Shape Of Front Research Articles

Speed and Shape of Population Fronts with Density-Dependent Diffusion

There is growing empirical evidence that animal movement patterns depend on population density. We investigate travelling wave solutions in reaction-diffusion models of animal range expansion in the case that population diffusion is density-dependent. We find that the speed of the selected wave depends critically on the strength of diffusion at low density. For sufficiently large low-density diffusion, the wave propagates at a speed predicted by a simple linear analysis. For small or zero low-density diffusion, the linear analysis is not sufficient, but a variational approach yields exact or approximate expressions for the speed and shape of population fronts.

Effect of Microstructure on Chemo-Mechanical Damage Evolution in Aluminum Foil Anodes for Lithium-Ion Batteries

Aluminum-based foil anodes could enable lithium-ion batteries with high energy density comparable to silicon and lithium metal. However, mechanical pulverization and lithium trapping within aluminum tend to cause capacity fading. The complex interplay between these damage modes is not well understood, as well as the role of microstructure on reaction front evolution. Here, we investigate aluminum foils with different compositions and processing conditions to understand how microstructure influences chemo-mechanical degradation. Backscattered electron imaging of ion-milled foil cross sections is used to visualize reaction front evolution and chemo-mechanical degradation. We find that the shape of the reaction front during lithiation is strongly affected by foil composition, defect distribution, and grain size, which, in turn, affects the evolution of chemo-mechanical damage within the foils. Furthermore, a key finding is that the extent of fracture upon delithiation is inversely related to lithium trapping, with foil compositions that exhibit uniform lithiation, and therefore, less fracturing showing greater lithium trapping. Nonreactive precipitate inclusions within alloy foils are also found to induce void formation. This work shows that material design strategies designed to overcome the inverse fracture-lithium trapping relationship could be useful for improving performance. Published by the American Physical Society 2024

Thermal Evaluation of Solar Dryer’s Curve-Front utilized Heat Transfer Analysis

The sun is most sustainable renewable energy, environmentally friendly and utilized for preservation of food and agricultural crops. The main objective of this experiment research work has focused on using renewable energy for evaporated moisture of foods fruit vegetables and herbs by drying system. The heat transfer equation are analyzed to effectively harness the temperature from the sun. Experimental data obtained were used to evaluate the properties of dry air on boundary region condition. Initial, testing was carried out under without load condition, and the result shows that the ambient and dryer’s internal temperature range between 29.3-40.2˚C and 37.4-60.3 ˚C, respectively, in Thailand a latitude of 14°0'48.46" North and longitude of 100°31'49.76" East (recorded average solar radiations and temperature on January 2023 - June 2024), average solar radiations range between 312 W/m2 and 513 W/m2. The indirect natural convection was design and calculated energy base on average temperature not higher than 55˚C, utilized sun daylight at 08:00 a.m. to 04:00 p.m. local time and clear sky or partially cloudy. Second, determination of design parameters; heat energy equation and steam table analysis. Final, utilization of the design under local time, solar radiation and the climatic local conditions and test with ginger slices (represent product in order to examine weight loss). The solar dryer’s curve front shape conduced on without load showed the heat transfer coefficient natural convections range between 3.7 and 4.5 W/m2 ˚C, the energy of dry air analysis range between 54.7 and 155.2 J/s and performance of drying rate range between 0.06 and 0.82 g/s, under increasing and decreasing trends of solar radiations from the time, date and climatic local region condition.

Effect of fiber orientation of adjacent plies on the mode I delamination fracture of carbon fiber reinforced polymer multidirectional laminates

AbstractThe extensive use of multidirectional composite laminates requires to understand the delamination behavior at interfaces between plies with different fiber orientations. In this study, double cantilever beam testing was performed to investigate the mode I interlaminar fracture of carbon fiber reinforced polymer laminates with different central interfaces (0//0, 0//+45 and +45//−45). X‐ray microtomography revealed the curved crack front shape that was incorporated to calculate fracture toughness. The fracture toughness varies with the crack length in a typical delamination resistance curve, which can be quantified by an empirical equation. Incorporation of variable fracture toughness into a cohesive zone model can better predict the delamination fracture of the laminate, compared to constant toughness. It was found that the delamination mechanism is independent of central interfaces. However, compared to unidirectional laminates, multidirectional laminates are less resistant to crack initiation, but more resistant to propagation with higher toughness and shorter fiber bridging zone.Highlights Mode I interlaminar fracture of CFRP laminates with different central interfaces was investigated experimentally and numerically. Curved crack front shape was incorporated to calculate fracture toughness. Incorporation of variable fracture toughness into a cohesive zone model can better predict the delamination fracture of the laminate. Multidirectional laminates are less resistant to crack initiation but more resistant to propagation with higher toughness and shorter fiber bridging zone.

Effects of charge motion on knock and thermal efficiency under high load condition of a heavy-duty natural gas engine

Nowadays, the carbon-neutral trend and the crude oil crisis have brought natural gas into increasing focus. However, heavy-duty engines fueled by natural gas have been plagued by thermal efficiency and knocking limitation problems. Well-structured charge motions can enhance thermal efficiency and concurrently mitigate knock, however, there is a lack of comprehensive work involving charge motions. In this paper, numerical simulation is employed to investigate the impact of charge motion on knock and thermal efficiency under high load conditions for a heavy-duty spark-ignition natural gas engine. The findings indicate that in the configuration with intense swirl, the diminished turbulent kinetic energy (TKE) at the combustion chamber’s base lessens the convective heat exchange between the fresh charge and the heated exhaust gases, resulting in a noticeable high-temperature zone and triggering hot spots. In configurations with inclined swirl and strong tumble motion, the extensive tumble motion near the spark plug region close to top dead center leads to an asymmetric flame front shape, determining the location of hotspots. The research also revealed that excessive tumbling motion and TKE can increase the likelihood of engine knock, while appropriate cylinder charge motion can improve the knock resistance of the engine to some extent, the maximum reduction in knocking intensity can reach 92.5%. The optimized combustion systems can significantly improve the initial combustion rate, shorten the ignition delay period, and advance the combustion center. With the combined effects of ignition timing and charge motion, the total indicated specific power per unit of fuel mass is increased in the optimized systems. Compared to the original combustion system, the indicated thermal efficiency within the knocking boundary can be improved by 1.11%.

Study of chemiluminescence of methane–air flame stabilized on a flat porous burner

In this work, the spatial distribution and spectral characteristics of the chemiluminescence of chemically excited species, OH∗ and CH∗, are experimentally and numerically studied by using a stationary premixed methane–air flame stabilized on the surface of a flat porous burner for various equivalence ratio and normal pressure. Numerical simulations are carried out using detailed reaction mechanisms, and the experimental study includes high-resolution spatial and spectral optical measurements. Despite the data reported in the literature, it is found that (i) the rotational degrees of freedom of OH∗ and CH∗ are not in thermal equilibrium with the surrounding gas and therefore cannot be used to measure flame temperature; (ii) there is no direct correlation between the heat release rate and the distribution of OH∗ and CH∗; (iii) the detailed reaction mechanisms not only quantitatively, and also qualitatively differ in description of the OH∗ and CH∗ concentrations. Since the chemically excited species are well localized in a direction normal to the flame surface, they are demonstrated to be a very accurate markers of flame location. The shape of the combustion front can be reconstructed and resolved up to the accuracy of tens of microns, which is very important for estimation of blow-off critical parameters and measurement of the laminar burning velocity.Novelty and significance statementCurrently, there is a growing interest in the development of sensors for combustion control systems, including active control and suppression of instabilities, in combustion chambers of various devices and engines based on chemiluminescence of excited reaction species. The possibility of non-invasive determination of parameters such as flame temperature, stoichiometry, heat release rate location, etc. using this technique is discussed. We have found that most of these parameters cannot be estimated either due to fundamental limitations or insufficient knowledge of the reaction kinetics involved in the production of these species. Nevertheless, since OH* and CH* are well localized in the direction normal to the flame surface, they can be used as very accurate markers of flame shape and position, allowing us to reconstruct the flame surface to within tens of microns resolution, which is very important for estimating blow-off critical parameters and measuring laminar burning velocity.

Experimental and numerical study of lean combustion of propane in divergent porous media burners

Porous inert media burners for industrial applications demand the utilization of flame front stabilization methods, among which the convective or cross-section variation technique stands out. In this work, combustion of lean premixed propane-air mixtures in cylindrical and divergent alumina packed-bed porous inert media burners was numerically and experimentally conducted. Three burners of 0°, 15° and 30° of divergence were used to study the variation of equivalence ratio and inlet velocity. A bidimensional transient mathematical model was developed and solved numerically, whose results show good agreement with experimental measurements. The maximum temperature along the central axis is location dependent, with upstream augmentation of up to 86 %, meaning an increase of ∼ 815 K in the case of the 30° burner. Combustion front propagation velocity of upstream regime flames show acceleration in both divergent burners due to heat transfer and increment of thermal power in relation to cross-sectional areas when reaching the inlet. In comparison to cylindrical burner, a concave shape of the combustion front and a stretch of the maximum temperature zone was obtained, due to the diffusive nature of the velocity field. Stabilized flames on both divergent burners were achieved in the equivalence ratio range from 0.4 to 0.6. Residence time of product gases is greatly prolonged with burner wall angle and the decrease in overall temperature towards the outlet.

Non-Local Problems for the Fractional Order Diffusion Equation and the Degenerate Hyperbolic Equation

This research explores nonlocal problems associated with fractional diffusion equations and degenerate hyperbolic equations featuring singular coefficients in their lower-order terms. The uniqueness of the solution is established using the energy integral method, while the existence of the solution is equivalently reduced to solving Volterra integral equations of the second kind and a fractional differential equation. The study focuses on a mixed domain where the parabolic section aligns with the upper half-plane, and the hyperbolic section is bounded by two characteristics of the equation under consideration and a segment of the x-axis. By utilizing the solution representation of the fractional-order diffusion equation, a primary functional relationship is derived between the traces of the sought function on the x-axis segment from the parabolic part of the mixed domain. An explicit solution form for the modified Cauchy problem in the hyperbolic section of the mixed domain is presented. This solution, combined with the problem’s boundary condition, yields a fundamental functional relationship between the traces of the unknown function, mapped to the interval of the equation’s degeneration line. Through the conjugation condition of the problem, an equation with fractional derivatives is obtained by eliminating one unknown function from two functional relationships. The solution to this equation is explicitly formulated. For a specific solution of the proposed problem, visualizations are provided for various orders of the fractional derivative. The analysis demonstrates that the derivative order influences both the intensity of the diffusion (or subdiffusion) process and the shape of the wave front.

Research on the propagation characteristics of multiple cracks in steel bridge joints

This study explores the morphological changes and interaction mechanisms of multiple crack propagations in steel bridge joints. Fatigue testing was conducted to determine the locations at which multiple cracks initiated and to obtain fatigue fracture surfaces with easily discernible crack propagation traces. Based on the theory of fracture mechanics, the propagation behavior of coplanar and out-of-plane cracks in joints was simulated using ABAQUS and FRANC3D joint simulation technology. The characteristics of the morphological changes were analyzed, and the interaction mechanism between different crack spacings was investigated to quantitatively characterize the relative positions at which cracks were enhanced or suppressed. The results showed that coplanar cracks exhibited different morphological trends and propagation rates in different stages of propagation. The shape of the crack front continuously changed, and the merging point that appeared during fusion rapidly expanded and evolved into a semi-elliptical crack. The fatigue life was more sensitive to the relative position of multiple cracks. In particular, the fusion of coplanar cracks significantly reduced the fatigue life, and the mutual suppression effect between heterogeneous cracks increased the fatigue life. When the ratio of coplanar crack spacing to crack length (s/2c) was less than 0.2, the crack fusion process significantly accelerated. In addition, when the a2/a1 ratio of the crack propagation depth dropped below 0.5, the suppression effect was significant. Finally, by determining the spacing between multiple cracks, the method established this study can provide a reference for the design of fatigue resistance and joint optimization.

Hypervolume-Based Cooperative Coevolution With Two Reference Points for Multiobjective Optimization

An important issue in hypervolume-based evolutionary multi-objective optimization (EMO) algorithms is the specification of a reference point for hypervolume calculation. However, its appropriate specification has not been carefully studied in the literature. Some recent studies have pointed out the importance and difficulty of the reference point specification. Its appropriate specification depends on problem characteristics such as the Pareto front shape and the number of objectives. In this paper, the difficulty of the reference point specification in hypervolume-based EMO algorithms is circumvented by using two reference points. Instead of using only a single reference point, we propose a new hypervolume-based EMO algorithm that can effectively utilize two reference points cooperatively. Experimental results show that the proposed algorithm has good and robust performance on a wide range of test problems. In comparison to hypervolume-based EMO algorithms with only a single reference point, the proposed algorithm can find a wider and more uniformly distributed solution set. On a recently proposed real-world problem suite, the proposed algorithm shows competitive performance in comparison to state-of-the-art algorithms.

A steady-state weight adaptation method for decomposition-based evolutionary multi-objective optimisation

In decomposition-based multi-objective evolutionary algorithms (MOEAs), the inconsistency between a problem’s Pareto front shape and the distribution of the weights can lead to a poor, unevenly distributed solution set. A straightforward way to overcome this undesirable issue is to adapt the weights during the evolutionary process. However, existing methods, which typically adapt many weights at a time, may hinder the convergence of the population since changing weights essentially means changing sub-problems to be optimised. In this paper, we aim to tackle this issue by designing a steady-state weight adaptation (SSWA) method. SSWA employs a stable approach to maintain/update an archive (which stores high-quality solutions during the search). Based on the archive, at each generation, SSWA selects one solution from it to generate only one new weight while simultaneously removing an existing weight. We compare SSWA with eight state-of-the-art weight adaptative decomposition-based MOEAs and show its general outperformance on problems with various Pareto front shapes.

Reactive transport modelling of iron bentonite interaction in the FEBEX in situ experiment

The evolution of steel/bentonite interfaces in engineered barrier systems of radioactive waste disposal is governed by the corrosion of the steel and the interaction of corrosion products with the bentonite. In the early post-closure phase of the repository, the transition from aerobic to anaerobic corrosion in combination with evolving temperature conditions and chemical gradients due to the hydration of the bentonite take place. In situ tests in underground laboratories provide a high degree of representativeness for the early transient evolution of the interfaces. Complex Fe-bentonite interaction patterns have been observed, which include a concave Fe accumulation front and distinct coloured halos around the corroding steel. A reactive transport model for the FEBEX in situ test is presented, which describes the transition from aerobic to anaerobic corrosion, the transport of O2 in the gas and liquid phase and the chemical evolution of the steel/bentonite interface during the 18 years of the experiment. The model successfully reproduces the major steps of the interface evolution: an aerobic corrosion phase characterized by accumulation of goethite in the corrosion layer, and an anaerobic corrosion phase, where Fe(II) and Fe(II)/Fe(III) corrosion products form, including a gradual re-dissolution of the aerobic corrosion products. In the anaerobic corrosion phase, some of the Fe(II) diffuses into the bentonite, where it partly reacts with remaining O2 to form Fe(III) precipitates or interacts with the clay minerals via surface complexation or cation exchange. Two different approaches for the implementation of a potential electron transfer from sorbed Fe(II) to structural Fe(III) are presented, but the lack of experimental data does not allow evaluation of their representativeness for the FEBEX in situ experiment. The model calculations qualitatively reproduce the concave shape of the Fe accumulation front in the bentonite and a distinct zonation with an iron-oxide precipitation dominated zone adjacent to the steel and a Fe(II) sorption dominated zone further into the bentonite. Sensitivity cases with respect to the hydration of the bentonite and the transport parameters point to the importance of the fast O2 diffusion in the gas phase for the formation of these characteristic interface features. The calculated thickness of the Fe-bentonite interaction zone varies from 1 to 4 cm, which is smaller than observed in some areas of the experiment, where locally this zone extended >10 cm into the bentonite. It is possible that this difference is due to a more complex flow pattern in the in situ experiment that is not captured by the model or due to an additional decoupled electron transport across oxide rich layers.

A damage localization technique using wave front shapes in composite laminates without knowing the velocity profile

Composite laminates are widely used in various fields, but their structures are prone to cracks and damage. Due to the difference in angles of the instantaneous direction of the wave front propagation and the direction of the energy flow in an anisotropic material, the use of Lamb waves for damage localization in composite laminates is a challenging task. Establishing the wave front shape equation can overcome the difficulty of damage localization caused by anisotropy, but this usually requires a priori knowledge of the acoustic velocity distribution of the laminates, which is not convenient for efficient damage localization. In this paper, a damage localization method based on wave front shapes for composite laminates without any knowledge of the velocity profile is presented. Numerical simulation and experimental results show that the proposed method works. This method shows good damage localization accuracy and has broad application prospects in non-destructive testing for plate structures with strong anisotropy.

A Comprehensive Study of NF3-Based Selective Etching Processes: Application to the Fabrication of Vertically Stacked Horizontal Gate-All-around Si Nanosheet Transistors.

In this paper, we demonstrate a comprehensive study of NF3-based selective etching processes for inner spacer formation and for channel release, enabling stacked horizontal gate-all-around Si nanosheet transistor architectures. A cyclic etching process consisting of an oxidation treatment step and an etching step is proposed and used for SiGe selective etching. The cyclic etching process exhibits a slower etching rate and higher etching selectivity compared to the direct etching process. The cycle etching process consisting of Recipe 1, which has a SiGe etching rate of 0.98 nm/cycle, is used for the cavity etch. The process achieved good interlayer uniformity of cavity depth (cavity depth ≤ 5 ± 0.3 nm), while also obtaining a near-ideal rectangular SiGe etch front shape (inner spacer shape = 0.84) and little Si loss (0.44 nm@ each side). The cycle etching process consisting of Recipe 4 with extremely high etching selectivity is used for channel release. The process realizes the channel release of nanosheets with a multi-width from 30 nm to 80 nm with little Si loss. In addition, a selective isotropic etching process using NF3/O2/Ar gas mixture is used to etch back the SiN film. The impact of the O2/NF3 ratio on the etching selectivity of SiN to Si and the surface roughness of SiN after etching is investigated. With the introduction of O2 into NF3/Ar discharge, the selectivity increases sharply, but when the ratio of O2/NF3 is up to 1.0, the selectivity tends to a constant value and the surface roughness of SiN increases rapidly. The optimal parameter is O2/NF3 = 0.5, resulting in a selectivity of 5.4 and a roughness of 0.19 nm.

Deep and wide search assisted evolutionary algorithm with reference vector guidance for many-objective optimization

Many-objective optimization problems appear in a large many practical cases, but maintaining the convergence and diversity of solutions becomes a big challenge. In response to this, a deep and wide search assisted evolutionary algorithm with reference vector guidance (RVEA-DWC) is proposed. In the algorithm, a novel environmental selection criterion based on substituting Iɛ+ indicator for distance is introduced to enhance the convergence, and once the selected individuals exceed the population size after multiple traversals, those with poor convergence or diversity are randomly eliminated. In addition, to tackle the irregular Pareto front shapes, the invalid reference vectors are deleted regularly, and a certain number of reference vectors with local diversity and global diversity are added, so as to conduct a overall search that combines deep search and wide search to balance exploitation and exploration. An experimental study of 5, 10, 15, 20 objectives is conducted on 60 test instances. The results demonstrate that the proposed algorithm is superior to the other twelve many-objective evolutionary algorithms.

Experimental study on the explosion behavior of nonuniform hydrogen/methane/air mixtures in a duct

An experimental study is performed on the explosion behavior of a nonuniform hydrogen/methane/air mixture with varying hydrogen volume fractions (α(H2)) in the fuel used and different mixing levels of the fuel/air mixture (characterized by the diffusion time (td) of the hydrogen/methane mixture). Results show that both α(H2) and td considerably impact the explosion behavior of the nonuniform hydrogen/methane/air mixture. Increasing α(H2) and td can increase the uniformity of the hydrogen/methane/air mixture. A triple flame is observed in highly nonuniform mixtures instead of the finger- and tulip-shaped flames seen in more uniform mixtures. The shape of the flame front varies with the degree of fuel/air mixing. As α(H2) and td increase, the propagating flame gradually transitions from a triple flame to a tulip-shaped flame. The flame tip velocity and overpressure increase with α(H2) and td. For a fixed td, the flame tip velocity and overpressure increase slightly as the α(H2) rises from 0 to 40% and rapidly for a large α(H2). These findings suggest that improving the uniformity of hydrogen/methane/air mixtures could increase the severity of explosions for fuels with high hydrogen contents.

Enhancing business by procuring and dispensing items among supply chain members using multi-objective approach

ABSTRACT Manufacturers in various sectors encounter several challenges in providing timely delivery to a wide range of stakeholders. This article focuses on the issues that manufacturers have while purchasing various commodities from suppliers, processing them in manufacturing plants, and distributing them to retailers for customer delivery. These tasks must be done within unique limits. To demonstrate this situation, a mathematical model was developed, yielding to a multi-objective optimization problem subsequently it was solved using a Genetic Algorithm (GA). The location, shape, range, and distribution of the nondominated Pareto front were shown using 3DRadVis techniques. In addition, certain limits were considered such as selecting suppliers, plants, and distributors at the manufacturing level. The numerical example demonstrated the model’s usefulness and efficiency. It was also observed that with the use of GA and 3DRadVis techniques, timely delivery to the stakeholders is achievable.

Experimentally detected aerodynamic drag coefficient of the agricultural tractor form considering effects of windshield angle and hood front shape

Agricultural tractors are improving their capacity, speed, and performance. However, the characteristic form of the agricultural tractors is not known in terms of aerodynamics. This is required in modeling transportational duties and their impacts on energy and environment, especially considering tractor-trailer couples. In this work, this characteristic form solely investigated apart from the couple to base a foundation. The geometry was adapted from a commercial model. The model was simplified greatly to isolate numerous parameters yielding a generic shape. Only geometrical features as parameters were selected as the nose shape as the leading surface and the windshield angle. Scaled models were tested in a wind tunnel. Drag coefficients independent from Reynolds number, drag forces, pressure distributions on the symmetry planes and pressure coefficients were obtained. An extrapolation was made in order to predict drag force related fuel consumption and CO2 emission for a full-scale tractor on-road transportation scenario based on experimentally obtained drag coefficient. It is understood that changes in tractor front surface topology and wind shield angle can lead to drag changes up to 3%. A 0.72 value of drag coefficient may be assumed for the generic agricultural tractor form. Based on this value, an on-road agricultural tractor cruising with 70 km h−1 is predicted to have a drag sourced fuel consumption of 3.9 kg h−1 and CO2 emission of 10.19 kg h−1. Tractor trailer couples and their platoons are of interest in terms of research and computational simulations that may utilize present results as validator.

The Inner Disk Rim of HD 163296: Linking Radiative Hydrostatic Models with Infrared Interferometry

Previous studies of the protoplanetary disk HD 163296 revealed that the morphology of its sub-au infrared emission encompasses the terminal sublimation front of dust grains, referred to as the inner rim, but also extends into the (supposedly) dust-free region within it. Here, we present a set of radiative hydrostatic simulations of the inner rim in order to assess how much the rim alone can contribute to the observed interferometric visibilities V, half-light radii R hl, and fractional disk fluxes F in the wavelength range 1.5–13 μm. In our set of models, we regulate the cooling efficiency of the disk via the boundary condition for radiation diffusion and we also modify the shape of the sublimation front. We find that when the cooling efficiency is reduced, the infrared photosphere at the rim becomes hotter, leading to an increase in R hl sufficient to match the observations. However, the near-infrared disk flux is typically too low ( F≃0.25 at 1.5 μm), resulting in H-band visibility curves located above the observed data. We show that the match to the H-band observations up to moderate baselines can be improved when a wall-shaped rather than curved sublimation front is considered. Nevertheless, our model visibilities always exhibit a bounce at long baselines, which is not observed, confirming the need for additional emission interior to the rim. In summary, our study illustrates how the temperature structure and geometry of the inner rim need to change in order to boost the rim’s infrared emission.

Identifying Pareto Fronts Reliably Using a Multistage Reference-Vector-Based Framework

Evolutionary multi-objective and many-objective optimization (EMO and EMaO) algorithms are increasingly being used to identify the true shape and location of the Paretooptimal front using a few representative well-converged and welldistributed solutions. The reason for their popularity is due to their ability to provide a better understanding of objective relationships for optimal solutions, and also to facilitate the choice of a preferred solution using an interactive or postoptimal multi-criterion decision analysis. However, since EMO and EMaO algorithms are stochastic, a single application may not provide a true representative set with a desired number of Pareto solutions reliably in repetitive runs and importantly with a well-distributed set of solutions. In this paper, we propose a multistage framework involving reference-vector based evolutionary multi-and many-objective algorithms (MuSt-EMO and MuSt-EMaO) that attempts to recursively rectify shortcomings of previous stages by careful executions of subsequent stages so that a prescribed number of well-distributed and well-converged solutions are achieved at the end. The proposed multi-stage approach is implemented to a number of popular reference vector based EMO/EMaO algorithms and is applied on various multiand many-objective test and real-world problems.