Optimization Method Research Articles

Pharmacometric and statistical considerations for dose optimization.

The probability of target attainment (PTA) is a common metric in drug dose optimization, but it requires a specific known target concentration threshold. Such target thresholds are not always available for some treatments, and patient and disease groups, particularly when treating children. This study performed pharmacokinetic and pharmacokinetic-pharmacodynamic (PKPD) simulations to explore different statistical approaches for determining the optimal dose for unknown PK and PKPD targets. To determine an optimal dose, PK and PKPD outcomes in typical patients with a standard adult dosing regimen were simulated and set as the reference profile, and compared to simulated outcomes for different dosing regimens in the population of interest. Statistical distances between the empirical cumulative distribution functions of the outcomes from all possible dosing regimens were calculated and compared to the reference profile. An optimal dose for known PK and PKPD target outcomes was selected to maintain the outcome above the assigned target, while optimal dosing in a population of interest with an unknown target was selected to generate equivalent PK and PKPD outcomes as the typical population. All of the dose optimization methods with commonly used PK and PKPD models and covariates were implemented as an open source freely available Shiny web-application. The developed pharmacometric method for dose optimization in populations with known and unknown target levels were robust and reproducible, and the implementation of a freely accessible Shiny web-application ensures widespread use and could be a useful tool for dose optimization in populations of interest.

Pred-AHCP: Robust Feature Selection-Enabled Sequence-Specific Prediction of Anti-Hepatitis C Peptides via Machine Learning.

Every year, an estimated 1.5 million people worldwide contract Hepatitis C, a significant contributor to liver problems. Although many studies have explored machine learning's potential to predict antiviral peptides, very few have addressed the problem of predicting peptides against specific viruses such as Hepatitis C. In this study, we demonstrate the application and fine-tuning of machine learning (ML) algorithms to predict peptides that are effective against Hepatitis C virus (HCV). We developed a fine-tuned and explainable ML model that harnesses the amino acid sequence of a peptide to predict its anti-hepatitis C potential. Specifically, features were computed based on sequence and physicochemical properties. The feature selection was performed using a combined strategy of mutual information and variance inflation factor. This facilitated the removal of redundant and multicollinear features, enhancing the model's generalizability in predicting anti-hepatitis C peptides (AHCPs). The model using the random forest algorithm produced the best performance with an accuracy of about 92%. The feature analysis highlights that the distributions of hydrophobicity, polarizability, coil-forming residues, frequency of glycine residues and the existence of dipeptide motifs VL, LV, and CC emerged as the key predictors for identifying AHCPs targeting different components of HCV. The developed model can be accessed through the Pred-AHCP web server, provided at http://tinyurl.com/web-Pred-AHCP. This resource facilitates the prediction and re-engineering of AHCPs for designing peptide-based therapeutics while also proposing an exploration of similar strategies for designing peptide inhibitors effective against other viruses. The developed ML model can also be used for validating peptide sequences generated using generative artificial intelligence methods for further optimization.

Global Optimization of Molybdenum Subnanoclusters on Graphene: A Consistent Approach toward Catalytic Applications.

The development of novel subnanometer clusters (SNCs) catalysts with superior catalytic performance depends on the precise control of clusters' atomistic sizes, shapes, and accurate deposition onto surfaces. The intrinsic complexity of the adsorption process complicates the ability to achieve an atomistic understanding of the most relevant structure-reactivity relationships hampering the rational design of novel catalytic materials. In most cases, existing computational approaches rely on just a few structures to draw conclusions on clusters' reactivity thereby neglecting the complexity of the existing energy landscapes thus leading to insufficient sampling and, most likely, unreliable predictions. Moreover, modeling of the actual experimental procedure that is responsible for the deposition of SNCs on surfaces is often not done even though in some cases this procedure may enhance the significance of certain (e.g., metastable) adsorption geometries. This study proposes a novel systematic approach that utilizes global search techniques, specifically, the particle swarm optimization (PSO) method, in conjunction with ab initio calculations, to simulate all stages in the beam experiments, from predicting the most relevant SNCs structures in the beam and on a surface, to their reactivity. To illustrate the main steps of our approach, we consider the deposition of Molybdenum SNC of 6 Mo atoms on a free-standing graphene surface, as well as their catalytic properties with respect to the CO molecule dissociation reaction. Even though our calculations are not exhaustive and serve only to produce an illustration of the method, they are still able to provide insight into the complicated energy landscape of Mo SNCs on graphene demonstrating the catalytic activity of Mo SNCs and the importance of performing statistical sampling of available configurations. This study establishes a reliable procedure for performing theoretical rational design predictions.

Intelligent design of steel–concrete composite beams based on deep reinforcement learning

In this work, an automated member design method is proposed based on deep reinforcement learning (DRL). Using steel–concrete composite beam design as a case study, the design procedure is conceptualized as a sequential optimization process and modeled as a Markov Decision Process (MDP). A design agent equipped with two deep neural networks, is trained using the proximal policy optimization (PPO) method to complete the complex design task of steel–concrete composite beams, adhering to the Chinese standard for design of steel structures GB50017-2017 provisions. The structural provisions are integrated into a simulated design environment, which can respond to the agent’s actions. A universal reward shaping function is introduced to guide the agent towards success and minimize material cost. The design quality and generation performance of trained PPO agent are compared with those of the Differential Evolution (DE) in 100 random training cases, 100 random testing cases, and 95 real-world engineering cases, demonstrating significant promise and reduced time consumption for automated steel–concrete composite beam design. An approach combining PPO with DE is proposed to enhance the robustness and reliability of the original agent. Finally, a brief discussion is conducted on the essence and prospects of the proposed method.

Application and Practice of Mathematical Optimization Method in Structural Mechanics Design

Application and Practice of Mathematical Optimization Method in Structural Mechanics Design

Analysis of War Optimization Algorithm in a Multi-Loop Power System Based on Directional Overcurrent Relays

In electrical power systems, ensuring a reliable, precise, and efficient relay strategy is crucial for safe and trustworthy operation, especially in multi-loop distribution systems. Overcurrent relays (OCRs) have emerged as effective solutions for these challenges. This study focuses on optimizing the coordination of OCRs to minimize the overall operational time of main relays, thereby reducing power outages. The optimization problem is addressed by adjusting the time multiplier setting (TMS) using the War Strategy Optimization (WSO) algorithm, which efficiently solves this constrained problem. This algorithm mimics ancient warfare strategies of attack and defense to solve complex optimization problems efficiently. The results show that WSO provides superior performance in minimizing total operating time and achieving global optimum solutions with reduced computational effort, outperforming traditional optimization methods (i.e., SM, HPSO, GA, RTO, and JAYA). The proposed algorithm shows a net time gains of 7.77 s, 2.57 s, and 0.8484 s when compared to GA, RTO, and JAYA respectively. This robust protection coordination ensures better reliability and efficiency in multi-loop power systems.

Research on supply chain efficiency optimization algorithm based on reinforcement learning

Supply chain efficiency is critical to enterprises and can affect their competitiveness. The supply chain faces an uncertain and complex external market environment, facing the problem of supply chain efficiency optimization; the traditional optimization method is ineffective, which can better face the current environment and deal with problems. It has advantages in optimizing supply chain efficiency and has been widely used. This paper first expounds on the importance of supply chain management status, the limitations of traditional supply chain management methods, and reinforcement learning in the application of supply chain optimization. Then, through experiments, reinforcement learning, supply chain optimization problems, and the analysis of related algorithm design, the optimal algorithm focuses on inventory management optimization. Finally, this paper points out the future research directions and development trend of the supply chain efficiency optimization algorithm based on reinforcement learning.

Multi-head attention-based variational autoencoders ensemble for remaining useful life prediction of aero-engines

Abstract Accurate remaining useful life (RUL) prediction of aero-engines through condition monitoring (CM) data is of great significance for flight reliability and safety. Although deep learning (DL)-based approaches have been widely considered, individual DL models suffer from significant stochasticity and limited generalizability when predicting the RUL. To solve this issue, a novel multi-head attention-based variational autoencoders (MHAT-VAEs) ensemble model is proposed. Two distinct MHAT-VAEs are designed, employing linear and convolutional operations to capture global and temporal compressed representations of the CM data. Additionally, a dual-level ensemble strategy is introduced to adaptively fuse the outputs of the two base learners. A hyperparameter optimization method is also implemented to further enhance the efficiency and performance of the base learners. The effectiveness of the proposed method is validated using the C-MAPSS and N-CMAPSS datasets, with experimental results showing that it outperforms state-of-the-art approaches.

Optimal design of neural network-based fuzzy predictive control model for recommending educational resources in the context of information technology

Abstract As the information technology develops, educational resource recommendation system has become an indispensable part of the education field. At the same time, people’s demand for personalised educational resources is also growing; therefore, how to accurately predict user demand and provide personalised recommendations has become an important issue. In this study, a fuzzy predictive control model on the grounds of neural network is proposed to optimise the design of educational resource recommendation in the context of information technology. After experimental testing, the model recommendation fit reached 95.16 and 92.91% on the two test datasets, which are significantly higher than the control model. The average F1 values of the proposed model also reached 95.21 and 88.77%, which are higher than the control model. In other control experiments, the proposed model of this study also has a better performance. The relevant outcomes showcase that the predictive performance and recommendation effect of the model can be further enhanced by improving the structure of the neural network and the parameter optimisation method. Meanwhile, the proposed model has high performance in information overload and personalised demand, which offers a useful reference for the optimal design of educational resource recommendation system.

Low-carbon economic optimization strategy for industrial loads in parks considering source-load-price multivariate uncertainty

A low-carbon economic optimization method is proposed for industrial loads in parks considering multivariate uncertainty. Model of dynamic load node carbon intensity is proposed considering the uncertainty of clean energy and dynamic conventional units carbon intensity based on system currents. The robustness is improved based on multi-interval uncertainty set. The gap is filled by hybrid copula model with Generalized Autoregressive Conditional Heteroskedasticity (GARCH) prices in the uncertainty model. The GARCH is used to built the marginal distribution function of prices, and a hybrid copula model is proposed to obtain the joint probability density function based on the weights calculated by Euclidean distance. The LNCI probability distributions of the regulation potential of loads are proposed with the virtual energy storage and the virtual power model to improve the descriptive ability of uncertainty based on the expansion and contraction functions. Finally, the typical scenarios are extracted based on Monte Carlo and Wasserstein measures. The Column sum Constraint Generation algorithm and strong duality theory are used to get the robust-stochastic optimization. The method proposed in the paper has a positive effect on enterprises to rationalize their production schedules, reduce electricity and carbon emissions costs and increase the revenue from participating in grid regulation.

Mechanical and Civil Engineering Optimization with a Very Simple Hybrid Grey Wolf—JAYA Metaheuristic Optimizer

Metaheuristic algorithms (MAs) now are the standard in engineering optimization. Progress in computing power has favored the development of new MAs and improved versions of existing methods and hybrid MAs. However, most MAs (especially hybrid algorithms) have very complicated formulations. The present study demonstrated that it is possible to build a very simple hybrid metaheuristic algorithm combining basic versions of classical MAs, and including very simple modifications in the optimization formulation to maximize computational efficiency. The very simple hybrid metaheuristic algorithm (SHGWJA) developed here combines two classical optimization methods, namely the grey wolf optimizer (GWO) and JAYA, that are widely used in engineering problems and continue to attract the attention of the scientific community. SHGWJA overcame the limitations of GWO and JAYA in the exploitation phase using simple elitist strategies. The proposed SHGWJA was tested very successfully in seven “real-world” engineering optimization problems taken from various fields, such as civil engineering, aeronautical engineering, mechanical engineering (included in the CEC 2020 test suite on real-world constrained optimization problems) and robotics; these problems include up to 14 optimization variables and 721 nonlinear constraints. Two representative mathematical optimization problems (i.e., Rosenbrock and Rastrigin functions) including up to 1000 variables were also solved. Remarkably, SHGWJA always outperformed or was very competitive with other state-of-the-art MAs, including CEC competition winners and high-performance methods in all test cases. In fact, SHGWJA always found the global optimum or a best cost at most 0.0121% larger than the target optimum. Furthermore, SHGWJA was very robust: (i) in most cases, SHGWJA obtained a 0 or near-0 standard deviation and all optimization runs practically converged to the target optimum solution; (ii) standard deviation on optimized cost was at most 0.0876% of the best design; (iii) the standard deviation on function evaluations was at most 35% of the average computational cost. Last, SHGWJA always ranked 1st or 2nd for average computational speed and its fastest optimization runs outperformed or were highly competitive with their counterpart recorded for the best MAs.

Exact Solution of Nonlinear TVMD Based on Maximizing Damping Enhancement Effect for Acceleration Response Control

The tuned viscous mass damper (TVMD) exhibits superior control effect and energy dissipation capability compared to the viscous damper (VD). Existing literature has primarily focused on the control of absolute acceleration response in structures by linear TVMD, with limited research on nonlinear damper for controlling structural performance and efficiency. This study proposes a methodology for determining the optimal parameters of linear TVMD. The closed-form solution of the nonlinear TVMD is derived through stochastic linearization based on the linear TVMD, aiming to minimize the damping ratio of TVMD by utilizing the damping enhancement effect of the system. For lightly damped structures, the closed-form solution remains a reliable method for accurately approximating TVMD design parameters. Compared to traditional fixed-point theory, the TVMD developed through the proposed methodology demonstrates superior control performance, especially in terms of absolute acceleration, with a smaller damping ratio and minimal deviation from the optimal state of the TVMD. Additionally, the study investigated the influence of the damping index on the optimal parameters and the efficacy of the TVMD in vibration control. It is observed that reducing the damping index can improve structural performance, particularly in long-period structures with small mass ratios, although it may reduce the efficiency of the TVMD. Notably, TVMDs with lower mass ratios maintain higher efficiency regardless of the structural natural period. The damping index does not affect the optimal frequency ratio or the mean square response. Ultimately, the effectiveness of the optimization method is displayed through the examination of response spectra following 22 real seismic events, showcasing its adaptability across various structural types. The comparison of the root-mean-square response between the VD and TVMD across different periods shows consistent results, with a maximum deviation of only 10%. The TVMD is highly effective at regulating the structural response, excelling particularly in controlling the absolute acceleration of long-period structures, where it reduces maximum absolute acceleration by 20% more than displacement. The proposed exact solution rapidly and precisely identifies the design parameters of nonlinear TVMD by the desired specifications, thereby offering theoretical guidance for practical engineering applications.

Towards industry-ready additive manufacturing: AI-enabled closed-loop control for 3D melt electrowriting.

Melt electrowriting (MEW) is an emerging high-resolution 3D printing technology used in biomedical engineering, regenerative medicine, and soft robotics. Its transition from academia to industry faces challenges such as slow experimentation, low printing throughput, poor reproducibility, and user-dependent operation, largely due to the nonlinear and multiparametric nature of the MEW process. To address these challenges, we applied computer vision and machine learning to monitor and analyze the process in real-time through imaging of the MEW jet between the nozzle-collector gap. To collect data for training we developed an automated data collection methodology that eases the experimental time from days to hours. A feedforward neural network, working in concert with optimization methods and a feedback loop, is used to develop closed-loop control ensuring reproducibility of the printed parts. We demonstrate that machine learning allows streamlining the MEW operation via closed-loop control of the highly nonlinear 3D printing technology.

Optimization of trigonometric polynomials with crystallographic symmetry and spectral bounds for set avoiding graphs

AbstractWe provide a new approach to the optimization of trigonometric polynomials with crystallographic symmetry. This approach widens the bridge between trigonometric and polynomial optimization. The trigonometric polynomials considered are supported on weight lattices associated to crystallographic root systems and are assumed invariant under the associated reflection group. On one hand the invariance allows us to rewrite the objective function in terms of generalized Chebyshev polynomials of the generalized cosines; On the other hand the generalized cosines parameterize a compact basic semi algebraic set, this latter being given by an explicit polynomial matrix inequality. The initial problem thus boils down to a polynomial optimization problem that is straightforwardly written in terms of generalized Chebyshev polynomials. The minimum is to be computed by a converging sequence of lower bounds as given by a hierarchy of relaxations based on the Hol–Scherer Positivstellensatz and indexed by the weighted degree associated to the root system. This new method for trigonometric optimization was motivated by its application to estimate the spectral bound on the chromatic number of set avoiding graphs. We examine cases of the literature where the avoided set affords crystallographic symmetry. In some cases we obtain new analytic proofs for sharp bounds on the chromatic number while in others we compute new lower bounds numerically.

A projection-free method for solving convex bilevel optimization problems

AbstractWhen faced with multiple minima of an inner-level convex optimization problem, the convex bilevel optimization problem selects an optimal solution which also minimizes an auxiliary outer-level convex objective of interest. Bilevel optimization requires a different approach compared to single-level optimization problems since the set of minimizers for the inner-level objective is not given explicitly. In this paper, we propose a new projection-free conditional gradient method for convex bilevel optimization which requires only a linear optimization oracle over the base domain. We establish $$O(t^{-1/2})$$ O ( t - 1 / 2 ) convergence rate guarantees for our method in terms of both inner- and outer-level objectives, and demonstrate how additional assumptions such as quadratic growth and strong convexity result in accelerated rates of up to $$O(t^{-1})$$ O ( t - 1 ) and $$O(t^{-2/3})$$ O ( t - 2 / 3 ) for inner- and outer-levels respectively. Lastly, we conduct a numerical study to demonstrate the performance of our method.

Deep Lead Optimization: Leveraging Generative AI for Structural Modification.

The integration of deep learning-based molecular generation models into drug discovery has garnered significant attention for its potential to expedite the development process. Central to this is lead optimization, a critical phase where existing molecules are refined into viable drug candidates. As various methods for deep lead optimization continue to emerge, it is essential to classify these approaches more clearly. We categorize lead optimization methods into two main types: goal-directed and structure-directed. Our focus is on structure-directed optimization, which, while highly relevant to practical applications, is less explored compared to goal-directed methods. Through a systematic review of conventional computational approaches, we identify four tasks specific to structure-directed optimization: fragment replacement, linker design, scaffold hopping, and side-chain decoration. We discuss the motivations, training data construction, and current developments for each of these tasks. Additionally, we use classical optimization taxonomy to classify both goal-directed and structure-directed methods, highlighting their challenges and future development prospects. Finally, we propose a reference protocol for experimental chemists to effectively utilize Generative AI (GenAI)-based tools in structural modification tasks, bridging the gap between methodological advancements and practical applications.

Optimal adaptive heuristic algorithm based energy optimization with flexible loads using demand response in smart grid.

Demand response-based load scheduling in smart power grids is currently one of the most important topics in energy optimization. There are several benefits to utility companies and their customers from this strategy. The main goal of this work is to employ a load scheduling controller (LSC) to model and solve the scheduling issue for household appliances. The LSC offers a solution to the primary problems faced during implementing demand response. The goal is to minimize peak-to-average demand ratios (PADR) and electricity bills while preserving customer satisfaction. Time-varying pricing, intermittent renewable energy, domestic appliance energy demand, storage battery, and grid constraints are all incorporated into the model. The optimal adaptive wind-driven optimization (OAWDO) method is a stochastic optimization technique designed to manage supply, demand, and power price uncertainties. LSC creates the ideal schedule for home appliance running periods using the OAWDO algorithm. This guarantees that every appliance runs as economically as possible on its own. Most appliances run the risk of functioning during low-price hours if just the real time-varying price system is used, which could result in rebound peaks. We combine an inclined block tariff with a real-time-varying price to alleviate this problem. MATLAB is used to do a load scheduling simulation for home appliances based on the OAWDO algorithm. By contrasting it with other algorithms, including the genetic algorithm (GA), the whale optimization algorithm (WOA), the fire-fly optimization algorithm (FFOA), and the wind-driven optimization (WDO) algorithms, the effectiveness of the OAWDO technique is supported. Results indicate that OAWDO works better than current algorithms in terms of reducing power costs, PADR, and rebound peak formation without sacrificing user comfort.

Effect of Si on the Yield Strength of Medium-Carbon Steels Consisting of Ferrite and Pearlite

To enhance the intrinsic yield strength of the ferrite-pearlite microstructure that inevitably forms in a non-quenched-and-tempered steel for large structural components, this study analyzed the effect of adding Si. The resulting ferrite-pearlite microstructure in medium-carbon steels was examined, and the resulting increase in yield strength was interpreted based on strengthening mechanisms. Hot-rolled sheets of 0.3C-1.5Mn steels were fabricated with Si ranging from 0.22 to 2.21 wt. %. Austenitization was conducted at 880°C followed by slow continuous cooling, and ferrite-pearlite microstructures were formed. With increasing Si, the yield strength increased from 409.1 to 573.6 MPa. Although there was a negligible change in the austenitic grain size, the mean diameter of the ferritic grains decreased from 8.8 to 5.0 μm, while the mean interlamellar spacing of the pearlites decreased from 196.6 to 109.9 nm. Using these quantitative data about microstructural features and considering possible strengthening mechanisms, a model to predict yield strength was derived via a constrained optimization method. The resulting model indicated that the major mechanisms are the refinement of pearlitic interlamellar spacing and the solid solution strengthening of ferrite by Si. Their contribution to the increment in yield strength was over 75 %, while others such as ferritic grain refinement and increased pearlitic volume fraction have limited influence.

AQUILA OPTIMIZED NONLINEAR CONTROL FOR DC-DC BOOST CONVERTER WITH CONSTANT POWER LOAD

Constant power loads (CPL) can be operated by tight-controlled power electronic converters, which have negative impedance and absorb continuous power. Constant power load creates instability in an open-loop system because of its negative incremental impedance. To tackle this problem, a discrete sliding-mode (AQO-DSM) nonlinear control technique has been proposed for a DC-DC boost converter fed CPL based on Aquila optimization. In this paper, the proposed AQO-DSM controllers provide the system stability during a steady state and maintain output voltage regardless of input voltage or CPL variations. In this case, the DSM controller of a DC-DC boost converter's characteristics are adjusted using the Aquila optimization method (AQO). The Lyapunov stability concept is utilized to assess the system's overall stability. Under various system operating conditions, an experimental study and simulation are carried out to validate the proposed controller. The existing methods, such as sliding mode controller (SMC), fuzzy-based SMC (F-SMC), and super twisting algorithm (STA)-based SMC strategies, are compared with a proposed plan to demonstrate the superiority of the proposed AQO-DSMC. Simulated and experimental results have shown that the AQO-DSMC achieves the fastest convergence, the smallest steady-state, settling time under loaded conditions, and consistent chatter reduction compared with all contrasted control methods.

A NEW HYBRID OPTIMIZATION METHOD USED IN PREDICTIVE CONTROL OF A NONLINEAR FRACTIONAL MODEL BASED ON FRACTIONAL HAMMERSTEIN STRUCTURE

Fractional Hammerstein models represent various nonlinear processes, such as thermal and mechanical. Their major drawback is the non-convex optimization problem in a nonlinear model predictive control scheme due to its static nonlinearity. Indeed, an efficient optimization algorithm is needed. This work proposes a hybrid optimization algorithm combining the Nelder Mead optimization method and the Honey Badger one to synthesize a predictive control algorithm based on fractional Hammerstein models. As illustrated through simulation results, the proposed method offers clear improvements in convergence and tracking performances.