Optimization Criteria Research Articles

Clustering methods: To optimize or to not optimize?

Many clustering problems are associated with a particular objective criterion that is sought to be optimized. There are often several methods that can be used to tackle the optimization problem, and one or more of them might guarantee a globally optimal solution. However, it is quite possible that, relative to one or more suboptimal solutions, a globally optimal solution might be less interpretable from the standpoint of psychological theory or be less in accordance with some known (i.e., true) cluster structure. For example, in simulation experiments, it has sometimes been observed that there is not a perfect correspondence between the optimized clustering criterion and recovery of the underlying known cluster structure. This can lead to the misconception that clustering methods with a tendency to produce suboptimal solutions might, in some instances, be preferable to superior methods that provide globally optimal (or at least better locally optimal) solutions. In this article, we present results from simulation studies in the context of K-median clustering where departure from global optimality was carefully controlled. Although the results showed that suboptimal solutions sometimes produced marginally better recovery for experimental cells where the known cluster structure was less well-defined, capriciously accepting inferior solutions is an unwise practice. However, there are instances in which some sacrifice in the optimization criterion value to meet certain desirable constraints or to improve the value of one or more other relevant criteria is principled. (PsycInfo Database Record (c) 2024 APA, all rights reserved).

Training set optimization is a feasible alternative for perennial orphan crop domestication and germplasm management: an Acrocomia aculeata example.

Orphan perennial native species are gaining importance as sustainability in agriculture becomes crucial to mitigate climate change. Nevertheless, issues related to the undomesticated status and lack of improved germplasm impede the evolution of formal agricultural initiatives. Acrocomia aculeata - a neotropical palm with potential for oil production - is an example. Breeding efforts can aid the species to reach its full potential and increase market competitiveness. Here, we present genomic information and training set optimization as alternatives to boost orphan perennial native species breeding using Acrocomia aculeata as an example. Furthermore, we compared three SNP calling methods and, for the first time, presented the prediction accuracies of three yield-related traits. We collected data for two years from 201 wild individuals. These trees were genotyped, and three references were used for SNP calling: the oil palm genome, de novo sequencing, and the A. aculeata transcriptome. The traits analyzed were fruit dry mass (FDM), pulp dry mass (PDM), and pulp oil content (OC). We compared the predictive ability of GBLUP and BayesB models in cross- and real validation procedures. Afterwards, we tested several optimization criteria regarding consistency and the ability to provide the optimized training set that yielded less risk in both targeted and untargeted scenarios. Using the oil palm genome as a reference and GBLUP models had better results for the genomic prediction of FDM, OC, and PDM (prediction accuracies of 0.46, 0.45, and 0.39, respectively). Using the criteria PEV, r-score and core collection methodology provides risk-averse decisions. Training set optimization is an alternative to improve decision-making while leveraging genomic information as a cost-saving tool to accelerate plant domestication and breeding. The optimized training set can be used as a reference for the characterization of native species populations, aiding in decisions involving germplasm collection and construction of breeding populations.

H2 norm based parameter optimization of multiple tuned mass dampers for resonance suppression

Flexible dynamic behavior of ultra-precision motion stage significantly deteriorates control performance. To tackle this problem, this paper presents an [Formula: see text] norm based parameter optimization of multiple Tuned Mass Dampers (TMDs) for resonance suppression applied on linear flexible structures, assuming all parameters of multiple TMDs are independent, and considering locations of TMDs as variables. Linear flexible structures with multiple TMDs are modeled as a closed-loop control system through modeling in steps. Genetic algorithm is implemented employing [Formula: see text] norm as the optimization criterion. The effectiveness of the optimization is numerically verified on a free-free thin plate. The effects of uncertainties in TMDs parameters, linear flexible structure parameters, and TMDs failure on the vibration suppression effect are studied. The proposed modeling and optimization methods are promising for application to various flexible structures with provided modal frequencies and mode shape matrix.

On the Selection of Optimal Balanced Incomplete Block Design using Different Types of Designs

The choice of selecting the best among the types of balanced incomplete block designs (BIBDs) have brought about some controversies in combinatorial design. Prominent methods of constructing BIBD have been proposed by different authors, but none has been juxtaposed the designs with respect to type. In this paper, we proposed the adoption of the concept of optimality criteria such as: A-, D-, E- , and T – optimality criterion to select the best design based on their optimality values using a (15, 15, 7, 7, 3) simulated balanced incomplete block design. A dual design, residue design and derived design were selected as the major three types of BIBDs for investigation. The findings revealed that dual design is the best balanced incomplete block design based on its high optimal value. We discovered that residue and derived design obtained from the simulated balanced incomplete block design by method of block selection and intersection becomes a standard balanced incomplete block design.

Performance assessment of agricultural waste based eco‐friendly brake friction composites

AbstractThere has been growing interest in using sustainable and eco‐friendly products to produce engineering materials. For this purpose, composite material applications obtained from agricultural wastes are gaining popularity. This study examines the synergistic effect of rice husk and rice stalk wastes on the fade and recovery performance of brake friction composites. Brake friction materials were developed using rice husk and rice stalk separately and in two different weight percentages as a 5–10 ratio in the formulation. For comparison purposes, a reference brake pad using copper as a substitute and a commercially available brake pad were used. Various physical, mechanical and thermal properties were analyzed. The tribological behavior of friction composites was evaluated on the Krauss test device in line with the ECE R90 procedure. The worn surface properties were analyzed using scanning electron microscopy. Tribo test results of friction composites were taken as criteria for performance optimization. While the importance weight of the criteria was determined by AHP, the VIKOR method was used in the sorting of alternatives. The experimental results have revealed that rice husk‐added friction composites had a good coefficient of friction value with better fade and recovery performance compared to rice stalk‐added ones. Increasing the amount of rice husk and rice stalk in the formulation tended to decrease the fade performance; however, it has increased the wear rate and recovery properties. Optimization results have shown that the brake friction composite containing 5 wt % rice husk ranks first in meeting the desired tribological criteria.Highlights Cu‐free rice husk and rice stalk‐added friction composites were developed. Fibrous structure in the matrix developed the contact plateaus. Rice husk‐based tribo‐layer protected the composite from further wear damage. The addition of agro‐waste to friction composites exhibited good potential.

Structural state nonlinearity-based design and modification formulae of inerter-based systems

As structural safety emerges as a paramount concern and with the advancement in vibration control technology, a notable gap persists in accurately simulating structural state nonlinearity, especially within the field of inerter-based seismic control technology. Dealing with the need to upgrade the seismic performance of practical nonlinear structures, this study proposes a structural state nonlinearity-based design method for inerter-incorporated civil structures by incorporating the target seismic performance, structural nonlinearity level, and ground motion effects. By establishing mechanical models of inerter-based systems with straightforward parameters and a prototypical bilinear model for the primary structure, governing equations for inerter-incorporated structures were derived. Later, structural state nonlinearity-based design method for inerter-based systems, including optimization criteria and parameter distribution pattern, is elaborated. Simultaneously, this study also provides structural state nonlinearity-based design curves and modification formulae related to structural state nonlinearity and peak ground acceleration of earthquake. Validated using a 10-story multiple-degree-of-freedom (MDOF) structure subjected to earthquakes, the results highlight the effectiveness of the method, emphasizing its potential in controlling seismic responses of structures within the predetermined performance target. In addition, the absolute acceleration mitigation effect of inerter-based systems is investigated. The efficiency and robustness of the proposed method are also verified under near-fault and far-fault earthquakes. In essence, this research pioneers an approach in inerter-based design, bridging structural state nonlinearity, and potentially reshaping seismic control strategies to align with diverse structural states.

Clinical Outcomes and Left Ventricular Functional Remodeling after Extracorporeal Membrane Oxygenation Assisted Percutaneous Coronary Intervention in Patients with Ischemic Cardiomyopathy: A Single-Center Retrospective Observational Study of 76 Cases.

Ischemic cardiomyopathy (ICM) is a common condition that leads to left ventricular (LV) functional remodeling and poor prognosis. Extracorporeal membrane oxygenation (ECMO) can provide temporary circulatory support and facilitate percutaneous coronary intervention (PCI) in patients with ICM and hemodynamic instability. However, the impact of ECMO-assisted PCI on LV functional remodeling and clinical outcomes in ICM patients is unclear. We retrospectively analyzed 76 patients with ICM who underwent ECMO-assisted PCI at our institution between January 2013 and December 2022. We assessed the changes in LV functional remodeling using echocardiography at baseline and 12 months after the procedure. We also evaluated the incidence of major adverse cardiac and cerebrovascular events (MACCEs) and ECMO-related complications during hospitalization and at one-year follow-up. The mean baseline left ventricular ejection fraction (LVEF) was 29.98 ± 2.65%. The rate of complete revascularization was 58%. The median duration of ECMO support was 38.99 hours. The most common ECMO-related complications were bleeding (8%) and lower extremity ischemia (5%). The one-year mortality rate was 30%. The overall freedom from MACCEs at 12 months was 59% (95% confidence interval (CI): 49-71%). LVEF increased significantly after the procedure from baseline to 6 months, yet decreased slightly at 12 months, although it was still higher than the baseline value. Wall motion score index (WMSI), end-diastolic volume index (EDVI), and end-systolic volume index (ESVI) decreased significantly from baseline to 12 months, indicating an improvement in LV function and a reduction in LV size. In a high-volume tertiary center with extensive experience in advanced heart failure therapies and a dedicated ECMO team, ECMO-assisted PCI demonstrated feasibility and safety in patients with ischemic cardiomyopathy. However, the rate of complete revascularization was modest at 58%. Despite the high-risk profile of the patients, ECMO-assisted PCI was associated with a significant improvement in LV functional remodeling and a favorable 12-month survival rate. Further prospective studies are needed to confirm these findings and to identify the optimal patient and device selection criteria for ECMO-assisted PCI.

A phylogeographic analysis of the North American medicinal leech, Macrobdella decora (Say, 1824)

AbstractIn spite of their important roles in many ecosystems, data regarding population structure and biogeographic patterns of leeches are scarce. To begin to address this knowledge gap, we herein perform a phylogeographic analysis of the North American medicinal leech, Macrobdella decora (Say, 1824). A total of 224 M. decora specimens were collected from 35 localities across large swaths of USA and Canada and covering most of the known range of the species. Using four loci (mitochondrial cytochrome c oxidase subunit I [COI] and NADH dehydrogenase I [ND1], as well as nuclear 18S rRNA [18S] and 28S rRNA [28S]), we construct phylogenetic trees using several optimality criteria and superimpose geographic patterns onto the trees in order to tease out any potential structure among the populations. Rather surprisingly, given the large geographic range of the species and abundance of potential geographic barriers to gene flow, the analyses showed a conspicuous lack of structure among the different populations of M. decora. However, an AMOVA did show statistically significant differences between the genetic variation within populations and between populations (COI: FST = 0.65412, p < .00001; ND1: FST = 0.69245, p < .00001), which was largely driven by only 6 out of the 35 populations, and indicated a potential barrier for dispersal across the Appalachian Mountains. Finally, a Mantel test showed a weak, but significant, correlation between geographic distance and genetic distance (COI: r = 0.209, p = .027; ND1: r = 0.1289, p = .030); however, this correlation was primarily driven by a single locality. The overall weak structure suggests that M. decora is panmictic throughout its range, and we discuss this in light of previous population level studies in both bloodfeeding and non‐bloodfeeding species, concluding that the lack of structure in M. decora might be due to its high capacity for dispersal via hosts.

Nocturnal Hypoxemia Is Associated with Sarcopenia in Patients with Chronic Obstructive Pulmonary Disease.

Rationale: Chronic obstructive pulmonary disease (COPD) is the third leading cause of death worldwide. Our previous studies have identified that nocturnal hypoxemia causes skeletal muscle loss (i.e., sarcopenia) in invitro models of COPD. Objectives: We aimed to extend our preclinical mechanistic findings by analyzing a large sleep registry to determine whether nocturnal hypoxemia is associated with sarcopenia in patients with COPD. Methods: Sleep studies from patients with COPD (n = 479) and control subjects without COPD (n = 275) were analyzed. Patients with obstructive sleep apnea, as defined by apnea-hypopnea index ⩾ 5, were excluded. Pectoralis muscle cross-sectional area (PMcsa) was quantified using computed tomography scans performed within 1 year of the sleep study. We defined sarcopenia as less than the lowest 20% residuals for PMcsa of control subjects, which was adjusted for age and body mass index (BMI) and stratified by sex. Youden's optimal cut-point criteria were used to predict sarcopenia based on mean oxygen saturation during sleep. Additional measures of nocturnal hypoxemia were analyzed. The pectoralis muscle index (PMI) was defined as PMcsa normalized to BMI. Results: On average, males with COPD had a 16.6% lower PMI than control males (1.41 ± 0.44 vs. 1.69 ± 0.56 cm2/BMI; P < 0.001), whereas females with COPD had a 9.4% lower PMI than control females (0.96 ± 0.27 vs. 1.06 ± 0.33 cm2/BMI; P < 0.001). Males with COPD with nocturnal hypoxemia had a 9.5% decrease in PMI versus COPD with normal O2 (1.33 ± 0.39 vs. 1.47 ± 0.46 cm2/BMI; P < 0.05) and a 23.6% decrease compared with control subjects (1.33 ± 0.39 vs. 1.74 ± 0.56 cm2/BMI; P < 0.001). Females with COPD with nocturnal hypoxemia had an 11.2% decrease versus COPD with normal O2 (0.87 ± 0.26 vs. 0.98 ± 0.28 cm2/BMI; P < 0.05) and a 17.9% decrease compared with control subjects (0.87 ± 0.26 vs. 1.06 ± 0.33 cm2/BMI; P < 0.001). These findings were largely replicated using multiple measures of nocturnal hypoxemia. Conclusions: We defined sarcopenia in the pectoralis muscle using residuals that take into account age, BMI, and sex. We found that patients with COPD have a lower PMI than patients without COPD and that nocturnal hypoxemia was associated with an additional decrease in the PMI of patients with COPD. Additional prospective analyses are needed to determine a protective threshold of oxygen saturation to prevent or reverse sarcopenia due to nocturnal hypoxemia in COPD.

Innovative solutions to frontier exploration in Eastern Mediterranean salt basins

The Eastern Mediterranean region is expected to hold large undiscovered natural gas resources that could address critical energy supply needs of the surrounding countries. However, exploration is challenged due to regional geologic complexities. The combination of Messinian salt structures and diapiric shales in offshore Cyprus and Egypt often causes strong attenuation of seismic energy and severe seismic imaging illumination shadows, which lead to large uncertainty regarding subsalt reservoir presence and the underlying petroleum system assessment. As part of the efforts to solve these imaging challenges, we present innovative seismic acquisition solutions to address key exploration risks such as reservoir presence. A one-sided wide-azimuth configuration consisting of one streamer vessel and one dedicated source vessel operating under the simultaneous-source mode was used to acquire data in a cost-effective way. An 8000 in3 low-frequency source was used on both vessels to provide higher energy output in the low-frequency bands of less than approximately 4 Hz. Our preliminary results show evidence of seismic image uplift due to enhanced acquisition and processing, leading to greater confidence in interpretation, which is critical for positioning wells in future drilling campaigns. This paper highlights seismic testing results undertaken to design a large exploration-scale seismic survey in the Eastern Mediterranean and early results from the execution of that program. This will help better refine optimal design criteria for future acquisition, signal processing, and imaging in order to unlock additional resources beneath complex salt provinces and identify where additional imaging needs still exist.

P052 OPTIMAL ADRENAL VEIN SAMPLING LATERALIZATION CRITERIA FOR DIAGNOSIS OF UNILATERAL PRIMARY ALDOSTERONISM USING ALDOSTERONE CONCENTRATION MEASURED BY LC-MS/MS POST-ACTH STIMULATION

Background: Primary aldosteronism (PA) is characterized by excessive, autonomous secretion of aldosterone from one or both adrenal glands. Identification of unilateral disease and surgical resection can lead to cure, and is dependent on accurate criteria for lateralization of excess aldosterone during adrenal vein (AV) sampling (AVS). Current evidence for AVS lateralization cut-offs using plasma aldosterone concentration (PAC) measured by LC-MS/MS and post-surgical outcomes is limited. Aim: To determine optimal cut-off criteria to define lateralization of PA on AVS based on PAC measured by LC-MS/MS post-ACTH stimulation and post-surgical outcomes data. Methods: This study involved 60 subjects with PA who had PAC measured by LC-MS/MS post ACTH-stimulation during bilaterally-cannulated AVS, underwent unilateral adrenalectomy between July 2015-July 2021 and were followed up for ≥6 months. AVS lateralization parameters (lateralization index [LI; dominant PAC/cortisol(AV) ÷ non-dominant PAC/cortisol(AV)], contralateral suppression index [CSI; non-dominant PAC/cortisol(AV) ÷ PAC/cortisol(Peripheral Vein)], lateralization ratio [LR; dominant PAC/cortisol(AV) ÷ PAC/cortisol(Peripheral Vein)] and post-surgical outcome data were examined. Complete biochemical remission (CR) of PA post-surgery was defined using PASO International Consensus Criteria. Receiver operating characteristic (ROC) analysis was performed to determine optimal cut-offs for LI, CSI and LR based on cases who achieved CR of PA post-surgery (n=55) vs those who did not (n=5). Results: Optimal cut-off LI during ACTH-stimulated AVS to identify unilateral PA cases who achieved CR post-surgery was 5.1 (AUC=0.92, P&lt;0.001; 92.7% sensitivity, 80.0% specificity) while the optimal cut-off for CSI was 0.6 (AUC=0.887, P&lt;0.001; 82.1% sensitivity, 100.0% specificity), and for LR was 3.3 (AUC=0.695, P=0.202; 80.0% sensitivity, 80.0% specificity). Cases with LR of 2.0-3.3 also achieved CR post-surgery if it was associated with CSI &lt;0.6. Conclusion: LI of &gt;5.1 provides high sensitivity and CSI &lt;0.6 high specificity for identification of surgically curable unilateral PA during ACTH-stimulated AVS when PAC is analyzed by LC-MS/MS.

Iterated rational quadratic kernel - High-order unscented Kalman filtering algorithm for spacecraft tracking

The high-speed development of space defense technology demands a high state estimation capacity for spacecraft tracking methods. However, reentry flight is accompanied by complex flight environments, which brings to the uncertain, complex, and strongly coupled non-Gaussian detection noise. As a result, there are several intractable considerations on the problem of state estimation tasks corrupted by complex non-Gaussian outliers for non-linear dynamics systems in practical application. To address these issues, a new iterated rational quadratic (RQ) kernel high-order unscented Kalman filtering (IRQ-HUKF) algorithm via capturing the statistics to break through the limitations of the Gaussian assumption is proposed. Firstly, the characteristic analysis of the RQ kernel is investigated in detail, which is the first attempt to carry out an exploration of the heavy-tailed characteristic and the ability on capturing high-order moments of the RQ kernel. Subsequently, the RQ kernel method is first introduced into the UKF algorithm as an error optimization criterion, termed the iterated RQ kernel-UKF (RQ-UKF) algorithm by derived analytically, which not only retains the high-order moments propagation process but also enhances the approximation capacity in the non-Gaussian noise problem for its ability in capturing high-order moments and heavy-tailed characteristics. Meanwhile, to tackle the limitations of the Gaussian distribution assumption in the linearization process of the non-linear systems, the high-order Sigma Points (SP) as a subsidiary role in propagating the state high-order statistics is devised by the moments matching method to improve the RQ-UKF. Finally, to further improve the flexibility of the IRQ-HUKF algorithm in practical application, an adaptive kernel parameter is derived analytically grounded in the Kullback-Leibler divergence (KLD) method and parametric sensitivity analysis of the RQ kernel. The simulation results demonstrate that the novel IRQ-HUKF algorithm is more robust and outperforms the existing advanced UKF with respect to the kernel method in reentry vehicle tracking scenarios under various noise environments.

Dynamic Topology Optimization with Multiple Materials Based on Impedance Mismatching of Wave

Topology optimization with multiple materials studies were commonly adopted to address the issues of complex structures and dynamic loading cases. However, the perturbation excited from the transient load will be propagated and change the local stress level in the structure. Therefore, it is indispensable to consider impedance mismatching of waves at the interfaces of multi-materials layers in the optimization model. In this work, the wave impedance will be regarded as constraint conditions and assessment indicators in the optimization design. Firstly, a multi-material interpolation model using SIMP models is established based on the variable density method. Secondly, the optimization process is applied by combining using Newmark-[Formula: see text] method which is used to solve the dynamic response, an adjoint variable method for sensitivity study, and an optimization criterion method employed to update the design variables. Finally, the simulation examples are used to analyze the influence of impedance mismatching and volume fraction for multilayer dielectric on response. The results indicate that the position and content of the Polymethyl Methacrylate (PMMA) plays a key role in reducing vibration and buffering action.

Substantiating the reliability conditions for the production process at metallurgical enterprises through the fault-tolerant functioning of the system «extraction of raw materials – technological railroad routes – metallurgical production»

The object of this study is the process of formation of insurance reserves at enterprises in the metallurgical industry. Under conditions of uneven supply of raw materials to metallurgical enterprises due to disruption of the transportation process or other reasons, there is a need to create insurance stocks in order to ensure the continuity of production. At the same time, it is necessary to take into account existing restrictions, such as the limited capacity of railroad sections and the impossibility of organizing parallel movement of trains, etc. The presence of these limitations makes it impossible to use classical methods for solving similar problems, such as linear programming. Therefore, to resolve the task, a simulation model was built, based on the discrete-event principle in the AnyLogic University Researcher environment using Oracle libraries and the Java SE compiler. With the help of the model, the process of rotation of dispatch routes at the railroad yard with multiple suppliers and one consignee was formalized. The optimization criterion was chosen to be the minimum deviations of fluctuations in reserves of iron ore concentrate and coke. Analysis of the simulation results revealed that the optimal size of the fleet of railroad routes on the selected rotation polygon is 30 units; at the same time, their utilization rate will be 65 %. It was also established that fluctuations in raw material stocks have a «natural character», which is confirmed by the normal distribution of the density of stock volumes. Under these conditions, the value of fluctuations in the volumes of the main raw materials will be ±13115 t/day for iron ore concentrate, and ±5298 t/day for coke. Reducing the range of fluctuation of raw materials volumes could make it possible to optimize the costs of creating stocks and streamline the transport work of the enterprise for providing raw materials

Construction of weighted efficiency optimal designs for experiments with mixtures

This paper presents a weighted efficiency optimality criterion to obtain a compound optimal design that balances two different optimality objectives. An equivalence theorem and a search algorithm for a concave-concave combination of criteria for finding the weighted efficiency optimal design are given and applied to the Scheffé mixture model.

Bayesian estimation of some reliability characteristics for Nakagami model using adaptive progressive censoring

The focus of this research is to clarify both conventional and Bayesian parametric estimation methods for the Nakagami distribution making use of adaptive progressive Type II censored data. From a classical estimation perspective, two estimation methods are considered: maximum likelihood and least squares estimations. Along with the model parameters, three reliability metrics are estimated using point and interval estimation. Bayes estimates with gamma and inverse gamma priors are investigated by employing the squared error loss function. The Bayes computations are created using the Markov Chain Monte Carlo technique. Moreover, the classical and Bayesian intervals are also taken into consideration. For evidence of the effectiveness of the given methodologies, a simulation study and three applications from the physics, chemistry, and engineering domains are explored. Lastly three optimality criteria are applied to the stated data sets to pick the best progressive censoring strategy.

The importance of A-site cation chemistry in superionic halide solid electrolytes

Halide solid electrolytes do not currently display ionic conductivities suitable for high-power all-solid-state batteries. We explore the model system A2ZrCl6 (A = Li, Na, Cu, Ag) to understand the fundamental role that A-site chemistry plays on fast ion transport. Having synthesised the previously unknown Ag2ZrCl6 we reveal high room temperature ionic conductivities in Cu2ZrCl6 and Ag2ZrCl6 of 1 × 10−2 and 4 × 10−3 S cm−1, respectively. We introduce the concept that there are inherent limits to ionic conductivity in solids, where the energy and number of transition states play pivotal roles. Transport that involves multiple coordination changes along the pathway suffer from an intrinsic minimum activation energy. At certain lattice sizes, the energies of different coordinations can become equivalent, leading to lower barriers when a pathway involves a single coordination change. Our models provide a deeper understanding into the optimisation and design criteria for halide superionic conductors.

Historical evolution of structural optimization techniques for steel skeletal structures including industrial design applications

This study covers the review of algorithms developed for the optimum design of steel skeletal structures from the first article published in 1960 until to date. The paper initially describes the mathematical formulation of a simple truss structural design problem. The early optimum design algorithms that were based on mathematical programming techniques where the design variables are assumed to be continuous are reviewed. The optimum design of steel framed structures necessitates the selection of steel profiles from the standard list of discrete steel sections and requires the satisfaction of design code provisions. Both mathematical programming and optimality criteria techniques need more capability to produce solution to this type of optimum design problems. Soft computing techniques emerged recently provide solution directly without needing any approximation. These techniques are classified and reviewed and their use in obtaining the optimum solution of actual industrial steel design applications is given.

OPTIMIZATION AND FORECASTING OF A SECURITIES PORTFOLIO BASED ON MACHINE LEARNING METHODS

The article is devoted to the demonstration and analysis of the possibilities of connecting the Markowitz model, which is a classical model for forming a portfolio of securities, and forecasting methods based on machine learning data. The relevance of the chosen topic is justified by the fact that the use of machine learning methods makes it possible to simplify the activities of financial sector workers and the work of professional stock market players, as well as reduce the complexity of interpreting mathematical models and methods of their construction for private investors. The purpose of this work is to use machine learning methods to solve the problem of building an optimal securities portfolio and predicting its behavior. Tasks: - build a Markowitz model based on the selected data; - to build an optimal portfolio based on the proposed optimality criterion; - offer a time series forecast; - to assess the adequacy of the constructed model; - combine the Markowitz model, which belongs to the class of widely known classical models, with the construction of a prediction based on machine learning. Methods and models: machine learning methods are used in the work, the Markowitz model is built based on the selected data, then the Markowitz model is combined with the construction of a forecast based on machine learning. Research results: the optimal portfolio for AXP has been built and its forecast has been fulfilled. The formation of the portfolio was based on the Markowitz model. The data obtained were tested for adequacy and showed fairly good results. A portfolio was built, the optimality criterion of which is the ratio of average profitability and volatility of profitability (maximizing average profitability while minimizing its volatility). The Markowitz model, which belongs to the class of widely known classical models, was combined with the construction of a prediction based on machine learning.

An Ideal Four-factor Components Mixture Experiment Design Based on Prominent Optimality Criteria at Level Two

Aim: Mixture experiment designs are essential tools that need to be determined prior to conducting any mixture experiment in any field of study. The primary goal of these types of experiments are optimization that is either maximizing the profit/produce or minimizing the cost of production. Study Design: Any researcher anticipating to do any research work on the mixture experiment will not evade to talk about the design that he or she is likely to use. The common of such designs being either Simplex Lattice Design (SLD) or Simplex Centroid Design (SCD). Methodology: The choice of such design is wholly based on the optimality criteria employed. The classical of these criteria include on D-Determinant criterion, A-Average variance criterion, E- Eigen value criterion and T- Trace optimality criterion usually denoted as D-, A-, E- T- criteria. They are also known as prominent criteria. Results: This paper considered four-factor components at order two. The penalized moment matrices obtained from the information matrices whose primary source was the design points gave the values of the criteria aforementioned. These values were ranked independently with the least average rank termed as the best design. Conclusion: The {4,4} Simplex Lattice Design had the lowest rank value of 1.0 as compared to the other designs. This design is therefore to be used in any research work considering four factors when only two of factors are to be employed.