Multiple Response Optimization Research Articles

Multiple Response Optimization: Comparative Analysis Between Models Obtained by Ordinary Least Method and Genetic Programming

Purpose: This work aims to analyze and compare the performance between the Ordinary Least Squares (OLS) method executed in Minitab (v. 17) and the genetic programming performed in Eureqa Formulize (v. 1.24.0). Theoretical reference: Obtaining a model that mathematically describes the relationship between the independent variable and the response variable is essential to optimizing the process. The model can be described as an approximate representation of the real system or process, while the modeling process is a balance between simplicity and accuracy (X. Chen et al., 2018; Gomes et al., 2019; Sampaio et al., 2022; A. R. S. Silva et al., 2021). Method: An Evaluation of the best method for constructing mathematical models was performed using the Adjusted Coefficient of Determination (Radj2) and Akaike's Information Criterion Results and conclusion: The comparison between the use of the methods showed the superiority of genetic programming over OLS in the construction of mathematical models. Originality/Value: Genetic Programming produces mathematical models that are sometimes differentiated when several replicates are performed, but always with similar explanatory power and with biased characteristic that does not affect in any way the quality of prediction of the dependent variable being studied.

Machinability and surface morphology investigations of multiwall carbon nanotube reinforced aluminium 7075 metal matrix composite during electrical discharge machining: A grey relational approach

AbstractMultiwall carbon nanotube buttressed aluminium 7075 metal matrix composite was synthesized through an amended liquid metallurgy method, which consisted semisolid stirring, ultrasonic treatment and squeeze casting. Aim was to investigate its machinability and surface morphology during electrical discharge machining. Variable machining factors were peak current, pulse‐on time and gap voltage, whereas the responses under investigation were electrode wear rate, material removal rate and average surface roughness. Results revealed electrode wear rate, material wear rate and average surface roughness increased on increasing peak current and pulse‐on time, but all these responses behaved inversely with the increase of gap voltage. Average surface roughness reduced by around 44 % on reducing the peak current from 10 A to 4 A and increasing gap voltage from 55 V to 80 V at constant pulse‐on time of 300 μs; however, it increased by around 25 % on reducing the gap voltage from 80 V to 55 V and increasing the pulse‐on time from 100 μs to 300 μs at constant peak current of 10 A. Significance of the process parameters were verified, regression models were developed and morphology of the machined surfaces was studied. Finally, multiple response optimization was conducted following grey relational approach.

Pre-treatment of landfill leachate via coagulation-flocculation: Optimization of process parameters using response surface methodology (RSM)

Wastewater treatment is achieved mainly through the regeneration of resources and energy from wastewater, especially using pre-treatment technologies. In this study, coagulation pre-treatment of landfill leachate was performed using polymeric iron sulfate (PFS) as coagulation. Moreover, the whole experimental process was divided into two parts. In the first phase, the effects of PFS dosing, initial pH and PAM dosing on the removal of chemical oxygen demand (COD), total phosphorus (TP) and UV254 from the leachate were assessed using one factor one experiment (OFAT); In the second phase, the individual and interactive effects of parameters on COD%, TP%, and UV254% were evaluated using response surface methodology (RSM). Numerical multiple response optimization was conducted using RSM to maximize COD%. The COD%, TP%, and UV254% at optimum condition (PFS dose of 12.18 g/L, initial pH of 8.12, and PAM dosage of 11.29 mg/L) reached 62.30 %, 95.79 %, and 83.45 %, respectively. The 3D-EEM showed the effluent from the leachate after mixing. The chemical properties significantly changed, and the concentration of hard-to-degrade substances, such as humic acid, decreased. FTIR and ESM-EDX were used to delineate the intrinsic mechanism of contaminant removal, demonstrating that hydroxyl bonds are crucial in the extraction of leachate and the aggregation of folcs.

Preparation, Characterization and Optimization of Sustained Release Matrix Tablets of Repaglinide using Box–Behnken Design

The aim of this investigation was to develop and optimize the Sustained release Matrix formulations of Repaglinide (RLD) using response surface methodology by employing a 3-factor, 3-level Box–Behnken statistical design. The independent variables studied were the amount of hydroxypropyl methylcellulose (HPMC K4M), Ethyl cellulose (EC) and PVP K30. The Swelling index (Y1), drug release at 8 hr and 12hr were the target responses. The response surface methodology and multiple response optimizations utilizing a polynomial equation were used to search for the optimal formulation with a specific release rate at different time intervals. The results showed that the effect of combination of HPMC K4M and EC was the most influencing factor on the drug release from ER matrix tablets. The mechanism of drug release from RLD Matrix tablets was dependent on the added amount of EC. Validation of the optimization technique demonstrated the reliability of the model. The optimized formulation containing 50mg of HPMC K4, 35mg of EC, and 30mg of PVP K30 was prepared according to the software determined levels. DSC and FTIR studies combined with the stability study of the optimized formulation proved the integrity of the developed formulation. The Box–Behnken experimental design facilitated the formulation and optimization of extended release hydrophilic matrix systems of RLD in a short period of time and with the fewest number of experiments. The optimized Matrix tablet of Repaglinide showed good pharmacokinetic result over conventional formulation.

Oxidative degradation of electroplating wastewater by an electro-Fenton process using GO/TiO<sub>2</sub>NTs electrode

Electro-Fenton (E-Fenton) is a versatile treatment method; however, it has not yet been used for the treatment of electroplating wastewater using graphene oxide (GO) coated TiO<sub>2</sub> nanotubes (GO/TiO<sub>2</sub>NTs) electrode. A simple anodization technique has been adopted to synthesize GO/TiO<sub>2</sub>NTs electrode. The present work aimed to study an E-Fenton treatment to investigate the effect of different parameters on % COD removal and energy consumption using GO/TiO<sub>2</sub>NTs electrode. The performance of the treatment process was examined in terms of % COD removal and energy consumed at three process parameters: current, time, and ferrous sulfate concentration. The optimum operating conditions were determined using multiple responses optimization based on Box-Behnken design (BBD). At optimum operational parameters, the results revealed that the % COD removal and energy consumed were 96.27% and 15.35 kWh/m<sup>3</sup>, respectively. The pseudo-first-order reaction kinetics was fitted to the experimental data at optimum conditions. Possible intermediates were identified based on the GC-MS analysis, and a corresponding tentative degradation pathway has been proposed. Furthermore, a recyclability and stability study of the synthesized electrode has also been performed. Moreover, total organic carbon (TOC) study revealed that E-Fenton has the potential to detoxify electroplating effluents. Hence, GO/TiO<sub>2</sub>NTs electrodes can be highly efficient in degrading hazardous pollutants.

Comprehensive assessment and multiple-response optimization of serpentine channel pouring process for achieving high-quality semi-solid slurry

The convenient serpentine channel pouring (SCP) process is advantageous in broad industrial application. The key technique is the fast and stable production of semi-solid metal (SSM) slurry with non-dendritic microstructure. It is critical to take the whole technological process into consideration so as to achieve the optimal performance of SSM slurry rapidly and steadily. The present study makes an attempt to analyze and evaluate SCP process by comprehensive considering of the microstructure, mechanical property and yields. The established SCP process prediction models adequately approximated the actual values. The dimensional response surface accurately evaluated the interaction effects between process parameters on the characters of SSM slurry. Two kinds of numerical multiple-response optimization criteria were applied to achieve high-quality SSM slurry. The microstructure analysis and phase-field modeling clearly revealed the grain growth and microstructure evolution mechanism for SCP process. The comprehensive assessment concept and multiple-response optimization method in this work may bring positive and directive significance for the mass-scale production and application of SCP process.

Multiple Response Prediction and Optimization in Thin-Walled Milling of 6061 Aluminum Alloy

In this study, the multi-objective optimization method for thin-wall milling of 6061 aluminum alloy is addressed. The technological parameters including the cutting speed Vc, the feed of tooth fz, and the width of cut ar are considered input variables, while the manufacturing responses are surface roughness Ra, production rate MRR, and flatness deviation FL. The goal is to find the optimum cutting parameters to minimize Ra and FL and maximize MRR, at the same time. To solve this problem, the desirability function approach was used based on Taguchi orthogonal array. Twenty-seven experiments were conducted and the measured data were collected. The mathematical regression models for responses Ra, MRR, and FL were then generated and evaluated by using the analysis of variance method. Then, the multiple objective optimization problems were solved by using the desirability function approach. The optimum cutting parameters set are Vc=120m/min, fz=0.06mm, and ar=0.13131mm, corresponding to Ra=0.1613µm, MRR=17197.45cm3/min, and FL=0.0995mm.

Multiple response optimization for performance and emission of a CI engine using waste plastic oil and biogas in dual fuel mode operation

The availability of waste biomass and the advancement of waste-to-biogas technology has aided in the promotion of biogas as a viable alternative to fossil fuels. This research aims to find the best proportion of biogas to use in a blend of waste plastic oil (WPO) and diesel in the dual fuel mode (DFM) of engine induction for improved performance and emissions. In the CI engine, biogas (of 10%, 20%, 30%, and 40% by volume)is added as supplementary fuel alongside 20WPO-diesel blends.The optimal engine performance and emission are evaluated employing response surface methodology (RSM). The most desirable engine performance, i.e., higherenergy and exergyefficiency, and lowest BSFC, HC, and NOx emissions, is determined by using the response surface technique with potential engine parameters such as different engine loads, compression ratios, and various proportions of biogas with test fuel. The energy efficiency, exergy efficiency, BSFC, and CO, HC, and NOx emissions, of 18.6%, 50.05%, 0.46 kg/kWh, 0.16 ppm, 41.28 ppm, and 107.81 ppm respectively are found at optimum conditions of 57.12% engine load, 18 compression ratio, and 20% volume biogas with 20% WPO-diesel blend, with combined desirability, D of 0.90029.

Experimental Design and Multiple Response Optimization for the Extraction and Quantitation of Thirty-Four Priority Organic Micropollutants in Tomatoes through the QuEChERS Approach

The chemical contamination in fruit and vegetables represents a challenging analytical issue, with tomatoes deserving to be investigated as they are fundamental components of the Mediterranean diet. Polychlorinated biphenyls (PCBs), polycyclic aromatic hydrocarbons (PAHs) and nitro-PAHs contamination is of serious concern, due to particulate deposition and to uptake from contaminated soils and water. However, time-consuming, non-simultaneous and/or non-eco-friendly extraction procedures are typically used to investigate organic contamination in tomatoes, with nitro-PAHs that have not yet been studied. Based on these premises, this work reports the development of a QuEChERS-based approach, coupled with gas chromatography/mass spectrometry, for the simultaneous determination of 16 PAHs, 14 PCBs and 4 nitro-PAHs in three tomato cultivars. The effect of dichloromethane, cyclohexane and acetone, as well as of four clean-up phases were studied through the advanced combination of full factorial experimental design and multiple response optimization approaches. The final protocol, based on cyclohexane extraction followed by a double purification step with primary secondary amine and octadecyl silica and a sulfuric acid oxidation, led to 60–120% recoveries (RSD% < 15%). Good repeatability (inter-day precision <15%) and negligible matrix effect (<16%) were confirmed and the protocol was applied to the analysis of real tomato samples purchased in a local market.

Mechanical processing of hydroxyapatite through sintering and multi-objective optimization technique for biomedical application

Hydroxyapatite (HAp) has been widely applied in the area of tissue engineering, however, its poor mechanical properties limit it in load bearing biomedical application. To improve the mechanical integrity of HAp, this study reports the synthesis, optimization and the significance of processing parameters on the physic-mechanical properties of HAp. The HAp was produced from biogenic source through at 900 °C. The L9 Taguchi orthogonal array was employed, considering two processing parameters namely, HAp particle size (100, 300, and 600 mathrm{mu m}) and compaction load (3, 6, and 9 KN). The raw bones (RB) and the synthesized HAp were characterized for phase structure and functional groups analysis. The analysis showed the characteristics of a typical calcium phosphate material. The multiple response optimization revealed that 600 mathrm{mu m} particle size 6 KN compaction load are the optimal processing parameters in the manufacturing of high biomedical performance HAp.Graphical

Metaheuristics-based approach for multiple dynamic responses optimization of flexible mechanisms

Metaheuristics-based approach for multiple dynamic responses optimization of flexible mechanisms

Extraction of biologically active compounds from Aronia melanocarpa: Comparison of techniques and multiple response optimization

Abstract The presented paper deals with the selection of most efficient extraction method for obtaining biologically active compounds (mainly antioxidants) from the black chokeberry (Aronia melanocarpa) fruits. Two conventional methods (maceration and Soxhlet extraction) as well as a more recent accelerated solvent extraction (ASE) were employed. The extracts were evaluated by means of their overall yield, antioxidant activity (TEAC assay), total phenolic content (TPC), ascorbic acid (AA), and malic acid (MA) content. Both Soxhlet extraction and ASE led to the highest overall yields (42 %) of the extract; however, in terms of TEAC and TPC, the extracts obtained by ASE were usually superior. The highest TEAC value (227.7 mg TE/g) as well as the highest TPC (67.9 mg GAE/g) were obtained by ASE using 40 % (v/v) ethanol at 140 °C after 30 min. The ASE method was further analyzed using a 23-factorial design where the effect of temperature (40—140 °C), extraction time (5—30 min), and solvent composition (40—96 % ethanol) was investigated. While temperature and solvent composition significantly affected the extract properties, the effect of extraction time was small or even insignificant. The regression model obtained from ANOVA was further used for multiresponse optimization of ASE conditions using the global desirability function as a criterion for overall extract quality.

Energy-exergy-emission-economic performance and multi-response optimisation of a VCR CI engine using bio ethanol blended diesel fuel with Al<SUB align="right">2O<SUB align="right">3 nanoparticles

A variable ratio compression ignition engine is tested experimentally for different fuel type (diesel, e-diesel and nano fuel), load (4 kg, 8 kg and 12 kg), and compression ratios (14, 16, and 18) to determine its performance (energy and exergy efficiency), emission (NOx emission), and economic characteristics (% relative cost). Multiple response optimisation is carried out using response surface methodology for maximum performance, minimum emissions and cost. 5.2 kg load, 18 CR, and nano fuel are determined as the optimal input parameters for attaining maximum energy and exergy efficiency of 24.8% and 62.9%, minimum NOx emission and % cost variation of 208.4 ppm, and -6.5 respectively.

Multiple response optimization of sizing machine settings and sized yarn tensile properties using advanced method of experimental design

On a loom, the warp yarns experience exceptionally high mechanical stresses and strains, as well as significant abrasion from friction. As a result, significant yarn breakages cause loom stoppages and, hence, production and quality interruptions. To mitigate this problem, the warp yarns should be treated with a thin, strong film of an appropriate adhesive. The aim of this study is therefore, to investigate the effect of sizing machine parameters on tensile properties of the yarn and to optimize the sized yarn tensile properties. Design expert 11 software with Box-Behnken design has been employed to design the research, analyze the results of experiments, and optimize the responses. In this research, three factors, each at three levels (wet zone yarn tension (A) (340, 380, and 420 N), squeezing roller pressure (B) (13, 15, and 17 N), and sizing machine speed (C) (30, 49, and 68 m/min), as well as three response variables (gain strength, loss elongation, and stretch), are considered. 15 samples of sized yarn have been produced with various combinations of the given factors, and the values of the response variables are measured for each sample. It has been observed that wet zone yarn tension and squeezing roller pressure have a significant effect on gain strength, stretch, and loss elongation. According to the regression analysis, gain strength has a negative relationship with wet zone yarn tension and a positive relationship with squeezing roller pressure. In the other case, both wet-zone yarn tension and squeezing roller pressure have a positive and significant effect on loss elongation and yarn stretch. At 340 N wet zone yarn tension, 13 N squeezing roller pressure, and 51 m/min sizing machine speed, the optimum values of gain strength (32.7 cN/tex), loss elongation (18.5%), and stretch (1.4%) were obtained. The methodologies employed in this study revealed the empirical relationship between the factors and the responses, the interaction effects of the factors on the responses, and multiple response optimizations. The optimized result of this study can be applied to the warp yarn sizing and can improve the tensile properties of the yarn and the loom’s efficiency significantly.

A global optimization method for multiple response optimization problems

<p style='text-indent:20px;'>The multiple response optimization problem has been studied extensively. However, most existing methods only find locally optimal solutions to the concerned optimization problem. Several methods were proposed which tried to find a globally optimal solution of the problem, but there is no theoretical guarantee to obtain a globally optimal solution. In this paper, we investigate a global optimization method for the problem of a chemical process studied by Myers et al. which involves two input variables and three responses of interest. Based on the fitted polynomial functions of three responses, this multiple response problem is reformulated as a polynomial optimization problem where the primary response is objective while the other responses are put into constraints. We obtain a globally optimal solution to the concerned polynomial optimization problem when requirements of non-primary responses and experimental region are given. The satisfactory optimal designs can be obtained by adjusting non-primary responses appropriately. The method we proposed can be implemented easily, and it obtains a globally optimal solution to the multiple response optimization problem we considered.</p>

Multiple-Response Optimization of Aluminum Oxide Nanocoating Prepared by Pulsed Laser Deposition Using Taguchi Design

In this work, an aluminum oxide nanocoating was prepared using the pulsed laser deposition technique to study the properties of the coating and to find the optimal conditions to achieve the highest quality of the aluminum oxide nanocoating. The structural properties were studied using X-ray diffraction. The results showed that the aluminum oxide nanocoatings were alpha phase polycrystalline structures. The surface topography was studied using atomic force microscopy. The surface topography showed that the average surface roughness ranged from 1.26 nm to 7 nm. The optical properties were studied using a UV-VIS spectrometer. It showed the energy gap within the range 4.09 eV to 3.98 eV. The hardness of the aluminum oxide nanocoatings were calculated using the nanoindentation technique and found within the range of 32.79 GPa to 10.41 GPa. According to the present work, the effect of the input parameters represented by the pulse energy and the number of pulses on the responses represented by the energy gap, hardness, and surface roughness were studied. The experiments were designed based on the L9 orthogonal array with the Taguchi approach. A multiple responsive optimizations of Takeuchi's design was done using the desirability function.

Desirability Function Analysis (DFA) in Multiple Responses Optimization of Abrasive Water Jet Cutting Process

This paper introduces optimization of machining parameters for high-pressure abrasive water jet cutting of Hardox 500 steel utilizing desirability function analysis (DFA). The tests were carried out according to the orthogonal matrix (Taguchi) L9. The control parameters of the process such as pressure, abrasive flow rate, and traverse speed was optimized under multi-response conditions namely cutting depth and surface roughness. The optimal set of control parameters was established on the basis of the composite desirability value obtained from desirability function analysis and the significance of these parameters was determined by analysis of variance (ANOVA). The effects show that optimal sets for high cutting depth and small surface roughness is high pressure, middle abrasive flow rate, and small traverse speed. A confirmation test was also leaded to validate the test results. Results of the research have shown that machining efficiency at keeping good level quality of cut surface can be improved this approach.

Multiple response optimizations on the leached-spray-dried bancha green tea towards healthy ageing

Bancha is a popular type of green tea in Japan, rich in tea polyphenols (TPs) and has a more astringent aroma with a less aromatic and strong character that complements functional foods. The blanching process is used to extract TPs and remove unwanted microorganisms, as well as inhibit phenolic oxidation. This study proposed a green tea blanching process followed by spray drying the extracts with maltodextrin. Furthermore, it is focused on maximizing the major chemical components of green tea (i.e., catechins, caffeine, and phenolic contents) based on powder particle size obtained through Multiple Response Surface Methodology optimizations. The results show that the proposed model accurately predicts leached-spray dried green tea's total catechin and caffeine content, with a coefficient of 0.9475 and 0.8692, respectively. This process yielded composite desirability of 0.9751, while individual desirability yielded excellent results of 1.0000, 0.9188, 1.0000, and 0.9839 for catechin, caffeine, phenol content, and powder. The settings appear to yield functional results for entire responses. Due to the concerns in tropical skin nutrition applications, smaller particle size green tea can promote better adsorption than larger sizes.

A novel Bayesian approach for multi-objective stochastic simulation optimization

Multi-objective stochastic simulation optimization plays an important role in designing complex engineering systems. To identify optimal solutions via simulations, Bayesian optimization, which utilizes metamodels and an acquisition function to determine the next design point, has been popular in machine learning. However, studies on Bayesian optimization of multi-objective stochastic simulation are limited and can give undesired performances in terms of convergence and diversity metrics. Moreover, direct extension of Bayesian optimization algorithms of deterministic responses is unrealistic as stochastic responses are observed with heterogeneous noise. To handle these issues, we propose a novel framework for Bayesian optimization of multiple stochastic responses. Stochastic kriging metamodels are constructed independently for multiple stochastic responses considering heterogeneous simulation noise. To remove undesired effects of random simulation noise on comparing solutions, quantiles of stochastic kriging metamodels are employed to define the Pareto dominance. Acquisition functions are proposed by integrating the hypervolume-based and probability-of-improvement (PoI)-based acquisition functions from deterministic multi-objective optimization with typical acquisition functions from univariate stochastic response optimization. This not only enhances the convergence and diversity of Pareto-optimal solutions but also properly handles heterogeneous noise. Exact calculation formulas of the proposed algorithms are further developed. Typical numerical cases and two engineering examples (a rocket injector design example and a real inventory design scenario) demonstrate that the proposed algorithms give better Pareto-optimal solutions of which the proximity to true Pareto fronts and the diversity are improved.

Experimental investigation of the axial crushing behavior of aluminum/CFRP hybrid tubes with circular-hole triggering mechanism

The current study investigates the axial crushing behavior of filament-wound aluminum/carbon fiber reinforced plastic (Al/CFRP) hybrid tubes with circular-hole triggering mechanism. The proposed hybrid design consists of an inner aluminum thin-walled tube and an outer composite winding of three plies having 30°/−30°/90° angles. The diameter, number, and location of the triggering holes were chosen as design parameters, and Taguchi L9 orthogonal array experimental design was used to find the best configuration of design parameters. For the optimization of multiple responses, Additive Ratio Assessment (ARAS) has also been utilized along with mono-criteria optimization. The experimental results showed that the intact hybrid tube can absorb up to 50% higher crush energy compared with the sum of individual components of the structure. The progressive brittle fracture pattern accompanied by progressive local buckling mode exhibiting favorable energy absorption characteristics were observed in all triggered configurations. Analysis of variance results showed that the trigger location ratio has the most significant effect on the specific energy absorption while the hole diameter was the most significant factor in decreasing the peak crush force. The results revealed that the specific energy absorption and the crush force efficiency of the intact hybrid tubes can be enhanced up to 39.1% and 61.7%, respectively, by the use of optimal levels of design parameters.