In vitro dissolution and permeability testing aid the simulation of the in vivo behavior of inhalation drug products. Although the regulatory bodies have specific guidelines for the dissolution of orally administered dosage forms , this is not the case for orally inhaled formulations, as there is no commonly accepted test for assessing their dissolution pattern. Up until a few years ago, there was no consensus that assessing the dissolution of orally inhaled drugs is a key factor in the assessment of orally inhaled products. With the advancement of research in the field of dissolution methods for orally inhaled products and a focus on systemic delivery of new, poorly water-soluble drugs at higher therapeutic doses, an evaluation of dissolution kinetics is proving crucial. Dissolution and permeability testing can determine the differences between the developed formulations and the innovator’s formulations and serve as a useful tool in correlating in vitro and in vivo studies. The current review highlights recent advances in the dissolution and permeability testing of inhalation products and their limitations, including recent cell-based technology. Although a few new dissolution and permeability testing methods have been established that have varying degrees of complexity, none have emerged as the standard method of choice. The review discusses the challenges of establishing methods that can closely simulate the in vivo absorption of drugs. It provides practical insights into method development for various dissolution testing scenarios and challenges with dose collection and particle deposition from inhalation devices for dissolution tests. Furthermore, dissolution kinetic models and statistical tests to compare the dissolution profiles of test and reference products are discussed. Over the years, orally inhaled drug products (OIDPs) have been created to treat lung diseases locally. This method of administration is also presently being researched for the systemic distribution of medications because the lungs offer a significant absorption region and can bypass first-pass metabolism. Exubera, an insulin inhalation formulation sold in the United States and Europe, was the first commercially available formulation with this scope. Although this drug was withdrawn only after one year for business reasons , the useThe process of solid materials being dissolved in a solvent to produce a solution is known as dissolution. The affinity between the solid substance and the solvent, as well as the solid’s crystal packing factors, govern the process . AlthougThe dissolution of (solid) APIs is a necessary step before their absorption can occur via epithelial cells in the respiratory tract. It seems dissolution is especially important for poorly water-soluble drugs, as the absorption of highly soluble drugs is less restricted by dissolution and their therapeutic effects are not remarkably affected by the presence of other materials in the formulations. On the other hand, with poorly water-soluble drug powders, the slow dissolution rate in the airways may be limiting the absorption. Slow-dissolving drugs are also anticipated to be more susceptible to mucociliary clearance of drug particles . For theIn 2008, the inhalation Ad Hoc Advisory Panel of the USP decided that there was no concrete evidence to show that the dissolution of orally inhaled drugs was kinetically and/or clinically vital for the existing DPI formulations on the market . AlthougDissolution testing in vitro allows for the distinction between the efficiency of different formulation types and provides an approximation of how drugs would dissolve in vivo. In addition, it is frequently employed in quality control (QC) projects, including batch-to-batch uniformity and stability assessments, and the identification of manufacturing errors . DependiCompared with animal models, in vitro methods for assessing OIDPs offer mechanistic insight into the process of pulmonary drug bioavailability, as well as being advantageous in terms of cost-effectiveness, reproducibility, and accuracy of predictions. Contrary to oral dosage forms with standard dissolution and permeability testing methods, the in vitro methods for dissolution and membrane permeation of orally inhaled particles are challenging, and there is a lack of standardized testing methods for these formulations. This is due to the additional complexity arising from the reproducibility and appropriateness of methods for the collection of respirable particle doses  and the difficulty of designing a reliable dissolution and/or permeability method. A further consideration unique to inhalation products is the epithelial permeability occurring at the air/epithelium interface rather than the liquid/epithelium interface in gastrointestinal absorption, adding to the difficulty of simulating the process. This review will provide an overview of all the in vitro dissolution and permeability testing methods and recent developments in the technology. In vitro methods have seen some major advancements in recent years with technological developments such as 3D cell cultures, 3D printing of tissues, and organ-on-a-chip microfluidic devices, which are heading to replace animal testing in the near future. The potential applications of such advanced technology in in vitro testing of inhalation products and some directions for future research have been discussed, including aerosol particle collection, instrumentation, and optimization of dissolution medium for inhaled drug particles.There are several factors to consider during the design of a dissolution or permeability testing method for inhaled drug powders. These factors have been summarized in It will be noted that, due to technical restrictions, some in vitro dissolution testing methods may be very different from the physiological condition in the airways, where there is a thin layer of highly viscous mucus present on a large membrane surface area, which provides different levels of membrane permeability depending on the nature of the drug and mucociliary clearance. Nevertheless, a measure of the dissolution rate can still contribute to improving the prediction accuracy of in vitro-in vivo correlations. The goal of various designs of dissolution testing and permeability assessments is to best simulate the process of drug absorption from the lungs while accommodating various ranges of drug particles, including variabilities in particle size, crystal form, formulation, and drugs’ physicochemical properties.At present, there is no fixed and standardized dissolution technique accepted by regulators and pharmacopoeias. With growing evidence from studies showing the importance of the dissolution of OIDPs for better in vitro to in vivo correlations and the increasing use of this in the pharmaceutical industry, it is highly likely the dissolution testing of OIDPs will be implemented in pharmacopoeias in the future .The efficient dissolution of inhaled drug particles is one of the key parameters that ensures better performance of OIDPs in the lung. In the last two decades, researchers have developed many dissolution methods that can be used to trace the dissolution of drug particle depositions. It is vital that the methodology can provide reproducibility and robustness and that the dissolution medium can simulate the physiological lumen and discriminate the effect of particle size on the dissolution rate in vivo. There are several crucial factors in dissolution testing that should be considered when developing a method, including agitation rate, flow rate, temperature, and the viscosity and composition of the dissolution medium . In addiThe “Paddle over disc” method (USP apparatus V) was originally developed and approved by the FDA for transdermal dosage forms, but it has also been used for dissolution studies in OIDPs. The dose collected from DPIs on a membrane is placed in a cassette. The cassette is then placed in the USP 2 vessel, and the equipment is operated as illustrated in One of the critical steps in this method is dose collection, which is explained later in the article. The setup of the dissolution testing with respect to the process of collecting aerosol particles presents a challenge with this approach. Specifically, a porous filter is used to keep the particles on the collection surface , and low dissolution medium volumes that simulate gradual absorption of low permeability drugs. The paddle-over-disk method has been utilized by researchers to distinguish different inhalation products . AlthougThe flow through cell dissolution testers are specialized USP 4 apparatuses modified to accommodate the dissolution testing of inhalation powders . Most ofIn this method, the mechanisms of dissolution are diffusion and convection through the filter. Permanent sink conditions and a diminished impact of membrane diffusion during dissolution tests have been reported as the potential benefits of this method compared with the paddle-over-disk methods. However, this is subject to the conditions of flow through the dissolution cell. For example, very low flow rates, especially given the small particle size of the inhalation drugs, can still lead to considerable drug concentration in the vicinity of the powders. Hence, it is advisable that the sink conditions be examined by measuring the API concentrations in the fractions collected during the dissolution testing . In addiAn additional risk with this method is the possibility of air bubbles between the two filters in the system. This can inhibit the wetting of drug particles, which can slow down the dissolution process due to the reduced surface area available for dissolution. Given the flexible nature of this method, the key to overcoming any of the pitfalls is to manipulate variables of the system, such as the flow rate, the membrane, and the geometry of the dissolution cell, to optimize the method for better mimicking the in vivo process of dissolution.® systems were developed for testing the inhaled drugs.As the amount of fluid in the lung lining is very low compared to the volume of fluid in the GI tract and as the fluid in the lung lining is more static, a suitable dissolution apparatus should be developed to reflect the in vivo conditions in the lungs. Based on these limitations, the Franz cell and Transwell® has a variety of applications, including diffusion through membranes or passage through cell layers. For inhalation drugs, in these two systems, a small volume of donor phase is used to allow for the presence of an air-liquid interface, resulting in more biorelevant conditions for dissolution testing [® , this method seeks to more accurately simulate the in vivo environment. However, it is noteworthy that the measured effect is a sum of two distinct processes, namely dissolution and membrane diffusion, with diffusion expected to be the main driving mechanism [With an agitated (such as a Franz cell) or non-agitated system  [® Powder Chamber [Alongside developments in cell culture technology, some research efforts have focused on dose deposition devices to be used with these (mono/multiple) cell layers ,45. SpecPADDOCC) , Vitroce Chamber , and cus Chamber ,48 are e Chamber .®. PerfuPul is a perfusable cell-based system designed for permeability studies that allow aerosol deposition on the air/liquid interface of Calu-3 cells [Efforts have been made to develop specialized cell cultures that improve the modeling of the permeability properties in comparison with established cells such as Calu-3. These include the use of new immortalization methods for alveolar cells , the gen-3 cells . A full -3 cells .Benefitting from advancements in science and technology, numerous in vitro models have been developed to support pharmaceutical drug development as well as the safety assessment of consumer products and environmental pollutants. These in vitro systems aim to act as alternatives to animal testing, increase the experimental throughput, and present a more accurate model for clinical situations than animal models. Despite the availability of sophisticated systems such as 3D cell cultures, reconstructed tissues, and organs-on-a-chip, many of these are specialized for toxicity testing purposes rather than for use as pulmonary absorption models. Examples of tissue models that, according to their suppliers, have the barrier function and potential phenotype for drug delivery experiments are those developed commercially by Epithelix  and MatTek 3D . A wider application of these can be seen in the literature for toxicity studies, while the applicability for drug delivery research is being investigated . FurtherAnother emerging field that may contribute to the future of in vitro pulmonary drug delivery testing is organ-on-a-chip technology. This technology has been made possible due to advancements in cell-culture techniques and biomaterial microfabrication. A review of the currently available lung-on-a-chip models indicates greater accuracy may be achieved with these models compared with traditional monolayer cell cultures . With thFine Particle Dose, defined as particles with an aerodynamic diameter ≤ 5 μm, is an established pharmacopeial method for the in vitro assessment of dry powder inhalers. This particle size range is thought to be the dose that reaches the desirable site of deposition during respiration ,60, with® setups, and cell-based methods, a uniform and reproducible deposition of fine drug particles is a major consideration for the reproducibility of the results. In this case, specialized deposition devices may be employed. Many of the deposition devices do not allow particle size separation. Examples are Astra-type liquid impinger, customized for direct deposition of aerosolized particles onto the cell monolayers [®, which were originally designed for precise pulmonary administration of dry powders to laboratory animals. Alternative systems may allow size-dependent depositions, such as the widely used Astra-type multistage liquid impinger (MSLI) [® exposure system (XposeALI ®3D cell exposure module) and Vitrocell® Powder Chamber, which separate particle sizes by their time of flight.Product particles are normally aerosolized using various impactor designs and then the desired particle size range is collected on filters or membranes, which are then transferred to dissolution or permeability apparatus such as USP II, USP IV, Franz cells, or Transwells  . Other cSome of the most widely used commercial impactors for aerodynamic particle separation are the Next Generation Impactor (NGI), Andersen Cascade Impactor (ACI), fast screening impactor (FSI), or multi-stage liquid impinger (MSLI). For dissolution studies, specific filters and/or membranes are used for the collection of particles from these impactors . ThoughtWhen using the USP II apparatus for dissolution testing, membranes with deposited drug particles from impactors can be directly placed into the dissolution medium or be covered with an additional pre-soaked filter/membrane before being placed into the medium. In this case, a filter cassette is used to keep the filter in place . If partIn an investigation aimed at developing a standardized dissolution testing strategy, Arora et al.  focused When using the various particle collection and deposition methods, it is important to note the impact of the particle size distribution on the measured dissolution rates. Of note is the fact that particle separation in impactors is based on the aerodynamic particle size. In carrier-based dry powder formulations, the primary drug particle size (geometric diameter) drives the dissolution process, whereas the aerodynamic particle size, which is a function of agglomerate size, density, and aerodynamic properties, is responsible for the deposition in the lung. Franek et al., exhibited the effect of primary drug particle size (geometric size) on the dissolution of AZD5423 (obtained from AztraZeneca). They showed that drug particles with an average diameter of 3.1 µm have a much slower dissolution rate than particles with a 1.7 µm mean diameter . In addiIn these investigations, it is also important to note that the amount of drug collected at each stage of the impactors may have an impact on dissolution rate measurements. The effect of drug mass  on the dissolution behavior has been demonstrated for hydrocortisone particles collected from various stages of an NGI . In this®, and Dissolvit® are highly dependent on the diffusion process, hence the anticipated impact of the membrane type and efforts to mimic in vivo pulmonary membrane properties. With USP II methods, especially if the goal of experiments is purely the dissolution mechanism (and not permeation), an optimum membrane pore size may be identified that does not hinder the diffusion of the dissolved drug [Depending on the choice of the dissolution method, the results are affected by the membrane used to varying degrees. Cell-based methods such as Franz cell, Transwellved drug . It has ved drug ,65. A deved drug .The dissolution medium is an important factor that impacts drug solubility and, hence, the dissolution rate of drugs. Therefore, careful consideration should be given to the choice of dissolution media in terms of its composition, volume, and stirring rate during the in vitro assessment of OIDPs, especially due to the lack of standardized methods. Common APIs used in the formulation of orally inhaled products have a wide spectrum of solubility, with current trends in drug discovery moving towards high molecular weight and low solubility drugs . Moreove®, Alveofact®, and Curosurf®, which are commercially accessible and have been used in in vitro dissolution investigations [A number of studies have focused on the exact composition and pH of the fluid in the lung, and it has been reported that the composition is different in various parts of the lungs but also varies between healthy and diseased lungs  and chanigations ,74,75.There is between 10 and 30 mL of aqueous fluid in the lung, including lung surfactants, whereas the dissolution volume in the conventional apparatus ranges from 2 to 1000 mL, often much higher than the amount of fluid in the lungs. To use a low volume of dissolution medium, it has been suggested that the agitation rate should be enhanced to obtain the same dissolution as the large volume of dissolution medium . HoweverAnother factor that should be considered when evaluating the dissolution pattern of orally inhaled drugs is the effect of excipients used in the formulations of MDI or DPI. However, it seems the influence of excipients on the dissolution rate of drugs could be minimized in experimental settings that incorporate dose collection from DPI formulations. Here, the particle size of the lactose carrier is too large to enter Stage 3 of NGI when capturing the drug particles for a dissolution test. Despite this, some DPI formulations incorporate lactose fines (<10 µm) to boost the performance of DPI formulations ,78.In this case, the API may show faster dissolution due to the instant dissolution of the lactose fines from API-lactose agglomerates in the dissolution medium. It should be noted that the agglomerates reduce the specific surface area, hence slowing down the dissolution, unless the agglomerates undergo deagglomeration when in contact with the dissolution medium .The Influence of excipients on the efficiency of orally inhaled drugs is more pronounced in pMDI than DPI, as a wider variety of excipients are used in PMD formulations. For instance, it has been shown that an increase in the content of ethanol in solution-based MDI can alter the aerosol droplet size and the evaporation rate. Furthermore, the changes in the evaporation rate can change the morphology of particles after the evaporation, resulting in a notable alteration in the dissolution of the drug in a solution-based pMDI ,80. In aw/v polysorbate 80 (PBS). Gamble’s solution is a simulated lung fluid frequently utilized as a model for lung fluid even though it lacks surfactant [As an example of a suitable dissolution medium for a poorly water-soluble drug, Al Ayoubi et al. comprehensively studied the dissolution behavior of budesonide in diverse dissolution media in order to correlate the in vitro data to the in vivo data . They usrfactant ,85. The rfactant ,86 in thrfactant ,87,88.f1) and similarity factor (f2). Both approaches are briefly discussed below.Models are used to mathematically describe the dissolution profiles of OIDPs and allow a quantitative comparison of the dissolution profiles when examining data obtained from dissolution tests. This is useful, for example, when aiming to make statements about the similarity or dissimilarity of dissolution profiles. Although statistics are frequently used in the dissolution assessment of many OIDPs, the actual details of the statistical methodology and the data structure are not always clearly discussed, which makes it difficult to accurately assess the quality of the results and the validity of the conclusions. To compare two dissolution profiles, two approaches have been employed. One is comparing the mechanism of drug release by fitting various kinetic models into the dissolution data. Common kinetic models include zero-order release, first-order release, Higuchi, the Hixon-Crowell equation, Korsmeyer-Peppas, and Weibull. The second approach is the statistical comparison of two dissolution profiles by computing the difference factor  is investigated to select the model that can best fit the dissolution data. However, in some cases, other parameters such as the sum of square residuals, the mean square error, and the Akaike information criterion are also considered [Based on the kinetics of drug release and the identification of the release mechanisms, dissolution curves can be described using model-dependent kinetic functions, such as zero-order, first-order, Higuchi, Hixon-Crowell, and Peppas models. When different kinetic models are used, generally the coefficient of determination  is the already-dissolved amount in the dissolution medium at time 0, while in the first-order release model, it is the full amount of drug that existed in the formulation that will be delivered to the dissolution medium (Q0(undissolved)). K0, K1, KH, and KKP are the rate constants of these models. In the Weibull model, Ti denotes the lag time before the onset of the dissolution process, which may be zero in most OIDP cases, and a and b are model constants. In the Korsemey-Peppas model, n is the exponent parameter that indicates the mechanism of drug release.In the above kinetic equations, QGenerally, poorly water-soluble APIs may show zero-order release kinetics. An example of this has been shown for orally inhaled drugs when the flow through cell method was employed to assess the dissolution rate of fiber filter-containing drugs . Pseudo-An example of a first-order release was reported for the dissolution of budesonide when Franz cells and USP apparatus number II were used to investigate its dissolution profile. However, when the flow through cell method was used, the dissolution data did not fit well with the zero-order model .In the case of a controlled-release formulation for inhalation use developed by Salam et al., the dissolution rate was governed by the Higuchi model . This fon values for various dissolution profiles in various buffers were above 0.2, indicating a non-Fickian dissolution.The power law model has been reported for paclitaxel and doxorubicin OIDPs . In this® system [® system were used [® method to study the dissolution of OIDPs containing fluticasone propionate [The Weibull model, which assumes a linear plot between the logarithm of the dissolved amount of drug versus the logarithm of time, has been widely used for OIDPs. For example, Bhagwat et al. employed this to fit the dissolution data for corticosteroids obtained from a modified Transwell® system . In addiere used . The Weiopionate . Despiteopionate . Howeveropionate , indicatf1) and similarity factor (f2), developed by Moore and Flanner [For oral solid dosage forms, a variety of techniques are frequently utilized for the comparison of dissolution characteristics. The most widely used methods are model-independent methods known as the difference factor ( Flanner  and reco Flanner  for compt-test) or for multiple dissolution time points (MANOVA). Even though multivariate methods (such as MANOVA) compare full dissolution profiles, they might not have enough statistical power to identify significant differences. ANOVA and t-tests only compare one dissolution time point; they might be more robust when a meaningful time during the course of the dissolution is picked for the comparison.Tsong and Hammerstrom  offer stT) and reference (R) dissolution profiles is currently performed using two model-independent methods based on a difference factor (f1) and a similarity factor (f2):The comparison of the test , there is no difference .If the f2 values between 50 and 100 (above 50) suggest similarity . Additionally, authorities  want that the sponsor compares dissolution profiles using the similarity factor using at least 12 distinct dosage units. When comparing dissolution profiles to support “biowaivers” for process scale-up or formulation adjustments for oral solid dosage forms, regulatory advice has mostly focused on the f2 measure. Generally speaking, “suitable statistical testing with the rationale” is permitted under the FDA guidance [f1 and f2, is another factor for OIP particles fractionated by cascade impactors.guidance ,99. The guidance , which aThe percent inaccuracy across all time points is measured by the difference factor, or Parallel to technological advancements in cell-based methods, tissue engineering, and material fabrication techniques, the evaluation of the drug delivery efficiency of pulmonary drug delivery systems has evolved substantially. These techniques aim to eventually replace in vivo animal experiments, which can no longer be considered the gold standard in bioavailability, pharmacokinetics, or drug safety investigations. The lifting of legal requirements for animal testing of new drugs by the U.S. Food and Drug Administration (FDA), signed by President Joe Biden in December 2022, is a landmark change that is yet to be exploited by drug discovery and development disciplines utilizing the in vitro techniques discussed here as well as an in silico information-technology-driven approach. To be more aligned with in vivo conditions, new technology should be able to simulate the presence of a small amount of fluid in the lungs, mucociliary clearance, the presence of viscous mucus and its composition, along with adequate multi-cell diversity and sink conditions. Along with these complex cell-based techniques, such as microfluidic lung-on-chips, simpler in vitro experimental setups will continue to be used due to several advantages. First, these methods allow for detailed mechanistic studies since they focus on specific unit processes leading up to pulmonary drug absorption. The second advantage of these may be their higher throughput and cost-effectiveness, which makes them more accessible to specialized research and development entities. In addition, these less complex in vitro methods have fewer intervening experimental parameters, reducing the variability in experimental results. Moreover, a combination of various in vitro experiments may be employed to mathematically model the clinical bioavailability. This review is a compilation of various in vitro techniques that are used to simulate drug deposition, dissolution, and permeation from the lung epithelium. It has covered both the established techniques, with practical guidelines and experimental considerations, as well as upcoming novel techniques that may develop in the future for widespread use in product development research settings.Following the drug deposition in the lungs, the dissolution of APIs is the first step before absorption occurs via epithelial cells in the respiratory tract. Due to the poor solubility of many of the orally inhaled drugs and the recent shift in drug discovery towards highly lipophilic, high molecular weight drugs with poor water solubility, dissolution kinetics is an extremely important process to be considered when assessing new formulations. It is also evident from the literature that dissolution studies may be less important for highly water-soluble drugs, whose dissolution and absorption from lung depositions are also expedited due to their fine particle size. Currently, performing the dissolution test for orally inhaled drugs is not required by the regulatory authorities due to the small dose  of current OIDPs and their fine particle size in DPI formulation. However, with the market moving towards high-dose DPI formulations as well as an interest in DPI formulations for systemic delivery of a wider range of drugs that may be poorly water-soluble, this may change in the future. The established in vitro dissolution tests should have the capability to discriminate between different formulations and different APIs’ particle sizes. Although simple dissolution methods may not be able to closely mimic the exact in vivo conditions, they should be able to reproducibly differentiate various formulations with different performance efficiencies.Dissolution techniques such as the paddle dissolution tester, flow through cell apparatus, or Franz cell are still popular for orally inhaled drugs. The selection of a dissolution methodology is critical, as the method of choice can impact the resulting dissolution kinetics. Methods differ not only in their instrumentation but also in the mechanism by which the dissolution process happens within these experiments. In methods such as Franz cells, where dissolution occurs mainly by diffusion, it is important to investigate the impact of membranes. Considerations should also be given to maintaining sink conditions since some methods, such as Transwell and Franz cells, employ only a low volume of dissolution medium, which will saturate quickly with low-solubility drugs. In these cases, a careful choice of dissolution medium composition becomes specifically critical to aid in maintaining a sink condition through the use of solubility enhancers as well as mimicking the natural surfactants present in the lungs.®, Franz cell, and flow through. This is due to the variable wetting and agglomeration propensity of particles in high powder content areas of the membrane.When using the various particle collection and deposition methods, it is important to note the impact of the particle size distribution on the measured dissolution rates. It should be noted that particle separation in impactors based on the aerodynamic particle size may be affected by the presence of the filter used for the collection of particles. Hence, validation of particle collection methods is a crucial task required for robust results to be obtained. In addition, consideration should be given to the amount of the collected powder as well as a uniform powder distribution on the deposition membrane since these can affect the dissolution rate, especially in methods such as transwellFinally, it is also important to explore what statistical tests are most suitable to compare the dissolution profiles of two inhaled products. This is important when inhaled generic products are being developed and the dissolution behaviour of the test product should be compared with the dissolution profile of the reference product. To overcome the hurdles and challenges associated with the dissolution of OIDPs, a good collaboration between academic institutions, the pharmaceutical industry, and regulatory bodies seems to be essential.


We therefore design a hierarchical dynamic Bayesian learning network model that integrates an array of Gaussian mixture model – hidden Markov models (GMM-HMMs), where each GMM-HMM learns the multi-sEMG processes either during the idle state, or during the motion initiation phase of a particular motion task. To test the hypothesis and evaluate the new learning network, we design and build a upper-limb sEMG-joystick motion study system, and collect data from 11 healthy volunteers. The data collection protocol adapted from the psychomotor vigilance task includes repeated and randomized binary hand motion tasks (push or pull) starting from either of two designated idle states: relaxed , or prepared (with muscle tones). We run a series of cross-validation tests to examine the performance of the method in comparison with the conventional techniques. The results suggest that the idle state recognition favors the dynamic Bayesian model over a static classification model. The results also show a statistically significant improvement in motion prediction accuracy by the proposed method (93.83±6.41%) in comparison with the conventional GMM-HMM method (89.71±8.98%) that does not explicitly account for the idle state. Moreover, we examine the progress of prediction accuracy over the course of motion initiation and identify the important hidden states that warrant future research.Decoding human action intention prior to motion onset with surface electromyograms (sEMG) is an emerging neuroengineering topic with interesting clinical applications such as intelligent control of powered prosthesis/exoskeleton devices. Despite extensive prior works in the related fields, it remains a technical challenge due to considerable variability of complex multi-muscle activation patterns in terms of volatile spatio-temporal characteristics. To address this issue, we first hypothesize that the inherent variability of the  The technology of sEMG-based motion intention detection will enable intelligent user-driven functional movement training with the emerging wearable hand robot technology, while such training has demonstrated values for rehabilitation and assistive utilities in stroke survivors2. Other applications such as upper-limb prosthetic control5 and rehabilitation exoskeleton7 further illustrate its clinical value for patients with impaired mobility. This applied research discipline has seen a steady pace of acceleration in recent years thanks to the advent of low-cost high-user-compliance sensing solutions such as the Myo armband8.By probing muscle activation non-invasively, surface Electromyography (sEMG) has become a prominent neuroengineering tool for detecting voluntary upper limb motion intention, and accounts for approximately 40% of the motion intention detection strategies related to robotic upper-limb orthoses according to a recent reviewA large variety of detection algorithms have been reported that broadly fall into two categories. In the first category, the algorithms typically employ a time window and reduce the detection problem into classification of sEMG in the individual time windows. In the second, the algorithms seek to capture the complex dynamics of sEMG activities continuously.9, which often examine quasi-stationary sEMG patterns over a short time window typically of a few hundred milliseconds. For example, a forearm sEMG system10 used a 250ms time window and a parallel conditional classifier and achieved average classification accuracy rate of 6.6% for discrete (1 DOF) hand and wrist movement and 10.9% for combined movements (2 DOF). In another study11, a sliding window with a 256ms length and a 32ms step size was used with a Gaussian mixture model (GMM) classifier to recognize 6 upper-limb motions. Similar methods but using different pattern recognition techniques have also been reported, including K-Nearest-Neighbor (k-NN)12, Support Vector Machine (SVM)13, Linear Discriminant Analysis (LDA)14, and Extreme Learning Machines (ELM)15 etc. However, the static model approach may face inherent limitations associated with either fixed or variable window length and difficulties in capturing time dependency patterns of importance9.The first class of algorithms can be referred to as ”static” models18. Especially, a typical dynamic Bayesian network model called the hidden Markov model (HMM) has widely been applied to gesture recognition19. In a recent study, for example, a natural Bayesian nonparametric extension of the classical HMM was applied to recognize 17 gesture tasks18. It has also been demonstrated that a HMM model of sEMG can be used to estimate the elbow joint angle during the flexion/extension motion20.The second category of algorithms explore important temporal information associated with the inherently non-stationary sEMG over longer or indefinite time ranges. By capturing the temporal dependencies therein, these models may recognize inherent temporal structures of sEMG activation patterns21. It has also been demonstrated that sEMG and kinematics data may be combined to predict the head motion at the next 17.5ms, although the result has yet to demonstrate significant value of sEMG on top of kinematics for the prediction22.While these existing dynamic models usually consider classifying motion during the process of the motion or even at the end of it, other researchers have also explored predicting specific motion parameters in advance. For example, a deep-learning method was introduced to predict the knee angle at the next 100ms during walking23, in order to avoid any noticeable latency in prosthesis control, the motion intention should be predicted no later than 100 to 150ms after the onset of sEMG activation. In another independent study24, the authors have shown that Gaussian mixture models can predict upper-limb Go-forward or Go-backward motion at 100ms before the actual move begins.Comparing with the above research works, early prediction of motion intention during motion initiation has received much less attention so far, whilst early prediction is highly wanted in various rehabilitation and assistive applications. As suggested by an empirical studyidle state and the motion initiation process. However, to the best of our knowledge, the complexity and variability of these sEMG processes have not been sufficiently accounted for. In contrast to existing approaches, we propose that the idle state preceding the motion initiation process should be addressed explicitly, since the variability of this state will determine the process of how the skeletal-muscular system changes from the unintentional state of idle to activating the related multiple muscle groups individually.Prediction of motion intention during motion initiation (e.g. before motion onset) requires learning the sEMG processes over both the idle state and the uncertainty of the temporal processes of motion initiation. The research also needs to empirically examine our hypothesis that the new design can lead to higher accuracy in motion intention prediction.Therefore, this proof-of-concept research aims to demonstrate the feasibility of designing machine learning that explicitly accounts for both the variability of the idle state, or learns sEMG activity processes during motion initiation for any particular combination of the motion class and the idle state. Thanks to the Bayesian methodology, this method allows to compute, at any arbitrary time point before motion onset, the likelihood of the upcoming motion belonging to each motion class of interest.Particularly, we design a hierarchical machine learning method that comprises a set of dynamic Bayesian networks . Each of them either learns sEMG data in a particular class of the To empirically validate the new machine learning method, we design a data collection protocol to acquire upper limb sEMG recordings associated with different hand movements as well as different idle states. We seek ethical approval and recruit 11 participants in this proof-of-concept study. Various tests are employed to examine the new machine learning design in comparison with the conventional method.The rest of the paper is organized as follows. Section This section consists of the methodology of the data acquisition and the proposed hierarchical dynamic Bayesian learning network. We first introduce the data collection system and the upper-limb voluntary movement experimental paradigm to collect the sEMG signals during a binary upper-limb motion task in two separate idle states. The hierarchical architecture of the machine learning model and the motion intention prediction algorithm are then introduced. Lastly, we provide a detailed introduction to the algorithm of the feature extraction and the Gaussian mixture model- hidden Markov model (GMM-HMM).Human sEMG data collection was conducted with 11 healthy volunteers who gave written informed consents in advance. The study was performed in accordance with the protocol IRB Ref. No. 2020-006, which was approved beforehand by the ethics review board of the A*STAR Human Biomedical Research (HBR) office. The research followed all relevant guidelines/regulations. While anthropometric characteristics may affect the quality of sEMG, this protocol was not particularly designed to investigate these characteristics. Nevertheless, our participants were all within the normal range of Body Mass Index.The data collection system consisted of an integrated sEMG-hand-motion measurement device including a bio-potential amplifier (Neuroscan NuAmps) for sEMG measurement and a modified Logitech Extreme3D joystick for hand-motion measurement. Both the sEMG and the joystick measurements operated at the sampling frequency of 500Hz, while the hardware stimcode mechanism on the amplifier was used to precisely determine the sampling times of the received time samples. The recorded sEMG signals were high-pass filtered at 15Hz cutoff frequency by using a third order Butterworth high pass filter and notch filtered (50Hz) by using a third order Butterworth notch filter to remove unwanted noises and interference.25 paradigm, it used visual task cues on the computer display to designate which of the three tasks the user needs to perform as quickly as possible; hand pushing to the opposite side (hereafter push); hand pulling to the same side (hereafter pull); and thumb pressing the control button on the joystick. Note that the button press motion data were excluded from this research so that we should focus on binary-class motion prediction involving push and pull tasks only.The data collection session for each human subject consisted of a sequence of randomised and computer-guided hand motion tasks. Only one hand was considered for the motion tasks and the particular side was chosen according to individual preference. The system and the time structure of the task is illustrated in Fig. In relevance to the hand motion tasks, six muscle groups were selected for bipolar sEMG measurement, namely triceps, biceps, anterior deltoid, posterior deltoid, flexor carpi radialis, and extensor carpi radialis. See Fig. push and pull task repetitions for each human subject is 120, which is equally shared by the two motion tasks. The sequence of the tasks was randomized such that the user would not be able to anticipate the upcoming task, hence minimizing unwanted involuntary/voluntary activation of muscles. To further minimize possibly compounding neuromuscular factors related to unwanted motion planning and initiation that should not be present in the designated idle state, our computer programme also randomized the time interval (uniformly between 3 and 10 seconds) from the beginning of the designated idle time till the task cue onset. Additionally, we instructed the subjects to minimize any motion intention or thoughts related to the hand until the task cue was given. We believe these design elements would combine to create a clean state of idle free of motion intention related to the upperlimb.The total number of idle state. Specifically, we designated two possible idle states: relaxed and prepared. At the beginning of each motion task repetition , the computer programme would pseudo-randomly choose from the two idle states and prompted a visual cue on the display for the human subject to follow. The relaxed state means the upperlimb muscles would stay relaxed and see no more muscle activation beyond what were necessary for softly holding the hand in position. On the other hand, the prepared state means the upperlimb muscles could be engaged but to produce reasonable isometric contraction so that the hand firmly held onto the joystick. We did not prescribe further specifications about muscle activation patterns since we would accept certain variations of the two idle tasks.Another new feature of the protocol design relates to the aforementioned hypothesis about the variability of the prepared idle tasks and relaxed idle tasks. Henceforth, each subject’s data set consists of 30 repetitions of each of the four combinational tasks: Prepared-Push, Prepared-Pull, Relaxed-Pull, Relaxed-Pull.Each subject performed an equal number of Due to possible lapse and human errors, not every motion instance would constitute a valid trial data for our study. We have carefully compared the registered hand (joystick) motion signals with the event log from the computer programme while also assessing the sEMG quality visually. We removed those motion task trials of either apparent or suspicious incorrect task performance (e.g. no reaction after the cue). The statistics of valid trials after this data screening process are given in Table idle-period. Therefore, our motion onset detection algorithm used a threshold mechanism on this deviation to determined the motion onset time point, and the threshold value was empirically determined so as to reliably detect the first moment of the motion.There were two important time points of interest in each motion task trial: the task cue onset, and the actual motion onset. While the former can be readily extracted from the data log, the latter must be determined from the motion data  instead. Specifically, the hand motion onset was marked by the first abrupt deviation of the joystick’s X position signal (linked to the pull-push motion) from the signal level during the preceding The time interval between the two time points is the so-called reaction time, which indicates how quickly a human subject reacts to a visual motion cue. We provide the statistics of the reaction times in Table  idle states. The overall network design is depicted in Fig. a-posterior probability of each motion class given the idle state sEMG and the motion initiation process sEMG. Note that thanks to the dynamic Bayesian modelling, the method is able to compute the a-posterior probabilities at any time point during the motion initiation process, hence enabling motion prediction ahead of the motion onset.As described earlier, we aim to design and experimentally validate a hierarchical dynamic Bayesian learning network that can accurately learn and predict the continuous and complex process of motion initiation which may start from different a-posterior probability of each idle state, namely, P(Prepared) and P(Relaxed). Similarly, let the motion initiation sEMG be Let the idle sEMG be Push or the Pull class), and let the idle state class be Prepared or the Relaxed state).For simplicity of mathematical expression and also for generalization of the method, we denote the motion intention class by Hence, the a posterior probability of a particular motion intention for observed sEMG data is given byFigure Without loss of generality, let the power curve be A with n samples and m dimensions, after normalizing the data in every dimension to produce the normalized matrix B from A, the eigenvalues B is calculated. Then, the first few eigenvectors p in the following.In order to enhance the computational efficiency of the system, we used principal component analysis (PCA) to reduce the dimensionality of the data. Principal component analysis is a popular method for data compression. For a giving data matrix 27. HMM calculates the posterior probability of an observed sequence of features, which is expressed as a Gaussian mixture model.After extracting the feature sequences from the raw sEMG signals, the sequences will be used to build the hidden Markov model (HMM), which is a type of Bayesian classifier and has been used effectively to categorize EEG and sEMG signalsM, of Gaussian distributions, and it is a useful technique to quantify the statistical characteristics of the features when using the hidden Markov model (HMM). Following the modeling of the feature series by the GMM, the HMM will be used build the ISM/MIM.The Gaussian mixture model (GMM) is a probabilistic model that assumes that all data points are generated by a finite number, denoted as 28.t depends only on the previous moment’s state , which is based on the assumed values of the parameters, calculates the expected estimates of the unknown variables. In the second step, maximization (M-step), the maximum likelihood estimates of the parameters of the model are given based on the estimates of the unknown variables as follows,N means the number of states and T means the length of the observation sequences.In this way, for the HMM’s training phase, two components, transition matrix Decoding and the other is called Likelihood. In the Likelihood problem, the trained HMM model . Considering the difference between the different subjects, the models are trained and tested individually. All experiments in this paper were conducted with a five-fold cross-validation to obtain reliable model performance. The performance of the model in distinguishing Pull and Push motions in two pre-intention muscle force levels is shown in the first two columns in Table In this experiment, we evaluate the performance of the motion initiation models (MIMs) with the knowledge of the relaxed state is higher than that in the prepared state. On average, the accuracy was relaxed state, and prepared state. This indicates that the accuracy of motion recognition is about six percentage points higher in the relaxed state than in the prepared state, and the smaller variance means more consistent performance.From the results, it can be seen that the model has a high accuracy for motion intention prediction. The accuracy of motion recognition in the idle states (Prepared and Relaxed).To statistically analyze our results, we first used the Lilliefors test to figure out whether the data came from a normal distribution so that we could select an appropriate statistical test. The test results of accuracy rate data reject the null hypothesis. In other words, the accuracy rates are not normally distributed. Thus, we used Wilcoxon signed-rank test to statistically test our results. Because our experiment is conducted with a five-fold cross-validation, we make pairwise comparisons on the idle-state-dependent method and conventional method in each fold. For the idle-state-dependent method, we can also test of significance of differences in the model performances on the two idle states was statistically significant idle states have a significant effect on motion recognition.Wilcoxon signed-rank test shows that the accuracy difference between the two idle states separately, the idle state dependently trained models are compared with the GMM-HMM model trained conventionally . In the conventional way, the model is trained by all sEMG signals regardless idle states. This conventional method has been used to estimate the joint angle20 and hand movements31 successfully. The experiment uses mixed data from two idle states to train the GMM-HMM with four Gaussian distributions and three hidden states, and separate data from two idle states to measure the model’s performance in each idle state. The results are shown in the last two columns of the Table To further show the advantage of training different relaxed or prepared states. The differences between the two methods are significant idle states. Furthermore, in five of eleven subjects, the proposed method has a better performance than the conventional method in both idle states. In four subjects, the proposed method gets a higher accuracy rate in one idle state and the accuracy in the other idle state is equal to the conventional method. This indicates that training the motion intention sequences but ignoring the idle states leads to confusion in the model.As can be seen from the results, the accuracy rates in the conventional method are lower than the accuracy rates in separately training method in either idle states have an impact on motion intention recognition. So, recognition of different idle states benefits the whole model performance. For the recognition of idle states (prepared or relaxed), the signal from 600ms before the motion command (cue point) was used. For sEMG signals, Bartuzi et al. claims that 30-80Hz sEMG component depends on muscle force32. Thus, a linear discriminate analysis (LDA) model using frequency domain features is compared with the idle state model (ISM) model in this paper. In ISM, a GMM-HMM with four Gaussian distributions and three hidden states was trained with the features extracted through the method we introduced in “From the above section, the results indicated that the idle state discriminate rate in both models is around 50%, implying that the models don’t work, because in this task the chance level is 50%. Since the results of the model are good for most of the subjects, it can be inferred that the failure of the model to discriminate idle states for Subject 4 is not the problem with the model, but rather due to the fact that the subject did not respond well to the relaxation and preparation instructions while performing the experimental data collection. In other words, Subject 4 kept upper limb muscle groups in the same idle state throughout the experiment, so the idle state is not discriminant. This analysis can also be corroborated by Table idle states, relaxed and prepared, is 100%. Even though training the GMM-HMM model neglected the various idle states, the accuracy rates are still high.From the results, it can be found that the hidden Markov model is slightly more accurate for the majority of participants than the LDA method but the difference is not significant. Among the different participants, the difference in accuracy is significant. One point worth discussing is that the model is very variable for individual subjects. For Subject 3, Subject 5, and Subject 8, both models can achieve a near 100% correct rate. In contrast, for Subject 4, the To demonstrate the validity of the proposed hierarchical model, we compared the proposed hierarchical dynamic Bayesian model and the conventional GMM-HMM. Table It is interesting to investigate the two associated processes during the motion initiation: how the hidden states converge from the idle state to the definitive motion onset time point, and how the accumulated prediction power varies at the same time. To this end, we examine each time point up to 400ms ahead of motion onset, and run the proposed motion prediction algorithm on the partial multi-sEMG series (up to that particular time point). The result is illustrated in Fig. As expected, the accuracy rate increases monotonically from the chance level of 50%. The increase is minimal, if any, when the first-order hidden state is dominant. The 2nd state seems transitional but not well defined, as there is hardly any point of time that sees the state becomes the dominance. The 3rd state indicates the definitive stage, which may come into the dominant position either abruptly (Subject 6 and Subject 7 being notable examples), or quite gradually over a long time range (Subject 11 being the notable example). Furthermore, the progress of the 3rd state into the dominant position appears to correlate well with the increasing curve of the classification accuracy in each and every case.Pull vs Push) in multi-sEMG activation begins to form as early as 200ms.The graphs indicate that, generally, the prediction accuracy begins to increase noticeably at 100ms ahead of the motion onset. Subject 5 and Subject 10 are examples that this important time point can become as early as 200ms, indicating that predictive information  and a binary hand motion task (pull or push). We have integrated an sEMG device to record 6 muscle activities of 6 select muscle groups of the arm controlling the hand motion. We have run a series of offline training-prediction tests using cross-validation and examined the prediction accuracy of the proposed method in comparison with the conventional machine learning method that does not address the variability of the idle state.We have built a data collection protocol for acquiring human sEMG data associated with hand motion on a computer joystick while considering two specific relaxed or prepared) has a significant impact on the accuracy of dynamic Bayesian models for the motion initiation sEMG processes. The improvement in prediction accuracy is consistent across nearly all of the 11 human subjects in this study. It is noteworthy the prediction accuracy tends to be higher under the relaxed idle state. As we understand it generally, the Bayesian prediction accuracy is determined by the uncertainty (randomness) of the signal/pattern. This result seems to indicate that the designated prepared idle task would see a larger variability in the motion initiation sEMG process. This is related to the nature of the designated prepared idle task that would see a variety of variational isometric muscle contractions. The designated relaxed idle task, on the other hand, would not see such a variation in isometric muscle contractions. Hence, we may hypothesize that an appropriate break-down of the ‘prepared’ idle state class may lead to more accurate dynamic Bayesian modelling of the motion initiation sEMG processes.Our results have shown that, as expected, the knowledge about the idle state  activities.Apparently, the test result depicted in Fig. Note that the primary purpose of this research was to validate a new detection method designed with an experimental study. Tentatively we used a three-state configuration for the hidden states, and it will be interesting to see if a more articulated design will capture finer intricate details in the temporal structures of the multi-sEMG processes during motion initiation. Besides, the current study only considered two classes of movements. Future follow-up studies may look into more motion and idle classes.34. Deep learning is generally used as a discriminative classifier to recognize different intentions during the gesture process or after the gesture is completed, which differs from the present subject matter which aims to construct a generative model of the motion initiation process prior to the beginning of the motion. Nonetheless, deep learning provides for automatic learning of discriminative feature extraction from a large amount of data, which is in contrast to the general machine learning methodology that depends largely on the effectiveness of feature engineering. On the other hand, DL requires a large training data set from each individual since large inter-subject variations are often present in the EMG activation processes. That can be prohibitively demanding in actual use scenarios. To address this issue, recent years have seen proposals of new DL-EMG algorithms using transfer learning36. It will be interesting to study how transfer learning DL may apply to the decoding of motion initiation processes. Furthermore, this research currently focuses on modeling the dynamic processes of EMG activities prior to motion onset, than on analyzing specific EMG features. Hence only a small basic set of EMG features were used. Future research using DL may consider SHapley Additive exPlanations or alike to understand the behaviour of the machine learning model37.Recent years have seen increasing interest in deep learning (DL) for decoding human motion intention especially in hand gesture classificationidle state can significantly improve the intention prediction of motion initiation sEMG. Particularly, we designed a hierarchical machine learning method that comprises two sets of related dynamic Bayesian networks that either learns sEMG of the idle states, or learns idle-state-dependent sEMG activity processes during motion initiation. We also reported an experimental study in which we built a data collection protocol for human sEMG data associated with hand motion on a computer joystick, with designated idle state tasks and a binary motion task. Our results suggest that the idle state recognition favors the dynamic Bayesian model over a static classification model. We have also shown that the proposed machine learning method can produce significantly higher accuracy in a 2-class motion intention prediction task than the conventional GMM-HMM method. The performance of our work is still restricted by the limited dataset, including the number of participants and the complexity of the movements. We intend to collect more diverse data in the future in order to extend our work to predict human movement intention. Moreover, we suggest that future research may study the prepared idle state and explore more sophisticated models especially for the last two hidden states in the present dynamic Bayesian models.In conclusion, we have shown that integrated machine learning of the


The dynamic multi-objective optimization problem is a common problem in real life, which is characterized by conflicting objectives, the Pareto frontier (PF) and Pareto solution set (PS) will follow the changing environment. There are various dynamic multi-objective algorithms have been suggested to solve such problems, but most of the methods suffer from the inability to balance the diversity of populations with convergence. Prediction based method is a common approach to solve dynamic multi-objective optimization problems, but such methods only search for probabilistic models of optimal values of decision variables and do not consider whether the decision variables are related to diversity and convergence. Consequently, we present a prediction method based on the classification of decision variables for dynamic multi-objective optimization (DVC), where the decision variables are first pre-classified in the static phase, and then new variables are adjusted and predicted to adapt to the environmental changes. Compared with other advanced prediction strategies, dynamic multi-objective prediction methods based on classification of decision variables are more capable of balancing population diversity and convergence. The experimental results show that the proposed algorithm DVC can effectively handle DMOPs. At present, most multi-objective optimization solutions4 are used to solve static optimization problems8. Nevertheless, a reality multi-objective optimization problem is a complex optimization problem with a dynamic environment, changing parameters, conflicting objectives. Due to the constantly changing environment, the Pareto optimal front (POF) and the Pareto optimal set (POS) are not fixed. Static optimization methods have been widely used in the field of evolutionary computation, but they often suffer from the lack of fast response mechanisms. In particular, the populations in Dynamic Multi-Objective Optimization Problems (DMOPs) tend to lose diversity over time, which results in a gradual convergence of the populations at later stages of evolution. This convergence makes it increasingly difficult for the populations to adapt to new environments9. To address this issue, it is important to develop improved Multi-Objective Evolutionary Algorithms (MOEAs)11 that have fast response mechanisms, which can help to maintain the diversity of populations and ensure their adaptability to changing environments. In recent years, many dynamic multi-objective algorithms have been proposed, and these methods can be roughly divided into: diversity introduction methods, diversity maintenance methods, prediction-based dynamic multi-objective methods, and classification based on decision variables.Dynamic multi-objective optimization problems (DMOPs)12 and the diversity maintenance method13 is to increase the diversity of the population. Some mutant individuals are introduced into the population. With the help of mutant individuals, the population can better follow the environment changes and converge, instead of falling into convergence prematurely and unable to adapt to the environment changes. However, diversity-based methods have very significant disadvantages. Diversity-based methods rely too much on static algorithms, and can only find new optimal solution sets through static algorithms, so the convergence speed will continue to decline. Therefore, how to stop relying on static methods to find diversity points and how to add diversity points to make the population reach the ideal state?The ultimate goal of the diversity introduction method14 uses predictive models to predict quality populations after changing environments. Although, predictive models play a role in the convergence of populations. Nevertheless, most predictive models require training cycles and the performance of predictive models on certain problems is sometimes generally poor. Consequently, the predictive models required for prediction-based methods need to have two conditions: 1. They need to have a short training cycle and be able to respond quickly; 2. For predictive models to be robust they need to be able to cope with different types of test problems.The prediction-based dynamic multi-objective approach15 can be divided into three broad ways: (1) dominance relationship-based classification of decision variables16. At its core, the idea is to perturb the detected decision variables and observe whether all perturbations are mutually dominant. If all perturbations are not mutually dominant, then the decision variables are defined as diversity correlated. All cases other than this are defined as convergence-related. Adopting this category usually causes populations to be overly enmeshed in dominance relationships at the expense of population diversity. (2) Angle-based classification of decision variables17. A fitting line is formed using the perturbation points, and the angle between the fitting line and the hyperplane normal is judged by the angle between the fitting line and the hyperplane normal. An acute angle is close to a right angle, then the decision variables are defined as diversity related, otherwise they are defined as convergence related. (3) Monotonic-based classification of decision variables18. The method defines positive and negative correlations between decision variables and objectives. And on this basis, the Spearman rank correlation coefficient (SRCC)20 is used to evaluate the correlation between variables and objectives to avoid the defect of dominance relationship failure. These three approaches to categorizing decision variables all suffer from the same problem: how to design different evolutionary strategies to address different decision variables?The classification of decision variablesHow to introduce diversity correctly and keep the population convergence and diversity balanced?In order to respond quickly to environmental changes, what is the best way to design a prediction strategy that is both robust and efficient?If the decision variables are classified, what kind of method should be used and what is the response strategy after classification?Based on the above problems, this paper proposes a dynamic multi-objective optimization method based on the classification of decision variables. The classified decision variables can better predict the populations after environmental changes. Different prediction strategies are effective in balancing the diversity and convergence of populations. The main contributions of this paper are as follows:A static classification strategy is proposed to classify decision variables into three categories, which enables the algorithm to better identify the uses of decision variables. The different decision variables are explored more effectively to balance the diversity and convergence of the new middle group.One strategy is proposed to correct the classification of decision variables in a dynamic environment. The population is prompted to respond to environmental changes and adjust the evolutionary direction of decision changes to ensure that the population evolves in the right direction.Different prediction strategies are provided for different decision variables, and adaptive prediction strategies are selected according to different decision variable categories, thus enabling adaptation to dynamic environments. (3) Different prediction strategies are provided for different decision variables, and adaptive prediction strategies are selected according to different decision variable categories, thus enabling adaptation to dynamic environments.In summary, the dynamic optimization algorithm design needs to face the following problems: n-dimensional decision variables. m is the number of objectives, t included in the objective function of DMOPs represents the time variable, which is calculated as follows:DMOPs are defined as minimization problems, and their mathematical formulation can be defined as follows:t is related to the number of iterations of EA, so t.The value of Dynamic Pareto Dominance) At time t, assume that any two individuals  At time t, assume that there is no decision vector x, then x is a pareto optimal solution, the set of all non-dominated solutions is called the Pareto-Optimal set (POS), that is: At time t, the mapping of the  was proposed by Harrison et al.22 to address the shortcoming that the change detection mechanism relies on the observation of changes in the target space. Based on NSGA-II24, the DNSGA-II25 algorithm was proposed, which was divided into two adaptive algorithms, DNSGA-II-A26 as well as DNSGA-II-B, but was not conducive to solving complex environmental change problems.In recent years, various DMOAs have been proposed to address DMOPs, and the core idea of these DMOAs is to balance diversity and convergence in response to environmental changes. The first consideration after environmental changes is to maintain the diversity of the population and to introduce random or mutant individuals in relation to the detection of environmental changes, so the introduction of diversity becomes one of the solutions. The introduction of diverse individuals cannot be introduced randomly, as the dynamic problem Pareto solution set and Pareto frontier change with the environment. In other words, increasing population diversity needs to be added through theoretical methods, while blindly adding random points will only generate populations in a bad direction. Consequently, Deb et al.27 proposed a novel dynamic multi-objective optimization algorithm (DMOA-DM) based on region local search and memory, using NSGA2-DM to store useful information (memory) to guide the optimization of populations. Liang et al.28 proposed a novel dynamic multi-objective evolutionary algorithm which incorporates a hybrid algorithm of memory and prediction strategy (HMPS)30 and decomposition-based multi-objective evolutionary algorithm (MOEA/D31). Differential prediction based on two consecutive population centroids is utilized if the detected change is not similar to any historical change; otherwise, memory-based techniques are applied to predict the new position of the population.The diversity maintenance approach, which can also be called a memory-based strategy, focuses on using historical information in the stored environment and reusing them after the environment changes. In contrast to diversity introduction methods, diversity maintenance mechanisms usually directly store historical PS as initialized populations. Nevertheless, this method is limited to solving continuum optimization problems, and it is also difficult to cope with high degree of environmental changes. Li et al.32 proposed a population prediction strategy (PPS) that can initialize the entire population by combining the prediction center and the estimated stream shape. Zou et al.33 combined special points and centroids to create a prediction mechanism. This prediction mechanism uses the adjacent time interval as the prediction step and directly predicts the set of non-dominated solutions. Jiang et al.34 developed an inflection point-based migration learning method called KT-DMOEA. in the proposed method, a trend prediction model (TPM) was developed to generate predicted inflection points, and then an unbalanced migration learning method along with the TPM predicted inflection points were used to generate high-quality initial populations.The prediction-based dynamic multi-objective optimization algorithm also exploits some historical information, but in contrast to the diversity maintenance approach, the prediction-based approach is more reliant on the prediction strategy, and the optimal solution after the change of environment is dependent on the strength of the prediction model. Unfortunately, this method only takes into account changes in the center of the flow pattern and is only relevant to the historical information of the last moment, so it has significant limitations for population updating. Zhou et al.38. While the decision variable classification in static MOEAs is performed only once and the categories of decision variables will not revert after classification, for dynamic MOPs these strategies lose their effectiveness. Liang et al.39 proposed a dynamic multi-objective evolutionary algorithm based on the classification of decision variables. The Spearman rank correlation coefficient (SRCC)18 was used to determine the categories of the decision variables in static classification. A nonparametric t-test was utilized to further correct for variable categories after environmental changes when dynamic environments were in place. Liu et al.16 introduced a new DVC classification method for decision variables based on the monotonicity of the optimization objective, which does not make use of dominance relations but uses reference vectors to guide the analysis of decision variables.The methods of diversity introduction as well as the prediction methods do not consider the properties of the decision variables during the iteration, and these methods can be regarded as a probabilistic model for searching for optimal values of the decision variables. In other words, these methods assume that all decision variables have the same probability of functioning in diversity as well as convergence on the population. Nonetheless, in most DMOPs, the probabilities are different, and different nature of decision variables should be corresponded to different search models to get better solutions. In static MOPs, the categories of decision variables can be determined by perturbing the decision variables to produce a large number of individuals and then using fitness assessmentTo address the above problems, we propose a dynamic multi-objective optimization algorithm based on classification prediction. The algorithm consists of three important parts: The first part is the classification strategy of static decision variables, which divide decision variables into two categories: diversity-related decision variables and convergence-related decision variables. The diversity-related decision variables will be an important reference after environmental changes to prevent the population from falling into a local optimum and converging prematurely. The second part is the dynamic classification adjustment strategy after the environment changes, which further determines the predictability of the decision variables. The third part uses different prediction strategies based on the results of the dynamic classification respectively. The components of the algorithm are shown in Fig. 40 demonstrates that the POS of a continuous multi-objective optimization problem is a segmentally continuous Under relaxed conditions, the Karush-Kuhn-Tucker criterion42, where decision variables are perturbed and divided into three different categories according to different dominance: (a) The relationship between the representative solution and the disturbance solution is nondominated; (b) The relationship between the representative solution and the perturbation solution is dominated; c) Both dominated and nondominated relations exist between the representative solution and the perturbation solution.Classification with static decision variables in DMOEA helps populations to be able to search for quality individuals quickly when the environment changes. DMOEA ought to have not only efficient convergence performance but also good distributivity on PF. Nevertheless, the dynamic environment limits the diversity of populations, and early convergence and falling into local optima are common problems of DMOPs. The problem of classification of decision variables is mentioned in the literatureAmong them, category a as well as category b are defined as diversity-related variables, while category c is defined as convergence-related. The classification after perturbation is shown in Fig. This section presents a classification method for decision variables in static environments, as shown in Fig. Firstly, representative variables should be selected in the decision space. For the decision space in two-dimensional coordinates, the extreme value points on each objective value are found and defined as boundary points. Considering the first objective value, the region from the minimum of the boundary point to the maximum of the boundary point is evenly divided into three equal parts, in each region the nearest non-dominated point to the line of the boundary point and the farthest non-dominated point are selected respectively (if there is no point in the region then two points are randomly generated). In the decision space a total of 6 decision variables are selected and the selected decision variables are perturbed (the number of perturbations is 5).m representing the number of objectives) is computed. As shown in Fig. i represents the selected point and j indicates the pinch mark. Whether the decision variable In order to be able to determine the class of the decision variables, the values of the perturbation points generated by the decision variables are normalized and the normalized points are fitted to a reference line t-tests to adjust the categorization of decision variables to adapt to different predictive strategies. The formula for the non-parametric t-test is as follows:i at time t. i at time t. t. t. t. Then, the results of the classification of decision variables are observed historically. Subsequently, n points i-th decision variable in the i-th decision variable at moment i s adjusted to Environmental change is an important element in DMOPs that has an impact on the evolution of populations, and it is the change in the environment that leads to problems such as goal conflict and consequently the problem of responding during the evolution of the population. In the absence of environmental changes, population convergence can only reach the optimal state in the current environment. However, in order to prevent the population from being trapped in an optimum state and failing to respond to environmental changes, the categorization of decision variables needs to be adjusted in dynamic environments. This adaptive adjustment of decision variable categorization enables populations to efficiently and effectively respond to changes in their environment, thereby promoting their survival and evolution. Therefore, incorporating dynamic adjustments to decision variable categorization is crucial for population convergence in a changing environment. In a static environment, decision variables are divided into three categories: those related to diversity, those related to convergence, and those related to both diversity and convergence. The classification of decision variables in a static environment serves as a guide for the classification of decision variables in a dynamic environment. The classification of decision variables needs to be adjusted due to changes in the environment, and different decision variables correspond to different prediction strategies. In the case where a decision variable remains constant across several consecutive changing environments, it is possible that the variable may not change in the next environmental shift. Such variables can be considered similar variables and do not require initialization in the prediction process. When a variable undergoes significant changes between two consecutive environmental shifts, it can be identified as a variable with a longer prediction process. Conversely, when a decision variable shows no significant change between two consecutive environmental shifts, it is classified as a variable with a shorter prediction process. In response to environmental changes, we employ non-parametric Similar decision variables, directly add the point dir indicates the step between the centroid at time t, and the centroid at time The set of points corresponding to the diversity-related decision variables ith dimensional vector at time t, The prediction strategy for the point set As described in the section above, the selected points as well as the perturbed points are classified into three categories based on the classification of the decision variables: 43 test suite, the dMOP1-dMOP344 test suite and the F5–F1045 test suite. Among them, FDA1-FDA4 are non-convex, continuous or discontinuous, time-varying as well as non-time-varying. FDA4 and F8 are three objectives test problems, the others are problems with two objectives. Both the FDA test suite and the DMOP test suite have linearly correlated decision variables, and non-linearly correlated decision variables are present in the F5–F10 test suite.We tested 12 benchmarks featuring the FDA1-FDA446 is calculated as follows:The metric under consideration represents a comprehensive evaluation metric, whereby its underlying calculation concept involves computing the minimum sum of distances that exist between individuals belonging to the actual POF and individuals generated by the algorithm under evaluation. It is noteworthy that the smaller the distance, the better the algorithm’s convergence and distribution performance. The IGDt, v and the point in At time T is a set of discrete time points in a run and |T| is the cardinality of T.For DMOPs, MIGD provides a better evaluation of MOEAs. MIGD is expressed as:45 is used to measure the distance between the hypervolume of POF obtained by the algorithm and the real POF. HVD can be calculated as:t.HVDIt can be set as:In this paper, a comparison is made between the proposed algorithm DVC and six dynamic multi-objective algorithms, and all of them use the RM-MEDA algorithm in the optimization of the problem. The six compared algorithms are: feedforward prediction strategy (FPS), population prediction strategy (PPS), centroid and inflection point-based prediction strategy (CKPS), special point-based prediction strategy (SPPS), change response mechanism combining hybrid prediction and mutation strategy (HPPCM), and a prediction method based on diversity screening and special point prediction to solve dynamic optimization problems (DSSP). In order to compare the algorithms fairly, the parameters of each algorithm were basically set to the values of the parameters provided in the original paper, and some of the parameters were adjusted to ensure that they were compared in the same state as the present method. The experimental parameters are summarized as follows.Feed-forward prediction strategy (FPS)47 The order in Population prediction strategy (PPS)32 PPS used the same A novel prediction strategy based on center points and knee points (CKPS)33 The number of knee points is 9.A predictive strategy based on special points (SPPS)48 In the process of predicting the non-dominated set by feed-forward center points, set the Gaussian perturbation d to be 0.1.Change response mechanism combining hybrid prediction and mutation strategy (HPPCM)49 The autonomic evolution of the algebra A dynamic multi-objective evolutionary algorithm based on prediction (DSSP)42 The number of knee points is 9. The number of perturbations is set to 5.Each problem was tested 20 times independently, and 100 environmental changes were generated in each experiment. The degree of change of the environment Table From an overall perspective, the DVC algorithm performs well in all phases, although it is slightly inferior to HPPCM in the FDA3 problem and the dMOP3 problem, but performs better in all other test problems, thus demonstrating that DVC has a strong ability to respond to environmental changes. FDA3 is a nonlinear test problem with large fluctuations in the set of Pareto solutions following environmental changes. Observing the characteristics of HPPCM, the HPPCM algorithm which uses the strategy of precisely controlling the polynomial mutation, this strategy effectively controls the updating and keeping of new populations. In contrast, our proposed DVC strategy relies more on the effect of decision variables in the population. This may be the reason why HPPCM outperforms DVC. dMOP3 test problem has no connection between the decision variables, which affects the results of DVC to a certain extent, but on closer inspection, it is easy to find that DVC is only slightly inferior to HPPCM, which also shows that DVC and HPPCM have their own advantages. HPPCM performed slightly better on the FDA3 issue, but DVC’s MIGD values were near parity with HPPCM. In the first stage, DVC was only marginally inferior to HPPCM for the FDA3 problem, and DVC was only a bit worse than the other methods for the dMOP problem, but performed well for FDA1, FDA2, FDA4, dMOP1, and dMOP2. This indicates that DVC is able to respond to environmental changes faster in the early stages of environmental changes. The MIGD values for the FDA2 problem in both phase 2 and phase 3 show superiority over the other five strategies.Table DVC differs from CKPS, SPPS, HPPCM, and DSSP in that DVC does not focus on the selection and prediction of particular points, but more on the classification of decision variables and their changes in the environment. In CKPS, SPPS, HPPCM, and DSSP, these comparison algorithms adopt the strategy of special points, which are employed to increase the diversity of populations. Conversely, in contrast to randomly adding diversity to the population, increasing the diversity of the population using special points removes the instability of randomly adding special points. Nevertheless, the definition of special points is to some extent a coarse-grained definition. The advantage of DVC is that only the categories of decision variables need to be analyzed and then the attributes of decision variables are judged by historical information, and different attributes correspond to different prediction strategies, which can balance the diversity and convergence of populations.Tables Figure In order to examine the effectiveness and robustness of the algorithm, we conducted a specific comparison with its formidable competitor, HPPCM. In our experiment, we maintain the value of The role of decision variables in environmental change is fully considered in this paper, and a DMOP-DVC based on decision vector classification is proposed by integrating the historical information of static classification of decision variables. The proposed method reflects the evolutionary direction for decision variables in the current environment, and different classes of prediction strategies are used to optimize the evolution of populations to balance convergence and diversity.From the experiments, many advantages are shown on DMOP-DVC, but the algorithm also has some drawbacks. For example, the accuracy of prediction can be further improved in the prediction strategy, and future work can consider introducing some training models to consider global historical changes. If the environment changes little or the environment changes drastically, whether different prediction strategies are needed to cope with it, these are the future works that are worth looking forward to.