Simplex Optimization Research Articles

Methods of Multi-Criteria Optimization of Technological Processes in a Fuzzy Environment Based on the Simplex Method and the Theory of Fuzzy Sets

Many modern technological objects in practice are characterized by the uncertainty of the initial information necessary for their management. Recently, one of the pressing scientific and practical problems is the development of new optimization methods for controlling the operating modes of such objects in a fuzzy environment. In this regard, the objective of this study is to develop methods of multi-criteria optimization in a fuzzy environment by modifying the simplex method and various optimality principles based on fuzzy mathematics methods. The methodology of the proposed study is based on a hybrid approach, which consists of the integrated use and modification of simplex methods and optimization methods with various optimality principles for working in a fuzzy environment. The main results are as follows: a simplex method of multi-criteria optimization of immeasurable criteria (here, we are talking about the impossibility of physical measurements of criteria, the values of which are estimated by decision maker); a theorem on the convergence of the solution sequence obtained using the proposed method to the minimum value of the criteria; a heuristic method based on a modification for fuzziness and a combination of the maximin and Pareto optimality principles, which allows effectively solving multi-criteria optimization problems in a fuzzy environment. The heuristic method proposed will be used to solve a real production problem—optimization of the technological process of benzene production.

Optimization of CZM parameters of Norway spruce tested in mode I using multistart simplex method

The paper addresses the advanced fracture analysis of the SEN-TPB test on Norway Spruce in three anatomical directions: tangential (T), radial (R) and tangential–radial (TR). It utilizes reverse engineering to obtain cohesive zone model (CZM) parameters, which are then compared to the experimental values obtained using the compliance-based beam method (CBBM) and additional standard material tensile tests perpendicular to the grain. The optimization employs force–displacement curves to find their optimal fit using the multistart simplex optimization method. Results indicate that CZM modeling can be relatively problematic when realistic values are used; however, the best agreement with experimental data is observed for the group of cracks in the TR direction. A fundamental issue with CZM modeling in the elastic part has been identified and discussed. The sensitivity of the problem to various parameters was assessed, and an energy balance in the CZM at Fmax was performed. This work contributes to knowledge about realistic modeling of the interface and a fundamental understanding of fracture in wood.

Nonlinear analysis and control with nonlinear driving terms for small-emittance storage ring

Storage rings that use the hybrid multi-bend achromat (MBA) lattice concept [1] have been realized. The main characteristics of hybrid MBA as a typical lattice for a 4th generation storage ring are to adopt two large dispersion bumps in cell, and to make a -I-transformation between two dispersion bumps to cancel nonlinear effects. To increase the effectiveness of nonlinear control, analytical investigation of nonlinear phenomenon is essential. In this paper, we describe analytical investigation with a nonlinear driving term and simple model. We obtained similar results to the existing time-consuming MOGA optimization, but use a simplex optimizer with fewer nonlinear control knobs.

Estimation of constitutive parameters for shape memory polymer thermo-mechanical cycle by an integrated simulation and inverse optimization method

In this work, a method for inverse optimization of shape memory polymer material parameters is proposed to determine the intrinsic model parameters more quickly and accurately for simulated experimental test analysis. First, the basic mechanical properties of the material are characterized experimentally and the parameters of the generalized Maxwell model based on SMP material are fitted. Then, a joint simulation inversion optimization method is built in the ISIGHT-MATLAB-ABAQUS integrated environment to optimize the time domain Prony series parameters using downhill simplex optimization algorithm. The results show that the average errors of the stress curves before and after the optimization of the cooling solid phase and the experimental results are 0.31 MPA and 0.23 MPA, respectively, and the average errors of the strain curves in the warming recovery phase are 1.70% and 0.40%, respectively. After the inversion optimization, the average errors of the stress curves are optimized by 25.8% and the average errors of the strain curves are optimized by 76.5%. This method makes the simulation results more stable with the experimental results, which can effectively reduce the experimental cost and promote the shape memory property of SMP to be widely used in engineering.

Heat Loss Optimization of a Building with Different Window to Wall Area Ratios

Abstract The types of glass and exterior walls and the window-to-wall ratio (WWR) on building façades play a major role in heat losses that occur in every type of building, residential or commercial. The opaque and transparent surfaces of buildings have an important role in terms of both energy losses and energy gains. Windows are the parts of the building envelope where heat losses mostly occur. As the WWR increases on the façades of a building, heat losses increase, but heat gains from solar energy also increase, which assists in free heating of the building. In this study, a detached residential building located in Antalya, Turkey, a province with hot–humid climatic conditions, has been examined. A series of simulations were carried out to detect the effects of WWRs and different glass, frame, and exterior wall types on heat losses of the building. The heat loss values obtained from these simulations were processed by using a special mechanical installation calculation software. Simulations were performed for apartment rooms with levels of WWR ranging from 30 to 60 % of the wall areas facing the façade. In order to minimize heat loss, double-pane glass (or double-glazed glass) was used instead of single-pane glass. The aim of this study was to find the optimum value in terms of applicability and economy. The optimum value was calculated by minimization according to both the linear graphical method and the dual simplex optimization method. The values found in both methods were compared and interpreted. It is believed that the optimized glass, frame, joinery, and exterior wall parameters, which are influential to the energy performance of the building, will make a positive contribution to the architectural design phase in addition to improving the energy efficiency of existing buildings.

Enhancing understanding of moisture diffusion in wood: numerical approach and diffusion parameter optimization

Wood, an environmentally friendly construction material, is characterized by a critical attribute that significantly influences its mechanical properties and durability: its moisture absorption behavior. This study expands upon an existing one-dimensional model to develop an innovative two-dimensional numerical framework for simulating moisture propagation within wood. Utilizing the finite difference method, this approach offers a more detailed analysis of moisture behavior in wood structures. The research adopts an inverse modeling technique, integrating a simplex optimization algorithm programmed in VBA software. This algorithm is employed to deduce diffusion parameters from the evolution of moisture content over time. Focusing on the analysis of moisture diffusion parameters, the study examines both longitudinal and transverse directions in two temperate species (Beech and Fir) and two tropical species (Moabi and Ozigo). The findings provide insightful data on the hygroscopic behavior of these woods, revealing significant distinctions between temperate and tropical species. This research offers valuable information for the application of these wood species in construction and other fields, enhancing the understanding of their moisture-related properties.

Optimal CT windowing on low-monoenergetic images using a simplex algorithm-based approach for abdominal inflammatory processes

Background:ObjectivesTo determine optimal window settings for conspicuity of abdominal inflammatory processes on 50 keV low-monoenergetic images derived from dual-energy spectral CT (DECT). MethodsA retrospective study of 30 patients with clinically proven pancreatitis (15/30) or pyelonephritis (15/30) with inflammatory lesions visible on DECT scans were selected to serve as reference populations. 50 keV low-monoenergetic images in the portal venous phase were iteratively evaluated by 6 abdominal radiologists in twenty-one different windows (7-350HU center; 120-580HU width), selected using a simplex optimization algorithm. Each reader graded the conspicuity of the parenchymal hypodense lesions and image background quality. Three-dimensional contour maps expressing the relationship between overall reader grade and window center and width were constructed and used to find the ideal window for inflammatory pancreatic and renal processes and the image background quality. Finally, 15 appendicitis cases were reviewed on optimal pancreas and kidney windows and the manufacturer recommended conventional abdominal window settings for conventional imaging. ResultsConvergence to optimal windowing was achieved based upon a total of 3,780 reads (21 window settings × 6 readers × 15 cases for pancreas and kidney). Highest conspicuity grade (>4.5 ± 0.0) for pancreas inflammatory lesions was seen at 116HU/430HU, whereas hypodense pyelonephritis had highest conspicuity at 290HU/570HU. This rendered an ideal “compromise” window (>4 ± 0.2) of 150HU/450HU which differed substantially from conventional manufacturer recommended settings of 50HU/380HU (2.1 ± 1.0, p = 0.00001). Appendix mucosal enhancement was best visualized at manufacturer settings. ConclusionsOptimal visualization of inflammatory processes in abdominal organs on 50 keV low-monoenergetic images may require tailored refinement of window settings.

A MOSFET EMC modeling method based on electrical characteristic measurement and simplex optimization and particle swarm optimization

SummaryMetal oxide semiconductor field effect transistors (MOSFETs) are widely used in various power electronic systems, and the establishment of the electromagnetic compatibility (EMC) model for MOSFETs is crucial for EMC analysis of these systems, especially high‐frequency switching circuits. In this paper, a MOSFET EMC modeling method is proposed based on electrical characteristic measurement, simplex optimization, and particle swarm optimization (PSO), to make MOSFET models meet both functionality and EMC analysis requirements. First, systematic methods for extracting SPICE parameters based on physical MOSFETs are presented, including a proposed curve‐fitting method based on PSO for extracting the CDS‐VDS and ID‐VGS characteristic parameters. Second, parametric influence analyses are conducted on some important model parameters, and the law that these parameters affect the EMC of MOSFETs is obtained. Finally, the preliminary MOSFET model was optimized comprehensively using the simplex method. The measured and simulated results are in good agreement in both time domain and frequency domain. It proves that the established model meets the requirements for model accuracy in terms of both EMC and functionality. Therefore, the proposed EMC modeling method is feasible.

Optimal resource allocation for multiple shop floor tasks in collaborative assembly

Industries are adopting advanced technologies to attain the goals of the manufacturing system and the demands of the current industrial era. A collaborative and flexible manufacturing system that integrates human intelligence with a robotic workforce leads to customized automation and reinforces the safety of the human workforce. This system creates a flexible platform to assemble the parts as per the requirements and it supports reconfigurability with respective upcoming technologies. The proposed work involves an approach of a human-robot collaborative task allocation (HRTA) system. The HRTA can concern the demand for new product variants in the market and the upgradation of new technologies in the existing manufacturing system. The proposed work is organized into two phases such as resource allocation, and resource estimation using an assembly line balancing approach. The resource allocation approach is developed to identify the appropriate resource(human/robot) for each assembly task using the Nelder-Mead simplex optimization approach. Further assembly line balancing technique is used to quantify the number of resources to minimize the total idle time. The performance of the proposed method is corroborated by implementing it on an industrial case study and the obtained results are discussed with suitable illustrations.

A bipolar junction transistor EMC modeling method based on physical characteristic measurement and simplex optimization

A bipolar junction transistor EMC modeling method based on physical characteristic measurement and simplex optimization

Characterizing pulse reverse-pulse uranium recovery in molten LiCl-KCl with intermittent electrochemical impedance spectroscopy

In this work, EIS was applied to characterize the temporal recovery of uranium from UCl4 onto a tungsten electrode in molten LiCl-KCl salt between sets of pulse reverse-pulse (PRP) deposition steps. Impedance measurements were fitted to an equivalent circuit (EC) model of the electrode interface using Simplex optimization to calculate the double layer capacitance, charge transfer resistance, Warburg impedance, and CPE-restricted diffusion. Diffusion of uranium towards the electrode surface dominated the surface interactions for the first 80 cycles, followed by a transition to kinetic control for the remaining 520 cycles. A decrease in the Warburg impedance showed depletion of uranium from the bulk melt, which was confirmed to be a 52.5% reduction through ICP-OES. Reduction in the phasance from CPE-restricted diffusion suggested the formation of pores in the uranium deposits, which was confirmed through SEM characterization.

RED WoLF hybrid energy storage system: Algorithm case study and green competition between storage heaters and heat pump

Green house gases reduction is critical in current climate emergency and was declared as major target by United Nations. This manuscript proposes the progressive adaptive recursive multi threshold control strategy for hybrid energy storage system that combines thermal storage reservoirs, heat pumps, storage heaters, photovoltaic array and a battery. The newest control strategy is tested in numerical experiment against primal dual simplex optimisation method as benchmark and previous iterations of RED WoLF threshold approaches. The proposed algorithm allows improvement in reduction of CO2 emissions by 9% comparatively to RED WoLF double threshold approach and by 26% comparatively to RED WoLF single threshold approach. Besides, the proposed technique is at least 100 times faster than linear optimisation, making the algorithm applicable to edge systems. The proposed method is later tested in numerical experiment on two measured datasets from Luxembourg school and office, equipped with batteries and ground source heat pumps. The system allows the reduction of CO2 emission and improvement of self-consumption, size reduction of the photovoltaic array installed at the facilities by at least by half as well as substituting battery storage by thermal storage, reducing the initial investment to the system. Intriguingly, despite 3.6 times difference in efficiency between heat pumps and storage heaters, the system equipped with latter have potential to achieve similar performance in carbon reduction, suggesting that energy storage have more prominent carbon reduction effect, than the power consumption, making cheaper systems with storage heaters a possible alternative to heat pumps.

Integer Algorithm: A Useful Tool for Fault Diagnosis of Analog Circuits

This paper presents an efficient numerical method to solve systems of nonlinear algebraic equations. The method uses a homotopy simplicial approach associated with an integer algorithm. The integer algorithm is discussed in detail and supplemented with original procedures that play an essential role during computation. The fundamental problem of initial simplex generation was solved using the bounded variable simplex optimization method. Efficient root finding of nonlinear equations has wide applications in numerical mathematics and various engineering problems. The proposed method was applied to solve nonlinear equations that arise during the diagnostics of multiple parametric faults in electronic circuits. Circuits made with surface mount technology were considered, as well as circuits designed in complementary metal-oxide-semiconductor and bipolar technology. A universal diagnostic procedure enables testing different circuit classes using standard measurement equipment. Laboratory and numerical experiments demonstrate that the proposed diagnostic procedure is effective.

Chemometrics-assisted-liquid phase microextraction based on deep eutectic solvents followed by gas chromatography for determination of polycyclic aromatic hydrocarbons in aqueous and juice samples

In the present study, an optimized liquid-phase microextraction technique based on the deep eutectic solvent (LPME-DES) followed by gas chromatography-flame ionization detector (GC-FID) is developed to determine 13 carcinogenic polycyclic aromatic hydrocarbons (PAHs) in water and juice samples. In this regard, central composite design (CCD) was used to design, multiple linear regression (MLR) to model, and Nelder-Mead simplex optimization to optimize the effective LPME-DES factors. The optimum values for DES volume, temperature, extraction time, and salt amount were 112 µL, 72 °C, 9.14 min, and 2.5% (w/v), respectively. Afterward, multivariate calibration based on partial least squares regression (PLSR) was developed in the concentration range of (0.2–70 ng mL−1) and its performance in terms of sensitivity (SEN), analytical sensitivity (γ), limit of detection (LOD), limit of quantitation (LOQ), and root mean square error of prediction (RMSEP) was compared with classical univariate calibration. Finally, to test the applicability of the proposed method in real samples, sea/well waters and orange/apple juices were analyzed at 10 and 30 ng mL−1 concentration levels. The relative recoveries were obtained in the range of 66.5%–130.4% for 10 ng mL−1 and 65.4%–124.5% for 30 ng mL−1. In conclusion, the developed method based on LPME-DES combined with GC-FID and chemometric techniques can be used as an efficient method for determining PAHs in real matrices.

Efficiency-based design optimization of the H-type Darrieus wind turbine with fixed guiding-walls

In this work, metamodeling was performed to conduct efficiency-based design optimization (EBDO) of an H-rotor VAWT coupled with fixed guiding-walls surrounding its rotor. A design of experiments (DoE) created sampling points from the desired design space. Kriging generated surrogate models using input and output pairs calculated by CFD analyses. The Nelder–Mead Downhill Simplex optimization technique was used to determine the optimal design which satisfied the stated constraints. An estimated level of uncertainty was assigned to each random design variable for the efficiency analyses. Designing of guiding walls were considered, with different geometrical parameters. The results of the surrogate model were compared with those of the CFD, and an optimal solution was selected. The Open Darrieus VAWT and Optimal Darrieus​ VAWT with guiding-walls comparison revealed a considerable improvement of up to 177% at λ=3. It was evident that the enhancement in power coefficient due to augmentation of airflow velocity when VAWT is equipped with guiding walls. As a result, the placement and formation of the guiding walls has a significant role in the amount of power produced.

Data-adaptive kernel clustering with half-quadratic-based neighborhood relationship preservation

Kernel learning approaches have recently attracted much attention to improve the performance of clustering tasks. Although extensive studies have attempted to suppress the adverse influence of less confident samples, they cannot sufficiently take into account the different importance of samples in kernel learning. To alleviate this issue, our proposed algorithm utilizes a half-quadratic (HQ) paradigm to automatically determine the reliability of samples and to adaptively capture neighborhood relation information according to sample importance. We model an effective parameter-free kernel exploration by exploiting both global and HQ-based local data relationships. This paper designs an effective Alternative Direction Method of Multiplier (ADMM)-based algorithm to convert the fourth-order objective function to the second-order one, and offers an efficient closed-form solution for a simplex optimization problem based on the closest point theorem. Moreover, we prove the convergence of our proposed algorithm in theoretical and experimental fashions. Comprehensive experiments on benchmark and real-world datasets demonstrate that on average, the presented framework against competitors can improve clustering performance in terms of accuracy, NMI, and purity by about 5%–22%, verifying the efficacy and superiority of our proposed method.

A Factorial Design and Simplex Optimization of a Bismuth Film Glassy Carbon Electrode for Cd(II) and Pb(II) Determination

This work presents the use of a fractional two-level factorial design to determine the influence of different factors involved in the development of the square-wave anodic stripping voltammetry method. A fractional factorial design of eight different electrodes using a bismuth film glassy carbon electrode (BiFGCE) was formulated, and the impact of the factors on the analytical performance of the electrodes was determined. The impact of six factors (deposition potential, deposition time, potential step, amplitude, frequency, and the concentration of Bi(III)) was tested for Cd(II) and Pb(II) determination. Next, simplex optimization was carried out to improve the electroanalytical performance of the BiFGCE. The objective of simplex optimization was to simultaneously obtain a low limit of quantification, a wide linear concentration range, high sensitivity, high accuracy, and good precision for the new BiFGCE developed. By employing the latter approach, an optimization criterion was improved by several orders of magnitude. Moreover, the possible interference effect of different species was tested using two optimized BiFGCE. Furthermore, a real sample analysis of tap water with two optimized BiFGCEs was also carried out.

Discrete micro-volume suspension injection to microwave induced plasma for simultaneous determination of cadmium and lead pre-concentrated on multiwalled carbon nanotubes in optical emission spectrometry

A discrete sample introduction system (DSIS) for the direct micro-volume nanomaterials (NMs) suspension injection has been developed toward the simultaneous determination of Cd and Pb pre-concentrated (by dispersive micro solid-phase extraction (DMSPE)) on oxidized multiwalled carbon nanotubes (MWCNTs) to microwave induced plasma optical emission spectrometry (DMSPE-DSIS-MIP OES). On-axis low-volume spray chambers with flow focusing micro nebulizer (continues mode) and v-groove type pneumatic nebulizer (discontinues mode) for microliter-volume suspension introduction were tested.A univariate approach and the simplex optimization procedure were used to achieve optimized conditions and derive analytical figures of merit. Minimum dead volume, high nebulization and suspension transport efficiency were obtained by using miniaturized spray chamber/v-groove pneumatic nebulizer interface for 10 μL suspension injection in discontinues mode (at 0.5 mL min−1 pump speed).Analytical performance of DMSPE-DSIS-MIP OES method was characterized by determination of the limits of detection (0.7 and 0.1 ng mL−1 for Cd and Pb, respectively) and precision ranged from 6% to 8%. Quantitative data obtained for water reference materials (ERM-CA011b and SRM 1643e) were in good agreement, according to the t-test, for a confidence level of 95%, with the corresponding reference values, proving the potential of this analysis system for trace analysis via MIP OES. The proposed method had been successfully applied for the determination of Cd and Pb in water real samples.

Scheffe's Simplex Optimization of Flexural Strength of Quarry Dust and Sawdust Ash Pervious Concrete for Sustainable Pavement Construction.

Pervious concrete provides a tailored surface course with high permeability properties which permit the easy flow of water through a larger interconnected porous structure to prevent flooding hazards. This paper reports the modeling of the flexural properties of quarry dust (QD) and sawdust ash (SDA) blended green pervious concrete for sustainable road pavement construction using Scheffe's (5,2) optimization approach. The simplex mixture design method was adapted to formulate the mixture proportion to eliminate the set-backs encountered in empirical or trials and the error design approach, which consume more time and resources to design with experimental runs required to evaluate the response function. For the laboratory evaluation exercise, a maximum flexural strength of 3.703 N/mm2 was obtained with a mix proportion of 0.435:0.95:0.1:1.55:0.05 for water, cement, QD, coarse aggregate and SDA, respectively. Moreover, the minimal flexural strength response of 2.504 N/mm2 was obtained with a mix ratio of 0.6:0.75:0.3:4.1:0.25 for water, cement, QD, coarse aggregate and SDA, respectively. The test of the appropriateness of the developed model was statistically verified using the Student' t-test and an analysis of variance (ANOVA), and was confirmed to be acceptable based on computational outcomes at the 95% confidence interval. Furthermore, the scanning electron microscopy (SEM) and energy dispersive X-ray (EDX) were used to evaluate the morphological and mineralogical behavior of green prior concrete samples with various additive mixture compositions. The addition of QD and SDA, on the other hand, aided the creation of porous microstructures in the concrete matrix due to fabric changes in the concrete mixture, potentially aided by the formation of cementitious compounds such as calcium aluminate hydrate and calcium silicate hydrate.

Optimal occlusal force field of masticatory system under clenching by simplex method and principal component analysis

In the present paper, a method to evaluate the occlusal state and occlusal morphology that can integrate an optimal occlusal force field under clenching is proposed using simplex optimization and principal component analysis (PCA). The objective function of the optimization is taken as a sum of the weighted occlusal forces and reaction on temporomandibular joint (TMJ) to maximize the former and to minimize the latter. The optimized solutions in the region defined by the combination among three kinds of muscle forces were obtained by two-step simplex method, and the subregion with no reaction of TMJ was summarized as a ratio to the whole region, newly defined here as a good balance ratio. As a result of PCA of total 528 samples of the good balance ratios for 13 different muscle force combinations, two principal components (PCs) are enough to represent the optimized masticatory system. The first PC suggests the ideal state of occlusion and the second one implies the characterization of combination among muscles. From the consideration of PCA, with the wider equalizer angle, the easier it is to support the force of the temporalis muscle in an ideal occlusal position, and the more the occlusal contact point is shifted backward, the harder it is to support the force of the temporalis muscle. Comprehensively, the proposed good balance ratio becomes the effective quantity to evaluate the ideal masticatory system with the optimized occlusal force field for the statistically reduced indexes showing the combination of muscles.