Single-objective Optimization Research Articles

A review of nature-inspired algorithms on single-objective optimization problems from 2019 to 2023

The field of nature inspired algorithm (NIA) is a vital area of research that consistently aids in solving optimization problems. One of the metaheuristic algorithm classifications that has drawn attention from researchers in recent decades is NIA. It makes a significant contribution by addressing numerous large-scale problems and achieving the best results. This research aims to identify the optimal NIA for solving single-objective optimization problems. The NIA discovered between 2019 and 2023 is presented in this study with a brief description. About 83 distinct NIAs have been studied in this study in order to address the optimization issues. In order to accomplish this goal, we have taken into consideration eight real-world single-objective optimization problems: the 3-bar truss design problem, the rolling element bearing, the pressure vessel, the cantilever beam, the I beam, the design of a welded beam, and the design of a spring. Based on a comparative study and bibliographic analysis, we have determined that two algorithms—the flow direction algorithm, and prairie dog optimization—give us the best results and optimal solutions for all eight of the engineering problems listed. Lastly, some perspectives on the limitations, difficulties, and future course are provided. In addition to providing future research guidelines, this will assist the novice and emerging researcher in providing a more comprehensive perspective on advanced NIA.

Power allocation scheme for sum rate and fairness trade-off in downlink NOMA networks

Non-orthogonal multiple access (NOMA) is an essential enabler technology that is expected to help satisfy the key requirements of increased system throughput in future wireless networks. However, another equally important aspect that should go hand-in-hand with system throughput is user fairness for any network. But, to the best of our knowledge, even though there have been works that look at system throughput or user fairness maximization for NOMA-based networks, they looked at these as a single objective optimization problem, where one is the objective and the other is one of the constraints. However, quite often, joint optimization of both system throughput and user fairness is required to make optimized decisions in the face of trade-offs between these two equally important but conflicting objectives. In this regard, this paper formulates a multi-objective optimization problem to jointly maximize the sum rate and user fairness in a downlink transmission NOMA system, through optimize power allocation (PA), under system-imposed constraints. A weighted sum approach is used to turn the multi-objective optimization problem into a single-objective optimization problem to make it analytically tractable. The optimized PA is then obtained using Lagrange dual decomposition method and Karush–Kuhn–Tucker (KKT) conditions. Using our derived expressions, we propose an iterative PA algorithm that converges fast enough to be employed in practical NOMA networks. We also present simulation results to highlight the effectiveness of the proposed solution. Further, the performance of the proposed method is compared with that of the benchmark methods.

Route and charging planning for electric vehicles: a multi-objective approach

ABSTRACT Electric vehicle (EV) travel planning is a complex task that involves optimizing both the routes and the charging sessions for EVs. Existing algorithms rely on single-objective optimization, which limits their ability to consider EV users’ multiple, often conflicting objectives. In this paper, we introduce a new, genuinely multi-objective approach to EV travel planning, which can find Pareto sets containing multiple EV travel plans optimized simultaneously for multiple objectives. We focus on the bi-objective optimization for travel time and cost. To our knowledge, our algorithm is the first to perform such a genuine multi-objective optimization on realistically large country-scale problem instances involving 12,000 charging stations. We implemented our approach into a fully operational prototype application and extensively evaluated it on real-world data. Our results show that our approach can achieve practically usable planning times with only a minor loss of solution quality despite the very high computational complexity of the problem.

Augmenting bi-objective branch and bound by scalarization-based information

AbstractWhile branch and bound based algorithms are a standard approach to solve single-objective (mixed-)integer optimization problems, multi-objective branch and bound methods are only rarely applied compared to the predominant objective space methods. In this paper we propose modifications to increase the performance of multi-objective branch and bound algorithms by utilizing scalarization-based information. We use the hypervolume indicator as a measure for the gap between lower and upper bound set to implement a multi-objective best-first strategy. By adaptively solving scalarizations in the root node to integer optimality we improve both, upper and lower bound set. The obtained lower bound can then be integrated into the lower bounds of all active nodes, while the determined solution is added to the upper bound set. Numerical experiments show that the number of investigated nodes can be significantly reduced by up to 83% and the total computation time can be reduced by up to 80%.

The Multiobjective Control Based on Tolerance Optimization in a Multienergy System

To address the issue of multiobjective control in multienergy systems with diverse operational objectives, a two-stage optimization framework based on expected point tolerance has been proposed in this paper. In the first stage, a single objective function is used for optimization control to obtain the expected point of the multiobjective optimization problem. Then, in the second stage, by defining the allowable deviation between each optimization objective and the expected point, the original multiobjective optimization problem is transformed into a single objective optimization problem solution with tolerance measurement. Finally, in the simulation scene of a multienergy system, it is demonstrated that compared with the optimal results under each single objective method, the proposed method increases power line loss, maximum voltage deviation, new energy consumption, and economy by 2.22, 2.30, 1.02, and 2.45 times, respectively. Compared with the suboptimal results, the proposed method reduces power line loss by 22.26, 1.74, 1.09, and 0.97 times, respectively. Combining the shape of the Pareto frontier, it is demonstrated that the proposed method can comprehensively consider the needs of multiple power optimization objectives for forming a more reasonable and effective system optimization scheduling and also provide a new approach for solving multiobjective optimization problems.

Efficient Sizing and Layout Optimization of Truss Benchmark Structures Using ISRES Algorithm

This paper presents a comprehensive investigation into the application of the Improved Stochastic Ranking Evolution Strategy (ISRES) algorithm for the sizing and layout optimization of truss benchmark structures. Truss structures play a crucial role in engineering and architecture, and optimizing their designs can lead to more efficient and cost-effective solutions. The ISRES algorithm, known for its effectiveness in multi-objective optimization, is adapted for the single-objective optimization of truss designs with multiple design constraints. This study encompasses a wide range of truss benchmark structures, including 10-bar, 15-bar, 18-bar, 25-bar, and 72-bar configurations, each subjected to distinct loading conditions and stress constraints. The objective is to minimize the truss weight while ensuring stress and displacement limits are met. Through extensive experimentation, the ISRES algorithm demonstrates its ability to efficiently explore the solution space and converge to optimal solutions for each truss benchmark structure. The algorithm effectively handles the complexity of the problems, which involve numerous design variables, stress constraints, and nodal displacement limits. A comparative analysis is conducted to assess the performance of the ISRES algorithm against other state-of-the-art optimization methods reported in the literature. The comparison evaluates the quality of the solutions and the computational efficiency of each method. Furthermore, the optimized truss designs are subjected to finite element analysis to validate their structural integrity and stability. The verification process confirms that the designs adhere to the imposed constraints, ensuring the safety and reliability of the final truss configurations. The results of this study demonstrate the efficacy of the ISRES algorithm in providing practical and reliable solutions for the sizing and layout optimization of truss benchmark structures. The algorithm’s competitive performance and robustness make it a valuable tool for structural engineers and designers, offering a versatile and powerful approach for complex engineering optimization tasks. Overall, the findings contribute to the advancement of optimization techniques in structural engineering, promoting the development of more efficient and cost-effective truss designs for a wide range of engineering and architectural applications. The study’s insights empower practitioners to make informed decisions in selecting appropriate optimization strategies for complex truss-design scenarios, fostering advancements in structural engineering and sustainable design practices.

Global Opposition Learning and Diversity ENhancement based Differential Evolution with exponential crossover for numerical optimization

Since the inception of Differential Evolution (DE), the vast majority of studies on it indicate that exponential crossover does not solve the real-parameter optimization in continuous spaces very well. However, we find that once the appropriate crossover rate CR and its corresponding parameter control are found, the DE variants with exponential crossover can achieve comparable performance with the ones employing binomial crossover. In this paper, a new DE algorithm, called Global Opposition Learning and Diversity ENhancement based DE with exponential crossover (GOLDEN-DE), is proposed to fill the gap in this field. The GOLDEN-DE algorithm has the following highlights: First, a novel global opposition learning mechanism is proposed in our GOLDEN-DE algorithm; Second, a Novel Parameter Control, namely NPC technique, with fitness-independent characteristic is incorporated in the GOLDEN-DE algorithm. Third, a novel population Diversity ENhancement (DEN) mechanism is proposed, and individuals in the stagnation status can be re-calculated in order to enhance population diversity. Fourth, a time stamp mechanism for handling too old inferior solutions in the external archive is also put forward. We evaluate the GOLDEN-DE algorithm for real-parameter single-objective global optimization on 88 benchmarks from the three universal test sets, including CEC2013, CEC2014, and CEC2017 test suites, and experiment results show that our GOLDEN-DE algorithm is competitive with several state-of-the-art DE variants.

A cross-benchmark examination of feature-based algorithm selector generalization in single-objective numerical optimization

The task of selecting the best optimization algorithm for a particular problem is known as algorithm selection (AS). This involves training a model using landscape characteristics to predict algorithm performance, but a key challenge remains: making AS models generalize effectively to new, untrained benchmark suites. This study assesses AS models’ generalizability in single-objective numerical optimization across diverse benchmark suites. Using Exploratory Landscape Analysis (ELA) and transformer-based (TransOpt) features, the research investigates their individual and combined effectiveness in AS across four benchmarks: BBOB, AFFINE, RANDOM, and ZIGZAG. AS models perform differently based on benchmark suite similarities in algorithm performance distributions and single-best solvers. When suites align, these models underperform against a baseline predicting mean algorithm performance; yet, they outperform the baseline when suites differ in performance distributions and solvers. The AS models trained using the ELA landscape features are better than the models trained using the TransOpt features on the BBOB and AFFINE benchmark suites, while the opposite is true for the RANDOM benchmark suite. Ultimately, the study reveals challenges in accurately capturing algorithm performance through problem landscape features (ELA or TransOpt), impacting AS model applicability.

Quantum particle swarm optimization algorithm based on diversity migration strategy

Particle swarm optimization algorithm has been successfully applied to solve practical optimization problems due to its simplicity and efficiency. However, the traditional particle swarm optimization algorithm has inferior search performance in complicated high-dimensional optimization issues and is prone to falling into local optima. To address these problems, a new migration mechanism is introduced and a quantum particle swarm optimization method based on diversity migration is proposed. The strategy can capture different ranges of particles in the population, and the selection of migrating individuals depends not only on their fitness values but is also influenced by the positions within the population. The individual with the minimal average Hamming distance in the population can indicate the direction of iterative population optimization. After comparing the fitness values and the average Hamming distance between particles, the particles deviating from the central range of the population are replaced. The performance of the proposed algorithm is investigated under seven different sets of benchmark function optimization problems in the CEC2020 single-objective boundary-constrained optimization competition, and is compared with those of several other representative optimization algorithms. The quantum particle swarm optimization algorithm based on diversity migration strategy outperforms other typical optimization algorithms. Moreover, the proposed algorithm is convergent and stable.

A Bi-level optimization dispatch for hybrid shipboard microgrid considering electricity-gas-heat coupling

With the increasingly severe problem of air pollution and energy crisis, new energy power generation technology in ship has quickly become the focus of attention. Compared with traditional ships, hybrid shipboard microgrid systems can achieve pollution-free, renewable and high use value. However, the integration of electricity-gas-heat in hybrid energy shipboard microgrid system also poses challenges to current optimization methods. Therefore, this paper develops a bi-level optimization dispatch model for hybrid shipboard microgrid system based on multi-objective particle swarm optimization algorithm. Taking the diesel generators, photovoltaic generation system, energy storage system (ESS) and thermal energy storage equipment into account, a hybrid shipboard microgrid system model considering electricity-gas-heat coupling is constructed. Based on this, a bi-level optimization dispatch model is established to reduce total cost, GHG (GHG) emissions and lifespan loss of ESS. The upper-level model achieves the optimization dispatch of power generation equipment and loads; a lower-level optimization model with the goal of reducing the lifespan loss of ESS is constructed. The improved multi-objective and single-objective particle swarm optimization algorithms are introduced to find the optimal dispatch solutions for bi-level optimization dispatch model. Finally, simulation results show that the proposed optimization method can not only reduce the cost and GHG emissions by 8.7% and 10.9%, but also improve the cycle life of ESS by 9.2%.

Swarm-based multi-objective optimization of double-layered microchannel heat sink with hybrid solid-porous ribs

The current article focuses on the thermal and hydraulic optimization of a double-layered microchannel with hybrid solid-porous ribs. Therefore, for both upper and lower layers, solid-porous ribs, having different thickness ratios of porous and solid, are considered. The ratio of solid-porous thickness in the upper and lower layers and Reynolds number variations are taken into account as design variables. The present study is conducted to find an optimum design by which not only thermal performance improves, but also power consumption reduces. At the initial step, the double-layer microchannel is simulated using artificial neural network. The second step involves the application of the optimum network and the microchannel inputs for minimizing the thermal resistance and the power consumption single-objective and multi-objective type’s optimization problems are solved. The two mentioned optimization problems in the proposed strategy are targeted using four swarm-based algorithms. Results indicated that the designed neural network has a maximum error of 4% for producing the desired outputs. Moreover, the single-objective optimization of the second stage showed that by the porous ratios of 0.19 and 1 for the upper and lower layers, respectively, and Reynolds number of 578.7, the minimum values of pressure drop and overall thermal resistance are achieved.

Optimization design of heliostat field based on high-dimensional particle swarm and multiple population genetic algorithms

INTRODUCTION: Tower-type heliostat field is a new type of energy conversion, which has the advantages of high energy efficiency, flexibility and sustainability and environmental friendliness.
 OBJECTIVES: Through the research and improvement of the tower heliostat field to promote the development of solar energy utilization technology.
 METHODS: In this paper, we calculate and optimize the tower heliostat field by using single objective optimization, high-dimensional particle swarm algorithm and multiple group genetic algorithm.
 RESULTS: In this case of question setting, average annual optical efficiency is 0.6696; average annual cosine efficiency is 0.7564; annual average shadow occlusion efficiency is 0.9766; average annual truncation efficiency is 0.9975; average annual output thermal power is 35539.1747W; mean annual output thermal power per unit area is 0.5657W.The optimal solution after the initial optimization of the algorithm is that the total number of mirror fields is 6,384 pieces, and the average annual output power per unit area is 530.6W.
 CONCLUSION: The model of this paper can reasonably solve the problem and has strong practicability and high efficiency, but high dimensional particle swarm algorithm due to easily get local optimal solution, so can introduce the chaotic mapping to increase the randomness of the search space, improve the global search ability of the algorithm.

Auxetic lattice structures consisting of an enhanced trigram frame unit cell with superior stiffness

Superior stiffness is deemed essential for structures intended for several applications. The stiffness enhancement can be achieved by adopting structures that deform based on the stretching-dominated mechanism instead of the bending-dominated mechanism. This paper proposes a novel auxetic unit cell design and two distinct lattice structures dominated by stretching when subjected to quasi-static compressive and tensile loadings. The structures are manufactured via the fused deposition modeling (FDM) 3D printing method with the use of polylactic acid (PLA) filament as the patent material. The investigation also includes theoretical analyses and finite element (FE) simulations, all yielding consistent results. Response Surface Methodology (RSM) is also employed to understand the influence of three geometric parameters. Besides, single-objective optimization is conducted to maximize the stiffness through geometry design, and multi-objective approaches are implemented to improve the stiffness while simultaneously reducing relative density. Finally, different unit cells, which deform based on the stretching-dominated mechanism, are selected to represent their respective classifications, enabling a comparison of their potential stiffness capacity with the designed structures in this study. Remarkably, it is highlighted that the proposed unit cells and structures outperform others in terms of specific stiffness, making them a promising choice for use in structural engineering.

Experimental and meta-heuristic optimization for the highest thermo-hydraulic performance of a solar air heater with a V-notch pattern of hemispherical protrusions on absorber surfaces

Thermo-hydraulic performances of a new solar air heater with single V-notch patterns of hemispherical protrusions on the absorber plate are investigated experimentally for different relative protrusion heights (hp/Dh = 0.027–0.069), relative pitch (pp/hp = 6–14), attack angle (αap = 15°-75°), and Reynolds number (Re =3600–21,700). Three meta-heuristic algorithms, i.e., Ant colony optimization (ACO), Whale optimization algorithm (WOA), and Grass-hopper optimization algorithm (GOA), were used for single and multi-objective optimizations. Experimental results provide the maximum Nusselt number (Nu) as 127.07 at hp/Dh = 0.050, pp/hp = 10, αap = 600, and Re =21,700, whereas the minimum friction factor (f) becomes 0.0165 at hp/Dh = 0.027, pp/hp = 10, αap = 450, and Re =21,700. The highest normalized Nusselt number (Nu/Nus) is found to be 2.56 for hp/Dh = 0.050, pp/hp = 10, αap = 600, and Re =7200, and the maximum normalized friction factor (f/fs) is observed as 4.30 at hp/Dh = 0.050, pp/hp = 10, αap = 450, and Re =7200. The highest thermo-hydraulic performance parameter (THPP) was to be 1.60 at pp/hp = 10, hp/Dh = 0.050, αap = 600, and Re =7200. Empirical correlations were developed. In single objective optimization for Nu, WOA provided the best results. For f, WOA gives a minimum value. The WOA metaheuristic algorithm outperformed the other algorithms.

A single-objective optimization model for power systems with the introduction of line-heavy load rate index constraints

The increasing penetration of new energy sources in new power systems has exacerbated the volatility and complexity of power system currents. Grid planning is facing higher challenges. Established grid planning models usually use the upper and lower limits of grid transmission capacity as constraints, but this may lead to long-term heavy load operation of certain lines and increase system risks. Therefore, this paper designs a line-heavy load rate constraint and establishes a single-objective optimization model for grid planning based on this constraint. Example analyses verify the effectiveness of adding line-heavy load rate constraints in planning and the reasonableness of the single-objective optimization model.

Optimal Constrained Groove Pressing Process Parameters Applying Modified Taguchi Technique and Multi-Objective Optimization

Most engineering problems are complicated, and developing mathematical models for such problems requires understanding the phenomena through experiments. It is well known that as processing parameters with assigned levels increase, so does the number of experiments. By minimizing the number of experiments, Taguchi’s method of experimental design will help to furnish the idea of full factorial experimental design. Taguchi’s method is more appropriate for single-objective optimization problems and needs modifications while dealing with multi-objective optimization problems. Aluminum alloys are in great demand in today’s automotive and aerospace sectors due to their low density, good corrosion resistance, and excellent machinability. The material is subjected to a constrained groove pressing (CGP) process to obtain microstructural grain refinement with enhanced mechanical behavior. This paper considers AA6061 material having major alloys such as silicon and magnesium. For this work, 3 CGP process parameters (viz., displacement rate, plate thickness and number of passes) are assigned 3 levels to each parameter, acquired the test data, viz., grain size (gs), micro hardness (hs), and tensile strength (ult) based on L9 orthogonal array of Taguchi. Using a modified version of Taguchi’s methodology, it is possible to estimate the range of grain size (gs), micro hardness (hs), and tensile strength (σult) for effective combinations of the CGP processing parameters and validate the results with existing test data. A more dependable and simpler multi-objective optimization procedure is used to choose the optimal CGP processing parameters.

Multi-objective optimization of the dual-pressure organic Rankine cycle system based on the orthogonal design method under different external conditions

The dual-pressure organic Rankine cycle (DPORC) system can obtain a better temperature match between the heat source and working fluid due to the existence of two evaporation processes, which can significantly improve the utilization rate of the heat source and reduce the irreversible loss. Firstly, single-objective optimization of the DPORC system is conducted based on the orthogonal design method with thermal efficiency, exergy efficiency, electricity production cost (EPC) and annual emission reduction (AER) as the performance indicators, respectively. Then, multi-objective optimization of all performance indicators is carried out based on the comprehensive scoring method. Finally, the contribution rates of the operation parameters and the optimal working conditions under different external conditions are investigated. The results show that condensation temperature, high-pressure evaporation temperature and turbine isentropic efficiency are the most critical parameters for system comprehensive performance. When heat source temperature is 170 °C, thermal efficiency, exergy efficiency, EPC and AER under the optimal working conditions are 11.91%, 48.46%, 2.71 × 10−2$/kWh and 11.17 × 105kg, respectively. With the increase of heat source temperature, condensation temperature and turbine isentropic efficiency always have an important influence on system comprehensive performance. The contribution rates of high-pressure evaporation temperature and low-pressure evaporation temperature increase and decrease, respectively. Better comprehensive performance can be obtained by using HC working fluid.

Once and for All: Universal Transferable Adversarial Perturbation against Deep Hashing-Based Facial Image Retrieval

Deep Hashing (DH)-based image retrieval has been widely applied to face-matching systems due to its accuracy and efficiency. However, this convenience comes with an increased risk of privacy leakage. DH models inherit the vulnerability to adversarial attacks, which can be used to prevent the retrieval of private images. Existing adversarial attacks against DH typically target a single image or a specific class of images, lacking universal adversarial perturbation for the entire hash dataset. In this paper, we propose the first universal transferable adversarial perturbation against DH-based facial image retrieval, a single perturbation can protect all images. Specifically, we explore the relationship between clusters learned by different DH models and define the optimization objective of universal perturbation as leaving from the overall hash center. To mitigate the challenge of single-objective optimization, we randomly obtain sub-cluster centers and further propose sub-task-based meta-learning to aid in overall optimization. We test our method with popular facial datasets and DH models, indicating impressive cross-image, -identity, -model, and -scheme universal anti-retrieval performance. Compared to state-of-the-art methods, our performance is competitive in white-box settings and exhibits significant improvements of 10%-70% in transferability in all black-box settings.

Multi-objective optimization and evaluation of hybrid combined cooling, heating and power system considering thermal energy storage

Introducing thermal energy storage (TES) and solar energy effectively reduces fossil fuel consumption and greenhouse gas emissions in combined cooling, heating, and power (CCHP) systems. This study establishes a two-layer optimization framework to obtain the optimal configuration of the CCHP system coupling solar and thermal energy storage. The outer layer uses component sizes as decision variables to optimize the system's annual economic economy, annual carbon dioxide emissions, and annual primary energy consumption; the inner layer uses equipment output as decision variables to optimize the operation and maintenance costs. Firstly, the representative typical scenes were obtained using the k-means algorithm to reduce the computational complexity. Then, the multi-objective chaos optimization (MOCGO) algorithm is combined with mixed-integer linear programming (MILP) to obtain the established optimization model's configuration scheme and optimal operating strategy. TOPSIS is to rank the best Pareto solutions. Finally, a large hotel is a case study. The optimization results indicate that the proposed two-layer optimization model can achieve the optimal configuration scheme and scheduling strategy for hybrid CCHP. Compared to the rule-based multi-objective one-layer optimization model, the proposed two-layer optimization model can achieve maximum improvements of 30.63 %, 37.94 %, and 38.16 % in economic, energy, and environmental performance. Compared with the rule-based single-objective one-layer optimization model, the proposed two-layer optimization model can achieve maximum improvements of 34.95 %, 35.81 %, and 37.55 % in economic, energy, and environmental performance, respectively. In addition, TES can substantially increase the optimal performance of the two-layer optimization model.

Investigation on machining of GFRP through ANOVA, DFA, and CoCoSo method combined with Taguchi approach

Polymer-based composites (GFRP) are increasingly used in the mechanical industry due to their cost-profitability, durability, and good mechanical properties. In the present study, a metal carbide tool was employed to manufacture polyamide (PA66-GF30%) specimen in a dry environment. The impact of variations in cutting process parameters on the responses studied is investigated using two experimental techniques. The first is the OFAT approach. For the second technique (multifactorial), the effects of input parameters on technological parameters (Ra, Fz, MRR, and Pc) are quantified aided by the ANOVA method using an experimental design based on Taguchi’s L9 (3 × 3) orthogonal matrix. Based on the RSM methodology, the results were processed statistically to propose prediction models for the different outputs. In addition, a single-objective optimization study of Taguchi’s and a multi-objective optimization of the operating conditions using the classification method based on CoCoSo as well as the DF Approach according to two desired objectives were carried out. The first objective of this study concerns the minimization of (Ra, Fz, and Pc), and the second one considers the minimization of (Ra, Fz, and Pc) at the same time as maximizing (MRR). Finally, the surface roughness criteria (Ra and Sa) of PA66-GF30% were evaluated to study the effect of the feed (f) on the machined surface topography. The findings are of capital importance in that they provide the required and correct information about the working conditions of composite polymers. According to “OFAT” results, feed (f) is the predominant factor influencing roughness (Ra). Temperature in the cutting zone rises with increasing cutting conditions (Vc, f and ap). Variations in cutting conditions affect the morphology of the chip produced. The roughness criteria (Ra and Sa) results clearly show that the topography of the PA66-GF30% surface changes as (f) changes. Also, optimization of all performance parameters simultaneously indicates that the DFA offers the best combination of parameters: Vc = 187.50 m × min−1, f = 0.096 mm × rev−1, and ap = 0.866 mm, leading to the minimization of (Ra) and maximization of (MRR), with respective values of 1.24 µm and 15.614 cm3 × min−1. Furthermore, the CoCoSo method favors the minimization of (Fz and Pc) with values of 20.18 N and 69.285 W, respectively.