Direct-search penalty/barrier methods

In Nonlinear Optimization Penalty and Barrier Methods are normally used to solve Constrained Problems. There are several Penalty/Barrier Methods and they are used in several areas from Engineering to Economy, through Biology, Chemistry, Physics among others. In these areas it often appears Optimization Problems in which the involved functions (objective and constraints) are non-smooth and/or their derivatives are not know. In this work some Penalty/Barrier functions are tested and compared, using in the internal process, Derivative-free, namely Direct Search, methods. This work is a part of a bigger project involving the development of an Application Programming Interface, that implements several Optimization Methods, to be used in applications that need to solve constrained and/or unconstrained Nonlinear Optimization Problems. Besides the use of it in applied mathematics research it is also to be used in engineering software packages.

Adaptive Penalty and Barrier function based on Fuzzy Logic

Optimization methods have been used in many areas of knowledge, such as Engineering, Statistics, Chemistry, among others, to solve optimization problems. In many cases it is not possible to use derivative methods, due to the characteristics of the problem to be solved and/or its constraints, for example if the involved functions are non-smooth and/or their derivatives are not know. To solve this type of problems a Java based API has been implemented, which includes only derivative-free optimization methods, and that can be used to solve both constrained and unconstrained problems. For solving constrained problems, the classic Penalty and Barrier functions were included in the API. In this paper a new approach to Penalty and Barrier functions, based on Fuzzy Logic, is proposed. Two penalty functions, that impose a progressive penalization to solutions that violate the constraints, are discussed. The implemented functions impose a low penalization when the violation of the constraints is low and a heavy penalty when the violation is high. Numerical results, obtained using twenty-eight test problems, comparing the proposed Fuzzy Logic based functions to six of the classic Penalty and Barrier functions are presented. Considering the achieved results, it can be concluded that the proposed penalty functions besides being very robust also have a very good performance.

Penalty fuzzy function for derivative-free optimization

Penalty and Barrier methods are normally used to solve Nonlinear Optimization Problems constrained problems. The problems appear in areas such as engineering and are often characterised by the fact that involved functions (objective and constraints) are non-smooth and/or their derivatives are not know. This means that optimization methods based on derivatives cannot net used. A Java based API was implemented, including only derivative-free optimizationmethods, to solve both constrained and unconstrained problems, which includes Penalty and Barriers methods. In this work a new penalty function, based on Fuzzy Logic, is presented. This function imposes a progressive penalization to solutions that violate the constraints. This means that the function imposes a low penalization when the violation of the constraints is low and a heavy penalisation when the violation is high. The value of the penalization is not known in beforehand, it is the outcome of a fuzzy inference engine. Numerical results comparing the proposed function with two of the classic penalty/barrier functions are presented. Regarding the presented results one can conclude that the prosed penalty function besides being very robust also exhibits a very good performance.

Improvement of a filters method in a derivative free optimization

Constraints nonlinear optimization problems can be solved using penalty or barrier functions. This strategy, based on solving the problems without constraints obtained from the original problem, have shown to be e ective, particularly when used with direct search methods. An alternative to solve the previous problems is the lters method. The lters method introduced by Fletcher and Ley er in 2002, , has been widely used to solve problems of the type mentioned above. These methods use a strategy di erent from the barrier or penalty functions. The previous functions de ne a new one that combine the objective function and the constraints, while the lters method treat optimization problems as a bi-objective problems that minimize the objective function and a function that aggregates the constraints. Motivated by the work of Audet and Dennis in 2004, using lters method with derivative-free algorithms, the authors developed works where other direct search meth- ods were used, combining their potential with the lters method. More recently. In a new variant of these methods was presented, where it some alternative aggregation restrictions for the construction of lters were proposed. This paper presents a variant of the lters method, more robust than the previous ones, that has been implemented with a safeguard procedure where values of the function and constraints are interlinked and not treated completely independently.

Multiple Roots of Systems of Equations by Repulsion Merit Functions

In this paper we address the problem of computing multiple roots of a system of nonlinear equations through the global optimization of an appropriate merit function. The search procedure for a global minimizer of the merit function is carried out by a metaheuristic, known as harmony search, which does not require any derivative information. The multiple roots of the system are sequentially determined along several iterations of a single run, where the merit function is accordingly modified by penalty terms that aim to create repulsion areas around previously computed minimizers. A repulsion algorithm based on a multiplicative kind penalty function is proposed. Preliminary numerical experiments with a benchmark set of problems show the effectiveness of the proposed method.

Modified Discrete PSO to Increase the Delivered Energy Probability in Distribution energy Systems

This paper proposes a PSO based approach to increase the probability of delivering power to any load point by identifying new investments in distribution energy systems. The statistical failure and repair data of distribution components is the main basis of the proposed methodology that uses a fuzzyprobabilistic modeling for the components outage parameters. The fuzzy membership functions of the outage parameters of each component are based on statistical records. A Modified Discrete PSO optimization model is developed in order to identify the adequate investments in distribution energy system components which allow increasing the probability of delivering power to any customer in the distribution system at the minimum possible cost for the system operator. To illustrate the application of the proposed methodology, the paper includes a case study that considers a 180 bus distribution network.

Numerical experiments with a modified regularization scheme for mathematical programs with complementarity constraints

On this paper we present a modified regularization scheme for Mathematical Programs with Complementarity Constraints. In the regularized formulations the complementarity condition is replaced by a constraint involving a positive parameter that can be decreased to zero. In our approach both the complementarity condition and the nonnegativity constraints are relaxed. An iterative algorithm is implemented in MATLAB language and a set of AMPL problems from MacMPEC database were tested.

The development and optimization of a modified single-drop microextraction method for organochlorine pesticides determination by gas chromatography-tandem mass spectrometry

We have developed a new method for single-drop microextraction (SDME) for the preconcentration of organochlorine pesticides (OCP) from complex matrices. It is based on the use of a silicone ring at the tip of the syringe. A 5 μL drop of n-hexane is applied to an aqueous extract containing the OCP and found to be adequate to preconcentrate the OCPs prior to analysis by GC in combination with tandem mass spectrometry. Fourteen OCP were determined using this technique in combination with programmable temperature vaporization. It is shown to have many advantages over traditional split/splitless injection. The effects of kind of organic solvent, exposure time, agitation and organic drop volume were optimized. Relative recoveries range from 59 to 117 %, with repeatabilities of <15 % (coefficient of variation) were achieved. The limits of detection range from 0.002 to 0.150 μg kg−1. The method was applied to the preconcentration of OCPs in fresh strawberry, strawberry jam, and soil.

Gold electrode modified by self-assembled monolayers of thiols to determine DNA sequences hybridization

The process of immobilization of biological molecules is one of the most important steps in the construction of a biosensor. In the case of DNA, the way it exposes its bases can result in electrochemical signals to acceptable levels. The use of self-assembled monolayer that allows a connection to the gold thiol group and DNA binding to an aldehydic ligand resulted in the possibility of determining DNA hybridization. Immobilized single strand of DNA (ssDNA) from calf thymus pre-formed from alkanethiol film was formed by incubating a solution of 2-aminoethanothiol (Cys) followed by glutaraldehyde (Glu). Cyclic voltammetry (CV) was used to characterize the self-assembled monolayer on the gold electrode and, also, to study the immobilization of ssDNA probe and hybridization with the complementary sequence (target ssDNA). The ssDNA probe presents a well-defined oxidation peak at +0.158 V. When the hybridization occurs, this peak disappears which confirms the efficacy of the annealing and the DNA double helix performing without the presence of electroactive indicators. The use of SAM resulted in a stable immobilization of the ssDNA probe, enabling the hybridization detection without labels. This study represents a promising approach for molecular biosensor with sensible and reproducible results.

Economic, environmental and mixed objective functions in non-linear process optimization using simulated annealing and tabu search

Screening of topologies developed by hierarchical heuristic procedures can be carried out by comparing their optimal performance. In this work we will be exploiting mono-objective process optimization using two algorithms, simulated annealing and tabu search, and four different objective functions: two of the net present value type, one of them including environmental costs and two of the global potential impact type. The hydrodealkylation of toluene to produce benzene was used as case study, considering five topologies with different complexities mainly obtained by including or not liquid recycling and heat integration. The performance of the algorithms together with the objective functions was observed, analyzed and discussed from various perspectives: average deviation of results for each algorithm, capacity for producing high purity product, screening of topologies, objective functions robustness in screening of topologies, trade-offs between economic and environmental type objective functions and variability of optimum solutions.

Biosensor based on multi-walled carbon nanotubes paste electrode modified with laccase for pirimicarb pesticide quantification

This study focused on the development of a sensitive enzymatic biosensor for the determination of pirimicarb pesticide based on the immobilization of laccase on composite carbon paste electrodes. Multi- walled carbon nanotubes(MWCNTs)paste electrode modified by dispersion of laccase(3%,w/w) within the optimum composite matrix(60:40%,w/w,MWCNTs and paraffin binder)showed the best performance, with excellent electron transfer kinetic and catalytic effects related to the redox process of the substrate4- aminophenol. No metal or anti-interference membrane was added. Based on the inhibition of laccase activity, pirimicarb can be determined in the range 9.90 ×10- 7 to 1.15 ×10- 5 molL 1 using 4- aminophenol as substrate at the optimum pH of 5.0, with acceptable repeatability and reproducibility (relative standard deviations lower than 5%).The limit of detection obtained was 1.8 × 10-7 molL 1 (0.04 mgkg 1 on a fresh weight vegetable basis).The high activity and catalytic properties of the laccase- based biosensor are retained during ca. one month. The optimized electroanalytical protocol coupled to the QuEChERS methodology were applied to tomato and lettuce samples spiked at three levels; recoveries ranging from 91.0±0.1% to 101.0 ± 0.3% were attained. No significant effects in the pirimicarb electro- analysis were observed by the presence of pro-vitamin A, vitamins B1 and C,and glucose in the vegetable extracts. The proposed biosensor- based pesticide residue methodology fulfills all requisites to be used in implementation of food safety programs.

Multiresidue pesticides analysis in soils using modified QuEChERS with disposable pipette extraction and dispersive solid-phase extraction

QuEChERS original method was modified into a new version for pesticides determination in soils. The QuEChERS method is based on liquid–liquid portioning with ACN and was followed by cleanup step using dispersive SPE and disposable pipette tips. Gas chromatographic separation with MS detection was carried out for pesticides quantification. The method was validated using recovery experiments for 36 multiclass pesticides. Mean recoveries of pesticides at each of the four spiking levels between 10–300 µg/kg of soil ranged from 70–120% for 26 pesticides with RSD values less than 15%. The method achieved low limit of detection less than 7.6 µ g/kg. Matrix effects were observed for 13 pesticides. Matrix effects were compensated by using matrix-matched calibration. The method was applied successfully using d-SPE or DPX in the analysis of the pesticides in soils from organic farming and integrated pest management.

Laccase–Prussian blue film–graphene doped carbon paste modified electrode for carbamate pesticides quantification

A novel enzymatic biosensor for carbamate pesticides detection was developed through the direct immobilization of Trametes versicolor laccase on graphene doped carbon paste electrode functionalized with Prussianblue films (LACC/PB/GPE). Graphene was prepared by graphite sonication-assisted exfoliation and characterized by transmission electron microscopy and X-ray photoelectron spectro- scopy. The Prussian blue film electrodeposited onto graphene doped carbon paste electrode allowed considerable reduction of the charge transfer resistance and of the capacitance of the device.The combined effects of pH, enzyme concentration and incubation time on biosensor response were optimized using a 23 full-factorial statistical design and response surface methodology. Based on the inhibition of laccase activity and using 4-aminophenol as redox mediator at pH 5.0,LACC/PB/GPE exhibited suitable characteristics in terms of sensitivity, intra-and inter-day repeatability (1.8–3.8% RSD), reproducibility (4.1 and 6.3%RSD),selectivity(13.2% bias at the higher interference: substrate ratios tested),accuracy and stability(ca. twenty days)for quantification of five carbamates widely applied on tomato and potato crops.The attained detection limits ranged between 5.2×10−9 mol L−1(0.002 mg kg−1 w/w for ziram)and 1.0×10−7 mol L−1 (0.022 mg kg−1 w/w for carbofuran).Recovery values for the two tested spiking levels ranged from 90.2±0.1%(carbofuran)to 101.1±0.3% (ziram) for tomato and from 91.0±0.1%(formetanate)to 100.8±0.1%(ziram)for potato samples.The proposed methodology is appropriate to enable testing pesticide levels in food samples to fit with regulations and food inspections.

Application-specific modified particle swarm optimization for energy resource scheduling considering vehicle-to-grid

This paper presents a modified Particle Swarm Optimization (PSO) methodology to solve the problem of energy resources management with high penetration of distributed generation and Electric Vehicles (EVs) with gridable capability (V2G). The objective of the day-ahead scheduling problem in this work is to minimize operation costs, namely energy costs, regarding he management of these resources in the smart grid context. The modifications applied to the PSO aimed to improve its adequacy to solve the mentioned problem. The proposed Application Specific Modified Particle Swarm Optimization (ASMPSO) includes an intelligent mechanism to adjust velocity limits during the search process, as well as self-parameterization of PSO parameters making it more user-independent. It presents better robustness and convergence characteristics compared with the tested PSO variants as well as better constraint handling. This enables its use for addressing real world large-scale problems in much shorter times than the deterministic methods, providing system operators with adequate decision support and achieving efficient resource scheduling, even when a significant number of alternative scenarios should be considered. The paper includes two realistic case studies with different penetration of gridable vehicles (1000 and 2000). The proposed methodology is about 2600 times faster than Mixed-Integer Non-Linear Programming (MINLP) reference technique, reducing the time required from 25 h to 36 s for the scenario with 2000 vehicles, with about one percent of difference in the objective function cost value.