US$505.00 and the average indirect cost because of sick leave was US$249.00 per worker. Direct costs were more than twice the indirect costs and both were higher in women. Body mass index was a determinant of direct costs and smoking was a determinant of indirect costs. CONCLUSIONS Obesity and smoking among workers in a Brazilian airline company were associated with increased health costs. Therefore, promoting a healthy diet, physical activity, and anti-tobacco campaigns are important targets for health promotion in this study population.

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.

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.

Identification of respiratory virus in infants with congenital heart disease by comparison of different methods

Respiratory virus infections are the main cause of infant hospitalization and are potentially severe in children with congenital heart disease (CHD). Rapid and sensitive diagnosis is very important to early introduction of antiviral treatment and implementation of precautions to control transmission, reducing the risk of nosocomial infections. In the present study we compare different techniques in the diagnosis of respiratory viruses in CHD infants. Thirty-nine samples of nasopharyngeal aspirate were obtained from CHD infants with symptoms of respiratory infection. The Multiplex PCR (Seeplex® RV 12 ACE Detection) driven to the detection of 12 respiratory viruses was compared with the direct immunofluorescence assay (DFA) and PCR, both targeting seven respiratory viruses. The positivity found by DFA, Multiplex and PCR was 33.3%, 51.3% and 48.7%, respectively. Kappa index comparing DFA and Multiplex, DFA and PCR and PCR and Multiplex PCR was 0.542, 0.483 and 0.539, respectively. The concordance between techniques was considered moderate. Both Multiplex PCR (p = 0.001) and PCR (p = 0.002) detected significantly more respiratory virus than DFA. As the performance of the tests may vary, the combination of two or more techniques may increase diagnostic sensitivity favoring the diagnosis of co-infections, early introduction of antiviral therapy and implementation of appropriate measures.

COMPARISON OF PERMANENT STAINING METHODS FOR THE LABORATORY DIAGNOSIS OF TRICHOMONIASIS

Trichomonas vaginalis is the etiologic agent of trichomoniasis, the most common non-viral sexually transmitted disease (STD) in the world. The diagnosis is based on wet mount preparation and direct microscopy on fixed and stained clinical specimens. The aim of this study was to compare the performance of different fixing and staining techniques used in the detection of T. vaginalis in urine. The smears were fixed and submitted to different methods of permanent staining and then, the morphological aspects of the parasites were analyzed and compared. The Papanicolaou staining with ethanol as the fixative solution showed to be the best method of permanent staining. Our data suggest that staining techniques in association with wet mount examination of fresh specimens contribute to increase the sensitivity in the diagnosis of trichomoniasis.

Evaluation of a direct immunofluorescent antibody (difma) test using Leishmania genus - specific monoclonal antibody in the routine diagnosis of cutaneous leishmaniasis

A direct immunofluorescent antibody (DIFMA) test using a Leishmania genus- specific monoclonal antibody was evaluated in the routine diagnosis of cutaneous leishmaniasis (CL) in Ecuador. This test was compared with the standard diagnostic techniques of scrapings, culture and histology. Diagnostic samples were taken from a total of 90 active dermal ulcers from patients from areas of Ecuador known to be endemic for cutaneous leishmaniasis. DIFMA was positive in all lesions. It was shown to be significantly superior to standard diagnostic methods either alone or in combination. The sensitivity of DIFMA did not diminish with chronicity of lesions. This test proved to be extremely useful in the routine diagnosis of CL because it is highly sensitive, is easy to use and produces rapid results.

Production of anti-Cryptosporidium polyclonal antibodies and standardization of direct immunofluorescence for detecting oocysts in water

INTRODUCTION: The production of anti-Cryptosporidium polyclonal antibodies and its use in direct immunofluorescence assays to determine the presence of Cryptosporidium in water are described in the present work. METHODS: Two rabbits were immunized with soluble and particulate antigens from purified Cryptosporidium oocysts. The sera produced were prepared for immunoglobulin G extraction, which were then purified and conjugated with fluorescein isothiocyanate (FITC). Slides containing known amounts of oocysts were prepared to determine the sensitivity of the technique. To test the specificity, slides containing Giardia duodenalis cysts were prepared. RESULTS: The conjugate was successfully used in water samples experimentally contaminated with Cryptosporidium oocysts, and it was possible to detect up to five oocysts/spot, corresponding to contamination of 250 oocysts/mL. CONCLUSIONS: The three immunizations performed in the rabbits were enough to produce antibodies against Cryptosporidium, the standard direct immunofluorescence assay permitted the detection of five oocysts in 20% of the samples, and no cross-reaction with Giardia duodenalis cysts occurred.