Aluminum fluoride ($\mathrm{AlF_{3}}$) is a vital industrial material and its production is highly dependent on the precise blending of fluorspar. Conventional blending approaches rely heavily on manual expertise and often prove inefficient in handling complex ore compositions and multiple constraints. In this work, the fluorspar blending task is formulated as a constrained multiobjective optimization problem that simultaneously balances economic efficiency and production stability. Distinct from traditional cost-centric models, our approach explicitly incorporates the effects of fluorspar impurities on downstream reagent consumption, thereby achieving global cost minimization from raw material to final product. A novel constrained multiobjective state transition algorithm with self-adaptive shift-based penalty function under a dual-population framework is proposed to effectively handle complex constraints arising from inventory limits, compositional requirements, and impurity content. A fully functional intelligent fluorspar blending optimization system is developed and deployed using real-world data from multiple suppliers. Experimental results demonstrate superior performance in blending quality, cost-effectiveness, and industrial adaptability, offering a scalable solution for intelligent fluorspar blending optimization in$\mathrm{AlF_{3}}$production.

The state transition algorithm (STA), as an intelligent optimization method grounded in constructivist learning, has been demonstrated to be highly effective in solving complex optimization problems. However, the standard STA suffers from slow convergence, particularly in the later stages when dealing with flat landscapes. Additionally, users are required to set the maximum number of iterations based on intuition. To address these issues, an enhanced STA with guaranteed optimality is introduced. This improvement involves three key components. First, novel translation transformations (TTs), inspired by predictive modeling, are developed to generate a broader set of candidate solutions by leveraging historical data. Second, adaptive parameter control strategies are incorporated to accelerate convergence. Finally, a dedicated termination condition is designed to ensure that the algorithm converges at the optimal solution, analogous to the zero gradient condition in mathematical programming. The comprehensive experimental results validate the effectiveness and superiority of the proposed method. The source codes for ESTA and EXSTA will be publicly available athttps://github.com/tiezhongyu2005/ESTA

Visual-based working condition recognition methods are pivotal in the froth flotation process. However, the high dimensionality of visual features generated by the feature extraction technologies reduces the efficiency of recognition algorithms. This article proposes a multiobjective feature selection method based on binary state transition algorithm (MOFS-BSTA). First, a Shapley-based filter method is utilized to reduce the search space. Then, the MOFS-BSTA is employed to generate a set of nondominated solutions. However, selecting a satisfactory choice from a large set of solutions imposes a significant cognitive burden on users. Therefore, a clustering-based t-SNE method is proposed to visualize all nondominated solutions and determine the optimal feature combination. The MOFS-BSTA is applied to a gold-antimony froth flotation process. The experimental results demonstrate that six efficient features, namely high-frequency energy, bubble size, hue, relative red component, coarseness, and stability, significantly enhance the accuracy of working condition recognition.

The machine learning-based model is a promising paradigm for predicting invasive disease events (iDEs) in breast cancer. Feature selection (FS) is an essential preprocessing technique employed to identify the pertinent features for the prediction model. However, conventional FS methods often fail with imbalanced clinical data due to the bias towards the majority class. In this paper, a novel FS framework based on reinforcement learning (RLFS) is developed to identify the optimal feature subset for the imbalanced data. The RLFS employs an iterative methodology, wherein data resampling technique generates a balanced dataset before each iteration. A decision network is trained using a deep RL algorithm to identify the relevant features for the dataset in the current iteration. With such an iterative training strategy, numerous constructed datasets gradually boost the FS capacity of the decision network, resulting in a robust performance for imbalanced data. Finally, a weighted model is proposed to determine the most suitable FS solution. The RLFS is employed to predict breast cancer iDEs using real follow-up data. The comparison results demonstrated that RLFS effectively reduces the number of features while outperforming several state-of-the-art FS algorithms.

Many machine learning models are naturally multitask, which may involve regression and classification tasks, in which they can be trained by the multitask network to yield a more generalized model with the aid of correlated features. When these learning models are deployed on Internet-of-Things devices, the computation efficiency and the privacy of the data can pose a significant challenge to developing a federated learning (FL) algorithm for both higher learning performance and better privacy protection. In this article, a new FL framework is proposed for a class of multitask learning problems with hard parameter-sharing model through which the learning tasks are reformulated as a multiobjective optimization problem for better performance. Specifically, the stochastic multiple gradient descent approach and differential privacy are integrated into this FL algorithm for achieving a Pareto optimality that obtains a good tradeoff among different learning tasks while providing data protection. The outstanding performance of this algorithm is demonstrated by the empirical experiments on multiMINIST, the Chinese city parking dataset, and Cityscapes dataset.

Traffic accident prediction plays a vital role in Intelligent Transportation Systems (ITS), where a large number of traffic streaming data are generated on a daily basis for spatiotemporal big data analysis. The rarity of accidents and the absent interconnection information make it hard for spatiotemporal modeling. Moreover, the inherent characteristic of the black box predictive model makes it difficult to interpret the reliability and effectiveness of the deep learning model. To address these issues, a novel self-explanatory spatial-temporal deep learning model–Attention Spatial-Temporal Multi-Graph Convolutional Network (ASTMGCN) is proposed for traffic accident prediction. The original recorded rare accident data is formulated as a multivariate irregularly interval-aligned dataset, and the temporal discretization method is used to transfer into regularly sampled time series. Multiple graphs are defined to construct edge features and represent spatial relationships when node-related information is missing. Multi-graph convolutional operators and attention mechanisms are integrated into a Sequence-to-Sequence (Seq2Seq) framework to effectively capture dynamic spatial and temporal features and correlations in multi-step prediction. Comparative experiments and interpretability analysis are conducted on a real-world data set, and results indicate that our model can not only yield superior prediction performance but also has the advantage of interpretability.

Federated learning techniques provide a promising framework for collaboratively training a machine learning model without sharing users’ data, and delivering a security solution to guarantee privacy during the model training of IoT devices. Nonetheless, challenges posed by data heterogeneity and communication resource constraints make it difficult to develop an efficient federated learning algorithm in terms of the low order of convergence rate. It could significantly deteriorate the quality of service for critical machine learning tasks, e.g., facial recognition, which requires an edge-ready, low-power, low-latency training algorithm. To address these challenges, a communication-efficient federated learning approach is proposed in this paper where the momentum technique is leveraged to accelerate the convergence rate while largely reducing the communication requirements. First, a federated multi-task learning framework by which the learning tasks are reformulated by the multi-objective optimization problem is introduced to address the data heterogeneity. The multiple gradient descent algorithm is harnessed to find the common gradient descending direction for all participants so that the common features can be learned and no sacrifice on each clients’ performance. Second, to reduce communication costs, a local momentum technique with global information is developed to speed up the convergence rate, where the convergence analysis of the proposed method under non-convex case is studied. It is proved that the proposed local momentum can actually achieve the same acceleration as the global momentum, whereas it is more robust than algorithms that solely rely on the acceleration by the global momentum. Third, the generalization of the proposed acceleration approach is investigated which is demonstrated by the accelerated variation of FedAvg. Finally, the performance of the proposed method on the learning model accuracy, convergence rate, and robustness to data heterogeneity, is investigated by empirical experiments on four public datasets, while a real-world IoT platform is constructed to demonstrate the communication efficiency of the proposed method.

Real-time License Plate Recognition plays a significant role in traffic congestion control and road safety monitoring. Practically, a network camera may capture multiple license plates in one frame while the data collected by different network cameras cannot be shared due to privacy concern. In this paper, a federated learning framework is introduced to simultaneously detect multiple license plates over different network cameras through semantic communication. Specifically, to achieve a high efficiency of multiple license plates recognition in real time, the semantic segmentation model is applied to locally extract the important features of an image with multiple license plates. And then, an autoencoder is developed to carry out the semantic encoding which translates the meaningful information. Moreover, a multi-task learning approach for multiple license plates recognition is proposed through a multi-objective optimization technique which can train the license plate recognition model with stronger generalization. To improve the reliability, an asynchronous federated learning algorithm is also considered to ensure the training process can be tolerant to the transmission delay. Empirical experiments on the Chinese City Parking Dataset (CCPD) show that the proposed approach can effectively improve the recognition performance while providing robust service.

Driven by government incentive policies and heightened environmental awareness by individuals, many regions around the world have seen a rapid rise in distributed energy resource (DER) penetration in electricity distribution networks. While high penetration of DER significantly helps facilitate the decarbonization in power and utitlies, it also brings unexpected operational challenges, among which voltage compliance has been a significant concern. To address this issue, the efficient load profile forecast, the operational framework and related strategies are critical challenges that need to be addressed urgently. Hence, this paper presents a cloud-edge computing-based framework to effectively operate the coupled medium-voltage (MV) and low-voltage (LV) distribution network. The high computational efficiency in cloud computing and low data latency in edge computing are presented and explored to coordinate the day-ahead and intraday operations ranging from different framework layers. Under the framework, a customer-level forecasting algorithm is employed to predict both day-ahead and real-time load profiles. Based on the prediction results, an optimization model based on unbalanced-three phase optimal power flow is proposed and solved by an efficient and accurate linearization-based approach that considers the controllability of on-load tap changers, distributed static var generator and the PV inverters. Simulations based on an extensive mocked MV-LV distribution network show the proposed forecasting method is adopted in real-time operations in terms of high accuracy and demonstrate the efficiency of the proposed optimization method in enhancing the voltage compliance in the network.

Many actual industrial production processes are dynamic and uncertain. When uncertain information are described by subjective experience and experts' knowledge based on scanty or vague information, fuzzy uncertainty exists. Fuzzy chance-constrained dynamic programming are applicable to industrial production modeling accompanied by fuzzy uncertainty and dynamics, where constraints need not or cannot be completely satisfied. In this article, a fuzzy chance-constrained dynamic optimization (FCCDO) formulation on the basis of credibility theory is established, in which, the credibility is used to measure the fuzzy uncertainty level of constraints. To solve the FCCDO problem (FCCDOP), an improved fuzzy simulation technique based on Hammersley sequence sampling is raised to transform fuzzy chance constraints to their deterministic equivalents, and then a data-driven state transition algorithm (DDSTA) using deep neural networks (DNNs) is put forward to achieve a stable, global and robust optimization performance. Finally, the successful applications of the FCCDO method to industrial studies demonstrate its advantages.

This article investigates the approximate optimal control problem for nonlinear affine systems under the periodic event triggered control (PETC) strategy. In terms of optimal control, a theoretical comparison of continuous control, traditional event-based control (ETC), and PETC from the perspective of stability convergence, concluding that PETC does not significantly affect the convergence rate than ETC. It is the first time to present PETC for optimal control target of nonlinear systems. A critic network is introduced to approximate the optimal value function based on the idea of reinforcement learning (RL). It is proven that the discrete updating time series from PETC can also be utilized to determine the updating time of the learning network. In this way, the gradient-based weight estimation for continuous systems is developed in discrete form. Then, the uniformly ultimately bounded (UUB) condition of controlled systems is analyzed to ensure the stability of the designed method. Finally, two illustrative examples are given to show the effectiveness of the method.

In this article, a new robust optimization method is proposed to simultaneously optimize the expectation and variability of system performance with parametric uncertainties and fuzzy variables. The expectation-entropy model is presented to characterize the fuzzy robust optimization problem as an equivalent biobjective optimization problem. An approximate mapping method is developed to calculate the response of fuzzy variables, which improves the computational efficiency of objective functions. Then, according to the decision makers’ preference for objectives, the optimization framework based on Stackelberg game is established. A leader–follower state transition algorithm is designed to search for the equilibrium solutions. Two practical case studies are provided to show the effectiveness of the new optimization approach in both subjective judgment and objective assessment.

In this article, the problem of robust optimization is considered for dynamical systems with both constraints and uncertainties. Conditions are established to ensure the existence of solutions to the problem with both robust optimality and feasibility. The objective performance with respect to fuzzy uncertainties is evaluated based on the expectation-entropy model. A feasibility robustness analysis method is proposed to handle the uncertainties in the constraints. Using the hierarchy structure in robust design, the optimization framework based on Stackelberg–Nash game is developed. A leader–followers state transition algorithm is designed to search for the equilibrium solution. Two application examples are given to demonstrate that the proposed robust optimization method can accurately evaluate the robustness performance and successfully search for a compromise solution.

Realistic industrial process is usually a dynamic process with uncertainty. Chance constraints are applicable to industrial process modeling under uncertain conditions, where constraints cannot be strictly met, or need not be fully met. Therefore, chance constrained dynamic optimization (CCDO) formulation is available to address realistic industrial process issues. Because of the dynamic and uncertainty, chance constrained dynamic optimization problems (CCDOPs) arising from practical industries are hard to cope with. In this article, a novel CCDO method is proposed to resolve this issue, where an adaptive sample average approximation method, a control vector parameterization method, and a state constraint handling strategy are integrated. Specially, a hybrid intelligent optimization algorithm is introduced to realize a global and efficient optimization performance. The proposed method is applied to CCDOPs modified by dynamic optimization standard test functions and industrial experiments to demonstrate its effectiveness. The experimental results show that the proposed method has good performance in solving CCDOPs.

Load forecasting plays a critical part in grid operation and planning. In particular, the importance of multistep load forecasting for individual power customer is increasingly prominent. Due to the strong volatility of individual consumers' electricity consumption behavior, traditional machine learning methods that cannot capture time dependence are difficult to obtain good prediction results. The recurrent neural network (RNN) can capture the time correlations existing in the load data, and the sequence to sequence (Seq2Seq) model combining two RNNs of the encoder and decoder is very suitable for multistep prediction. The temporal pattern attention mechanism can further capture the periodic change pattern in historical load data, which further improves time series modeling. We combined their advantages to propose a new type of multistep individual load forecasting framework, called the temporal pattern attention based sequence to sequence (TPA-Seq2Seq) model. This model can overcome the difficulty of multi-step prediction and further capture the load change pattern. The proposed framework was tested on real residential smart meter data, the results show that the proposed model has good prediction accuracy and is well suited for longer prediction sequences.

Recently, several techniques using gravitational data such as gravitational field and its gradient tensor have been developed to localize underwater multiple objects. However, performances of these existed techniques largely rely on proper selections of the initial values and, thus, are likely trapped into local minima. To deal with this issue, a global optimization algorithm, named as the state transition algorithm (STA), is investigated to localize multiple objects with both gravitational field and gravitational gradient tensor data sets in this letter. Using a heuristic random search strategy, the proposed algorithm features good global search capability and avoids the dependence of using proper initial values. To assess the performance of the proposed method, different models which contain three and four underwater objects are tested. The experimental results demonstrate that the proposed method is promising with sound stability and strong antinoise ability for dynamic localization problem with multiple objects.

The copper removal process (CRP) aims to reduce the copper ion concentration in zinc sulphate solution to a specific range by zinc addition. The satisfaction of production constraints and minimization of zinc consumption are vital but difficult to achieve. In this article, the dynamic optimization for CRP is conducted for optimal zinc control trajectory design considering constraints at least cost. First, a dynamic optimization problem with both state and control constraints is constructed for CRP. Then, a constrained dynamic optimization method is proposed, where a wavelet-based control parameterization method and a smooth penalty method are adopted. Specially, a hybrid optimization strategy is proposed to achieve a robust and efficient optimization performance. Numerical experiments are provided to illustrate the effectiveness of the proposed method. Results show that the proposed method can produce not only the optimal control trajectory with a qualified outlet ion concentration but also the less zinc consumption.

The state transition algorithm (STA) has been emerging as a novel metaheuristic method for global optimization over the past few years. In our previous study, the parameter of transformation operator in continuous STA is kept constant or decreasing itself in a periodical way. In this paper, the optimal parameter selection of operators in continuous STA is taken into consideration. First, a statistical study with four benchmark 2-D functions is conducted to show how these parameters affect the search ability of the STA. Based on the experience gained from the statistical study, then, a new continuous STA with optimal parameter strategy is proposed to accelerate its search process. The proposed STA is successfully applied to 12 benchmarks with 20-D, 30-D, and 50-D space. A comparison with other metaheuristics has also demonstrated the effectiveness of the proposed method.

Feature selection problems often appear in the application of data mining, which have been difficult to handle due to the NP-hard property of these problems. In this study, a simple but efficient hybrid feature selection method is proposed based on binary state transition algorithm and ReliefF, called ReliefF-BSTA. This method contains two phases: the filter phase and the wrapper phase. There are three aspects of advantages in this method. First, an initialization approach based on feature ranking is designed to make sure that the initial solution is not easy to get tapped into local optimum. Then, a probability substitute operator based on feature weights is developed to update the current solution according to the different mutation probabilities of the features. Finally, a new selection strategy based on relative dominance is presented to find the current best solution. The simple and efficient algorithm k-nearest neighborhood with the leave-one-out cross validation is used as a classifier to evaluate feature subset candidates. The experimental results indicate that the proposed method is more efficient in terms of the classification accuracy through a comparison to other feature selection methods using seven public datasets and several real biomedical datasets. For public datasets, the proposed method improved the classification average accuracy by about 2.5% compared with the filter method. For a specific biomedical dataset AID1284, the classification accuracy significantly increased from 77.24% to 85.25% by using the proposed method.

In this paper, a framework of convex optimization algorithm with a fixed time convergence rate is investigated. Given a strongly convex optimization problem, two control algorithms are developed to solve the problem within a fixed time of which the upper bound is theoretically obtained. Moreover, the fixed time convergence rate based algorithms are extended into the distributed manner which is applied to two typical distributed optimization problems including the resource allocation problem and the coordination optimization problem. Laplacian graph matrix is employed to the weighted gradient based and the coordination based distributed optimization algorithms. By developing the characteristic of the objective function, the upper bound of the fixed time convergence is derived. Two numerical examples are given to verify the main results.