Optimization of Generator Based on Gaussian Process Regression Model with Conditional Likelihood Lower Bound Search

The noise that comes from finite element simulation often causes the model to fall into the local optimal solution and over fitting during optimization of generator.Thus,this paper proposes a Gaussian Process Regression(GPR)model based on Conditional Likelihood Lower Bound Search(CLLBS)to optimize the design of the generator,which can filter the noise in the data and search for global optimization by combining the Conditional Likelihood Lower Bound Search method.Taking the efficiency optimization of 15 kW Permanent Magnet Synchronous Motor as an example.Firstly,this method uses the elementary effect analysis to choose the sensitive variables,combining the evolutionary algorithm to design the super Latin cube sampling plan;Then the generator-converter system is simulated by establishing a co-simulation platform to obtain data.A Gaussian process regression model combing the method of the conditional likelihood lower bound search is established,which combined the chi-square test to optimize the accuracy of the model globally.Secondly,after the model reaches the accuracy,the Pareto frontier is obtained through the NSGA-II algorithm by considering the maximum output torque as a constraint.Last,the constrained optimization is transformed into an unconstrained optimizing problem by introducing maximum constrained improvement expectation(CEI)optimization method based on the re-interpolation model,which cross-validated the optimization results of the Gaussian process regression model.The above method increase the efficiency of generator by 0.76%and 0.5%respectively;And this method can be used for rapid modeling and multi-objective optimization of generator systems.

Optimization of Extraction Conditions of Pomegranate Peel Polyphenols and Its Protective Effect on Acute Alcoholic Liver Injury in Mice

[Objectives]This study was conducted to explore the optimization of ultrasonic-assisted organic solvent extraction of pomegranate peel polyphenols(PPPs),and to study the protective effect of PPPs on acute alcoholic liver injury in mice.[Methods]The optimal extraction conditions of PPPs were determined by single factor and orthogonal experiments,and an acute alcoholic liver injury model in mice was established.Bifendate was used as the positive control group to investigate the protective effect of low,medium and high doses of PPPs on acute alcoholic liver injury.[Results]The optimum extraction process parameters were followed as 60%ethanol concentration,solid-liquid ratio of 1:40(w/v),extraction temperature of 50℃,and extraction time of 1.5 h,and the yield was 1.42%.The results of animal experiments showed that PPPs could effectively reduce the degree of alcoholic liver injury in mice,reduce the levels of serum alanine aminotransferase(ALT)and aspartate aminotransferase(AST),and reduce the inflammation and necrosis of liver tissue in mice.Meanwhile,the total polyphenols from pomegranate peel also significantly reduced the expression levels of malondialdehyde(MDA),tumor necrosis factor(TNF-α)and interleukin-6(IL-6)in mice,and increased the levels of superoxide dismutase(SOD)and reduced glutathione(GSH)in liver tissue of mice,indicating its antioxidant and anti-inflammatory effects,further illustrating its protective effect on alcoholic liver injury.[Conclusions]PPPs could reduce the expression levels of TNF-α,IL-6 and MDA in mice,and increase the expression levels of SOD and GSH to achieve the protective effect on acute alcoholic liver injury in mice.This study will provide new ideas for the development of new anti-alcoholic liver injury drug resources.

Optimization of Extraction Conditions for Total Flavonoids from Fructus Aurantii Immaturus and Its Anti-UVB Radiation Activity

[Objectives]Optimum extraction conditions of total flavonoids from Fructus Aurantii Immaturus(TFFAI)and its resistance activity to ultraviolet radiation were investigated in present research.[Methods]The optimal extraction conditions of TFFAI were determined by single factor and orthogonal experiments,and the survival rate of TFFAI on HaCaT cells irradiated with UVB rays was investigated.It s antioxidant capacity was determined by ABTS.[Results]The results showed that the highest yield of TFFAI was obtained with 70%ethanol at a solid-to-liquid ratio of 1:50(w/v)and 40℃for 1.5 h by single-factor and orthogonal experiments.Total flavonoids(0.25-1.00 mg/ml)could significantly improve the survival rate of HaCaT cell line.Meanwhile,the maximum absorption peak of TFFAI was found at 283 nm,and in-vitro antioxidant experiment identified that TFFAI had a good clearance rate to ABTS.It suggestes that TFFAI could protect the cells from UVB damage by absorption of UVB rays and anti-oxidation.[Conclusions]TFFAI played a protective role on UVB irradiated cells through UVB ultraviolet absorption and antioxidant pathways.

A Modified Lagrange Method for Solving Convex Quadratic Optimization Problems

In this paper, a modified version of the Classical Lagrange Multiplier method is developed for convex quadratic optimization problems. The method, which is evolved from the first order derivative test for optimality of the Lagrangian function with respect to the primary variables of the problem, decomposes the solution process into two independent ones, in which the primary variables are solved for independently, and then the secondary variables, which are the Lagrange multipliers, are solved for, afterward. This is an innovation that leads to solving independently two simpler systems of equations involving the primary variables only, on one hand, and the secondary ones on the other. Solutions obtained for small sized problems (as preliminary test of the method) demonstrate that the new method is generally effective in producing the required solutions.

Nonlinear Optimization Method of Ship Floating Condition Calculation in Wave Based on Vector

Ship floating condition in regular waves is calculated. New equations controlling any ship＇s floating condition are proposed by use of the vector operation. This form is a nonlinear optimization problem which can be solved using the penalty function method with constant coefficients. And the solving process is accelerated by dichotomy. During the solving process, the ship＇s displacement and buoyant centre have been calculated by the integration of the ship surface according to the waterline. The ship surface is described using an accumulative chord length theory in order to determine the displacement, the buoyancy center and the waterline. The draught forming the waterline at each station can be found out by calculating the intersection of the ship surface and the wave surface. The results of an example indicate that this method is exact and efficient. It can calculate the ship floating condition in regular waves as well as simplify the calculation and improve the computational efficiency and the precision of results.

OPTIMALITY CONDITIONS AND DUALITY RESULTS FOR NONSMOOTH VECTOR OPTIMIZATION PROBLEMS WITH THE MULTIPLE INTERVAL-VALUED OBJECTIVE FUNCTION

In this paper, both Fritz John and Karush-Kuhn-Tucker necessary optimality conditions are established for a （weakly） LU-efficient solution in the considered nonsmooth multiobjective programming problem with the multiple interval-objective function. Further, the sufficient optimality conditions for a （weakly） LU-efficient solution and several duality results in Mond-Weir sense are proved under assumptions that the functions constituting the considered nondifferentiable multiobjective programming problem with the multiple interval- objective function are convex.

Optimization of Fermentation Conditions for Xylanase Production by Aspergillus niger NS-1

In this study, a xylanase-produeing Aspergillus niger strain, NS-1, was screened and isolated from agricultural and forestry wastes. Based on single-fac- tor experiments, the effects of different carbon sources, composite carbon sources, nitrogen sources, calcium carbonate concentrations, initial pH and surfactants on xylanase production by A. niger NS-1 were investigated. The results indicated that the most appropriate carbon source was corncobs ; the best composite carbon source was corncobs ＋ xylan, which was conducive to xylanase secretion; the most suitable nitrogen source was ammonium sulfate. Xylanase activity reached the highest in the medium added with 1.5% calcium carbonate and SDS as a surfactant with an initial pH of 5.0. This study provided the basis for the production of high-activity xylanase.

KUHN-TUCKER CONDITION AND WOLFE DUALITY OF PREINVEX SET-VALUED OPTIMIZATION

The optimality Kuhn-Tucker condition and the wolfe duality for the preinvex set-valued optimization are investigated. Firstly, the concepts of alpha-order G-invex set and the alpha-order S-preinvex set-valued function were introduced, from which the properties of the corresponding contingent cone and the alpha-order contingent derivative were studied. Finally, the optimality Kuhn-Tucker condition and the Wolfe duality theorem for the alpha-order S-preinvex set-valued optimization were presented with the help of the alpha-order contingent derivative.

THE OPTIMALITY CONDITIONS OF NONCONVEXSET-VALUED VECTOR OPTIMIZATION

The concepts of alpha-order Clarke's derivative, alpha-order Adjacent derivative and alpha-order G.Bouligand derivative of set-valued mappings are introduced, their properties are studied, with which the Fritz John optimality condition of set-valued vector optimization is established. Finally, under the assumption of pseudoconvexity, the optimality condition is proved to be sufficient.

Optimization of Extraction Conditions of Some Phenolic Compounds from White Horehound (<i>Marrubium vulgare</i>L.) Leaves

This research was aimed to optimize the extraction conditions of three phenolic compounds: total phenolics, flavonoids and condensed tannins, from White Horehound’s leaves (Marrubium vulgare L.). Distilled water and different organic solvents such as: methanol, ethanol and acetone, were used, with various concentrations (20% - 80%, v/v), temperatures (20&deg;C - 60&deg;C) and extraction times (30 - 450 min). Results showed that the maximum total phenolics amounts (293.34 ± 14.60 mg gallic acid equivalent/g dry weigh), were obtained with 60% aqueous methanol at 25&deg;C for 180 min;total flavonoids (79.52 ± 0.55 mg catechin equivalent/g dry weigh) with 80% aqueous methanol at 20&deg;C for 450 min, and condensed tannins (28.15 ± 0.80 mg catechin equivalent/g dry weigh) with 60% aqueous acetone at 50&deg;C and for 180 min. ANOVA test showed the significant effect (***P < 0.001) of the extraction conditions tested on phenolic compounds. The Principal Component Analysis (PCA) exhibited the positive effect of low temperatures on total phenolics and flavonoids extraction, and the effect of high temperatures on the condensed tannins extraction. The Response Surface Methodology (RSM) provided predicted values of extraction conditions and maximum polyphenols amounts similar to those obtained experimentally.

Design Optimization of TBM Disc Cutters for Different Geological Conditions

A novel optimization methodology for the disc cutter designs of tunnel boring machines (TBM) was presented. To fully understand the characteristics and performance of TBM cutters, a comprehensive list of performance parameters were investigated, including maximum equivalent stress and strain, specific energy and wear life which were closely related to the cutting forces and profile geometry of the cutter rings. A systematic method was employed to evaluate an overall performance index by incorporating objectives at all possible geological conditions. The Multi-objective & Multi-geologic Conditions Optimization (MMCO) program was then developed, which combined the updating of finite element model, system evaluation, finite element solving, post-processing and optimization algorithm. Finally, the MMCO was used to optimize the TBM cutters used in a TBM tunnel project in China. The results show that the optimization significantly improves the working performances of the cutters under all geological conditions considered.

Optimization of reaction conditions for the electroleaching of manganese from low-grade pyrolusite

In the present study, a response surface methodology was used to optimize the electroleaching of Mn from low-grade pyrolusite. Ferrous sulfate heptahydrate was used in this reaction as a reducing agent in sulfuric acid solutions. The effect of six process variables, including the mass ratio of ferrous sulfate heptahydrate to pyrolusite, mass ratio of sulfuric acid to pyrolusite, liquid-to-solid ratio, current density, leaching temperature, and leaching time, as well as their binary interactions, were modeled. The results revealed that the order of these factors with respect to their effects on the leaching efficiency were mass ratio of ferrous sulfate heptahydrate to pyrolusite 〉 leaching time 〉 mass ratio of sulfuric acid to pyrolusite 〉 liquid-to-solid ratio 〉 leaching temperature 〉 current density. The optimum conditions were as follows： 1.10：1 mass ratio of ferrous sulfate heptahydrate to pyrolusite, 0.9：1 mass ratio of sulfuric acid to pyrolusite, liquid-to-solid ratio of 0.7：1, current density of 947 A/m^2, leaching time of 180 min, and leaching temperature of 73°C. Under these conditions, the predicted leaching efficiency for Mn was 94.1%; the obtained experimental result was 95.7%, which confirmed the validity of the model.

Optimization of the operating conditions in a TiO_2/Fe_3O_4-SiO_2 photocatalytic reactor for the treatment of industrial wastewater containing Procion Red MX-5B

According to the design principle of the central composite experimental,the method of response surface analysis with three factors and three levels was adopted based on one factor test.A second-order quadratic equation for photocatalysis of Procion Red MX-5B was built.Response surface and contour were graphed with the decoloration rate of Procion Red MX-5B as the response value.Based on the analysis of the response surface plots and their corresponding contour plots,effects of pH value,irradiation time and catalyst loading were explored.By using this new method,the optimum decoloration condition was obtained as follows:pH value,1.3;irradiation time,49.9 min;catalyst loading,0.57 g/L.In the optimization,R-Squared and Adj R-Squared correlation coefficients for quadratic model were evaluated quite satisfactorily as 0.9310 and 0.8620,respectively.Under the optimum conditions established,the performance of 99.47% for color removal was experimentally reached.It was found that all factors considered have an important effect on the decolorization efficiency of Procion Red MX-5B.By the ANOVA analysis and model confirmation the optimal solution obtained using RSM was experimentally validated and credible with preferable instructional ability for experiments.

Pareto-Optimal Reinsurance Based on TVaR Premium Principle and Vajda Condition

Reinsurance is an effective risk management tool for insurers to stabilize their profitability. In a typical reinsurance treaty, an insurer cedes part of the loss to a reinsurer. As the insurer faces an increasing number of total losses in the insurance market, the insurer might expect the reinsurer to bear an increasing proportion of the total loss, that is the insurer might expect the reinsurer to pay an increasing proportion of the total claim amount when he faces an increasing number of total claims in the insurance market. Motivated by this, we study the optimal reinsurance problem under the Vajda condition. To prevent moral hazard and reflect the spirit of reinsurance, we assume that the retained loss function is increasing and the ceded loss function satisfies the Vajda condition. We derive the explicit expression of the optimal reinsurance under the TVaR risk measure and TVaR premium principle from the perspective of both an insurer and a reinsurer. Our results show that the explicit expression of the optimal reinsurance is in the form of two or three interconnected line segments. Under an additional mild constraint, we get the optimal parameters and find the optimal reinsurance strategy is full reinsurance, no reinsurance, stop loss reinsurance, or quota-share reinsurance. Finally, we gave an example to analyze the impact of the weighting factor on optimal reinsurance.

Optimization of Culture Conditions and Medium Composition for the Marine Algicidal Bacterium Alteromonas sp. DH46 by Uniform Design

Harmful algal blooms(HABs) have led to extensive ecological and environmental issues and huge economic losses.Various HAB control techniques have been developed,and biological methods have been paid more attention.Algicidal bacteria is a general designation for bacteria which inhibit algal growth in a direct or indirect manner,and kill or damage the algal cells.A metabolite which is strongly toxic to the dinoflagellate Alexandrium tamarense was produced by strain DH46 of the alga-lysing bacterium Alteromonas sp.The culture conditions were optimized using a single-factor test method.Factors including carbon source,nitrogen source,temperature,initial pH value,rotational speed and salinity were studied.The results showed that the cultivation of the bacteria at 28℃ and 180 r min-1with initial pH 7 and 30 salt contcentration favored both the cell growth and the lysing effect of strain DH46.The optimal medium composition for strain DH46 was determined by means of uniform design experimentation,and the most important components influencing the cell density were tryptone,yeast extract,soluble starch,NaNO3 and MgSO4.When the following culture medium was used(tryptone 14.0g,yeast extract 1.63g,soluble starch 5.0 g,NaNO3 1.6 g,MgSO4 2.3 g in 1L),the largest bacterial dry weight(7.36 g L-1) was obtained,which was an enhancement of 107% compared to the initial medium;and the algal lysis rate was as high as 98.4% which increased nearly 10% after optimization.

Optimization of cultural conditions for thermostable β-1,3-1,4-glucanase production by Bacillus subtilis ZJF-IA5

The optimization of cultural conditions for β-glucanase production by Bacillus subtilis ZJF-1A5 was investigated in flask trials. Temperature had great effect on β-glucanasc production which maximized atoptimal temperature of 37℃ and decreased significantly when temperature was over 37℃ . Charge quantity affected β-glucanasc production significantly. Adding oxygen vector N-dodecanc or acetic ether benefited β-glucanasc production, but it depended on the concentration and charge quantity. The results of fractional factorialdesign showed that age and size of inoculum and shaking speed were the key factors affecting β-glueanase production and the cultivation time span to reach the highest β-glucanasc activity. The optimal cultural conditionsfor p-glucanase production obtained with CCD were as follows: inoculum age and size (16 h, 3.82% (v/v)),shaking speed 210 r/rain, charge quantity of 30 mL in 250 mL flask and initial pH 7.0, cultured at 37℃ for 50 h. Repeated experimental results accorded with those predicted by a second-order polynomial model. The amount of p-glucanase, a-amylase and neutral protease produced by B subtills ZJF-1A5 was associated partially with cell growth. Those three enzymes' activities increased following the cell growth and increased signifi-cantly when cells entered the stationary phase.

Optimization of elastolysis conditions and elastolytic kinetic analysis with elastase from Bacillus licheniformis ZJUEL31410

The solubilization of elastin by Bacillus licheniformis elastase cannot be analyzed by conventional kinetic methods because the biologically relevant substrate is insoluble and the concentration of enzyme-substrate complex has no physical meaning. In this paper we report the optimization of elastolysis conditions and analysis of elastolytic kinetics. Our results indicated that the hydrolyzing temperature and time are very important factors affecting elastolysis rate. The optimized conditions using central composite design were as follows: elastolysis temperature 50 °C, elastase concentration 1×104 U/ml, elastin 80 mg, elas-tolytic time 4 h. Investigation of the effects of substrate content, elastase concentration and pH was also revealed that low or high elastin content inhibits the elastolysis process. Increasing elastase improves elastin degradation, but high elastase may change the kinetics characterization. Alkaline environment can decrease elastin degradation rate and pH may affect elastolysis by changing elastase reaction pH. To further elucidate the elastolysis process, the logistic model was used to elastolysis kinetics study showing clearly that the logistic model can reasonably explain the elastolysis process, especially under lower elastase concentration. However, there is still need for more investigations with the aid of other methods, such as biochemical and molecular methods.

Optimality conditions in set optimization employing higher-order radial derivatives

There are two approaches of defining the solutions of a set-valued optimization problem： vector criterion and set criterion. This note is devoted to higher-order optimality conditions using both criteria of solutions for a constrained set-valued optimization problem in terms of higher-order radial derivatives. In the case of vector criterion, some optimality conditions are derived for isolated （weak） minimizers. With set criterion, necessary and sufficient optimality conditions are established for minimal solutions relative to lower set-order relation.

A Note on the Guignard Constraint Qualification and the Guignard Regularity Condition in Vector Optimization

Some remarks are made on the use of the Abadie constraint qualification, the Guignard constraint qualifications and the Guignard regularity condition in obtaining weak and strong Kuhn-Tucker type optimality conditions in differentiable vector optimization problems.

Optimization of Screening Method for Feed Nutrition and Processing Conditions

On the basis of regressional relationship between nutritional indexes and technological conditions,when confronted with feed quality that contains multiple nutritional indexes,a comprehensive equation of evaluating feed quality was developed by using fuzzy mathematical method at first in this study,and then the optimum technological conditions were established by introduction of statistical frequency analysis method pursuant to the comprehensive evaluating equation mentioned above compared with conventional multi-aim nonlinear programming,this method can lead to easy solutions,and also can make adjustment of the importance of nutritional indexes to feed quality according to practical considerations.An example was given of soybean extruding to show how the method worked.