Many important physical systems belong to distributed parameter systems (DPSs), which require appropriate models for optimization, decision-making, and control. The modeling of DPSs is typically challenging due to their highly time-space coupled nature. Time/space separation-based modeling methods have attracted substantial attention due to their ability to decouple spatiotemporal dynamics. From a systematic perspective, we identify and clarify a developmental trajectory underlying these methods, which, to the best of our knowledge, has not been explicitly presented in prior surveys. Specifically, these methods have progressed through a trajectory from traditional physics-based methods, to physics-data hybrid methods, then to purely data-driven methods, and more recently to deep physics-informed learning methods. Motivated by this newly identified paradigm, this paper presents a comprehensive review of time/space separation-based modeling methods over the past 15 years. Furthermore, we systematically summarize uncertainty quantification that has been overlooked in existing related surveys. Building upon these findings, we reveal potential future research directions for this class of methods. In addition, several representative application examples are provided to offer practical guidance for researchers and practitioners.

Constrained multiobjective optimization evolutionary algorithms cope with various constraints through the combination of a constraint violation evaluation (CVE) framework with a constraint handling technique. The evaluation of constraint violation is a critical problem that determines how effectively constraint information is utilized. However, this topic has received limited attention in existing research. To bridge this gap, an adaptive CVE (ACVE) framework that considers the evolutionary state is proposed in this paper. ACVE first divides solutions into multiple clusters. Each cluster is then reassigned a constraint violation value. By adjusting the number of clusters based on the evolutionary state, ACVE adaptively utilizes constraint information at different levels of granularity. This design allows ACVE to achieve a more optimal balance between constraint satisfaction and objective optimization, thereby reducing the dependency on constraint handling techniques. Extensive experiments conducted on several benchmark test suites demonstrate the effectiveness of ACVE. Based on ACVE, we develop the dual-population dynamic coevolutionary algorithm (DDCo). In experiments on multiple benchmark test suites, DDCo demonstrates superior or competitive performance compared with state-of-the-art algorithms, as evaluated using indicators such as inverted generational distance and hypervolume. Moreover, DDCo is successfully applied to optimize the charging protocols of lithium-ion batteries.

When employing evolutionary algorithms (EAs) to solve multimodal optimization problems (MMOPs), effectively utilizing diversity information is crucial to prevent the population from converging to a single peak. This requires balancing diversity and objective value—a challenge that inherently constitutes a penalty problem. Although some implicit penalty methods have been proposed to address this issue, most lack flexibility in penalty formulation. In this study, we present a novel explicit penalty method (EPM) designed to effectively leverage diversity information for multimodal optimization. First, the diversity of a solution is quantified by its distance to the nearest neighbor with a better objective value. Then, an explicit penalty function is formulated by integrating diversity and objective value. This function facilitates the capture of multiple peaks and balances the search among them. If a reasonable number of peaks are identified, a local search is applied to each for refinement; otherwise, a global search is conducted across the decision space. Through this adaptive process, EPM locates multiple optima both efficiently and accurately. Extensive experiments demonstrate that EPM outperforms several multimodal optimization methods, including 11 popular approaches, eight recent state-of-the-art algorithms, and an IEEE CEC competition winner. Moreover, even when integrated with classic differential evolution (DE), EPM exhibits highly competitive performance.

In this paper, a reinforcement learning (RL) control method is developed for the formation control of multiple wheeled mobile robots (WMRs) with visual servoing. First, a multi-robot system model is constructed based on the kinematic models of mobile robots, the camera model, and the multiple-view geometry principles. The leader-follower structure is then applied to derive the distributed error system. Next, the error term is separated from the optimal performance index function, and the Bellman residual error is obtained based on the Hamilton-Jacobi-Bellman equation (HJBE). Subsequently, the gradient descent method is employed to design the weight update rate, which is implemented in an actor-critic neural network (NN) architecture. The proposed RL control method achieves formation tracking and performance optimization simultaneously, which previous approaches have not accomplished. Furthermore, under the Lyapunov stability theory, it is proven that the follower robots can track the leader in a predefined formation, and the tracking error converges ultimately. The simulation outcomes verify the effectiveness of the developed approach.

Many industrial processes are typically distributed parameter systems (DPSs) described by partial differential equations. Data-driven methods have become popular for spatiotemporal modeling of DPSs, which is crucial for system understanding, simulation, and control improvement. However, current data-driven methods rely heavily on data volume and fidelity. With limited high-fidelity data, they exhibit unsatisfactory long-term predictions for out-of-sample scenarios. To remedy this issue, a novel physics-enhanced separation framework (called PhysiT/S) is proposed. PhysiT/S is composed of a physics-enhanced spatiotemporal unit and a coefficient network. By enhancing physics utilization through the physics-enhanced spatiotemporal unit, PhysiT/S becomes less data-dependent while computationally efficient. Multi-fidelity learning of the coefficient network further alleviates the request for a large volume of high-fidelity data. As a result, PhysiT/S can accurately predict out-of-sample distributions, even when only limited high-fidelity data is available. PhysiT/S introduces a novel way of combining physics with multi-fidelity data for spatiotemporal modeling of DPSs. Extensive simulations on two benchmark DPSs and the thermal process of lithium-ion batteries demonstrate the merits of PhysiT/S. Note to Practitioners—This paper is motivated by the problem of data-driven spatiotemporal modeling of DPSs, which is also applicable to other prediction tasks for complex spatiotemporal systems. Existing data-driven approaches rely heavily on high-fidelity data, while physics-informed approaches struggle to extract coupled spatiotemporal features. These drawbacks limit their practical applications to engineering modeling. In this paper, we propose a new generic modeling framework that integrates physics with data through the theory of time/space separation. It aims to achieve accurate long-term predictions for out-of-sample scenarios by constructing spatiotemporal enhancement units and using multi-fidelity data to decrease reliance on high-fidelity datasets. We have applied the proposed method to the thermal processes of a catalytic rod and a cylindrical lithium-ion battery. Preliminary results show that this method is feasible with better predictions than others, but it is untested in production. Future research will address online modeling in practical engineering.

Accurately modeling the electrochemical process of large-scale lithium-ion batteries (LLBs), which involves estimating the electrochemical state distributions within the process, is crucial for the design and management of LLBs. A two-dimensional (2-D) physics-based model can describe the electrochemical process of LLBs accurately. However, due to the presence of complex partial differential equations (PDEs), solving the model becomes a challenging task. This article develops a physics-informed composite network (PICN) as a surrogate model of the 2-D physics-based model. Specifically, PICN consists of four deep neural networks (DNNs) to estimate the distributions of four key electrochemical states, respectively. Since the architecture of PICN is inspired by PDE characteristics, it can achieve high accuracies with four lightweight DNNs. Additionally, by incorporating physics and data, PICN achieves accurate estimations using limited data. It can even estimate the electrochemical state distributions that may not be measured directly. Moreover, PICN presents a low-frequency information-based pretraining strategy and a two-stage loss balance strategy to address the convergence failure and loss imbalance that may arise in the training of PICN. PICN is a new attempt to model the electrochemical process of LLBs by integrating physics with data. Extensive experiments show that it is better than state-of-the-art models.

This article introduces a novel time/space separation-based physics-informed machine learning (T/S-PIML) modeling method by making full use of the complementary strengths of the physics-informed neural network (PINN) and the time/space separation methodology. T/S-PIML is the first attempt to seamlessly integrate structural (including spatial and temporal) physical information with data for effective spatiotemporal modeling of distributed parameter systems (DPSs). With the help of the spectral method, spatial basis functions are first extracted to capture spatial physical information. Subsequently, a reduced-order system is derived to characterize the corresponding temporal physical information. Upon the structural physical information, PINN is developed for temporal modeling. Following the time/space synthesis, a small amount of sensing data is utilized to calibrate system errors. Experiments on a benchmark DPS and the thermal process of a lithium-ion battery demonstrate the effectiveness of T/S-PIML.

The wide spreading of COVID-19 all over the world raises numerous focus on the epidemic containment problem. Different from the traditional epidemic control strategies that focus on quarantine and vaccination, we seek to control the epidemic from a network science perspective, i.e., by adjusting the weights of the epidemic spreading networks. Moreover, considering the limitations on the available resources, the dynamic constrained optimization problem of weights’ adaptation for heterogeneous epidemic spreading networks is investigated. Due to the powerful ability of searching for global optimum, evolutionary algorithms (EAs) are used as optimizers. One major difficulty is that the dimension of the problem is increasing exponentially with the network size and most existing EAs cannot achieve satisfiable performance on large-scale optimization problems. To address this issue, a novel constrained cooperative coevolution ($C^3$) strategy, which can separate the original large-scale problem into different subcomponents, is used to achieve the tradeoff between the constraint and objective function.

The goal of constrained multiobjective evolutionary optimization is to obtain a set of well-converged and well-distributed feasible solutions. To achieve this goal, a delicate tradeoff must be struck among feasibility, diversity, and convergence. However, balancing these three elements simultaneously through a single tradeoff model is nontrivial, mainly because the significance of each element varies in different evolutionary phases. As an alternative approach, we adapt distinct tradeoff models in various phases and introduce a novel algorithm named adaptive tradeoff model with reference points (ATM-R). In the infeasible phase, ATM-R takes the tradeoff between diversity and feasibility into account, aiming to move the population toward feasible regions from diverse search directions. In the semi-feasible phase, ATM-R promotes the transition from "the tradeoff between feasibility and diversity" to "the tradeoff between diversity and convergence." This transition is instrumental in discovering an adequate number of feasible regions and accelerating the search for feasible Pareto optima in succession. In the feasible phase, ATM-R places an emphasis on balancing diversity and convergence to obtain a set of feasible solutions that are both well-converged and well-distributed. It is worth noting that the merits of reference points are leveraged in ATM-R to accomplish these tradeoff models. Also, in ATM-R, a multiphase mating selection strategy is developed to generate promising solutions beneficial to different evolutionary phases. Systemic experiments on a diverse set of benchmark test functions and real-world problems demonstrate that ATM-R is effective. When compared to eight state-of-the-art constrained multiobjective optimization evolutionary algorithms, ATM-R consistently demonstrates its competitive performance.

Physics-informed machine learning (PIML) has proven to be a valuable approach for overcoming data scarcity challenges by incorporating physical models into machine learning methods. However, PIML faces limitations in handling complex spatial relationships, as its process information is obtained from disordered collocation points. Fuzzy systems, based on expert knowledge, can provide an interpretable way for tackling strong process nonlinearities. This article proposes a brand-new physics-informed spatial fuzzy system framework (PiFuz) to capture the essential system information of complex distributed parameter systems. PiFuz utilizes spatial membership functions to transform collocation points into a 3-D fuzzy input. This input is processed by the inference mechanism, leveraging its 3-D nature to produce fuzzy outputs with distinctive spatial characteristics. A feature fusion module is utilized to integrate these characteristics and generate the distributed system state. Utilizing the known physical knowledge base, the proposed framework undergoes automatic tuning while preserving process interpretability, resulting in an optimal model that aligns with the actual physical process. A reliable prediction of strong spatial nonlinear behaviors is achieved without the dependency of process data. For modeling higher dimensional spatiotemporal problems, the extension, a multikernel PiFuz framework (MKPiFuz), is further developed to improve the representation of heterogeneous time-varying nonlinear behaviors. By incorporating spatial and wavelet kernels, MKPiFuz extracts underlying features from spatial and temporal dimensions, respectively. Experimental investigations on thermal process of the battery module demonstrate the good accuracy in modeling complex spatiotemporal systems.

Modeling the temperature distribution of a battery is critical to its safe operation. Data-based modeling methods are computationally efficient, but require a large number of sensors, whereas physics-based modeling methods have better generalization, but the unknown dynamics of the actual scene are ignored. A physics-dominated neural network is presented to integrate electric–thermal mechanism of the battery and data information through a weight adaptive function. The electric–thermal coupling equation of the battery under complex conditions is taken as the prior knowledge to update parameters of the network, whereas the characteristic data obtained by the unique sensor are used to compensate the unknown disturbance in the actual scene. A well-trained model can predict the temperature distribution of the battery over entire space with a single sensor, and can also provide reasonable predictions for longer periods of time under extreme conditions. Experiments show that the proposed method outperforms traditional methods that rely only on pure data or pure physics.

The charging process design is crucial for optimizing the performance of lithium-ion batteries by identifying protocols that meet diverse demands. The main challenges include: 1) the high costs of battery experiments; 2) the multiple user preferences associated with the demands; and 3) the intricate high-dimensional search space of charging protocols. In light of this, this article presents a Gaussian process-accelerated multiobjective evolutionary design method for effective charging process design. To resolve the first concern, an electrochemical-thermal-aging model is constructed to evaluate charging protocols precisely, substituting the need for expensive battery experiments. Besides, the Gaussian process is applied to accelerate the evaluation process further. Regarding the second issue, a Gaussian process-accelerated two-archive evolutionary algorithm (GPA-TAEA) is developed to efficiently search for a set of optimal charging protocols that satisfy multiple user preferences. To address the third challenge, differential evaluation—an evolutionary algorithm proven effective for large-scale optimization—is employed to enhance the search process. The simulation results demonstrate that: 1) the proposed method effectively reduces the time required for charging process design, yielding a collection of optimal charging protocols that includes 530 solutions within 1000 simulations; 2) compared with five other multiobjective optimization algorithms, GPA-TAEA exhibits superior convergence and diversity; and 3) compared with fixed preference-based methods, GPA-TAEA demonstrates greater efficiency, saving 54% in simulation evaluations and 70% in time when considering seven user preferences.

State-of-charge (SoC) balancing in distributed energy storage systems (DESS) is crucial but challenging. Traditional deep reinforcement learning approaches struggle with real-world multiagent cooperation for SoC balance in these decentralized systems. To address these significant hurdles, this article pioneers an innovative fully-decentralized multiagent reinforcement learning (FDMARL) strategy, specifically tailored for DESS. First, the SoC balancing problem is formulated into a finite decentralized Markov decision process with action constraints derived from the microgrid context. Then, the average consensus algorithm is introduced for expanding the agent's observation and obtaining global information through a communication network. To improve multiagent system cooperation, a novel demand balance algorithm is proposed to refine agent actions for precise demand distribution. By the above modules, the FDMARL reveals outstanding performance in a fully-decentralized system without any expert experience or modeling. Finally, numerous simulations were carried out on pymgrid, (i.e., a Python-based open-source microgrid platform), which shows that: The FDMARL exceeds traditional reinforcement learning in decentralized cooperation, effectively manages large-scale systems with random states and demand/PV series, and maintains robustness with ESU failure or integration.

Human-in-the-loop for reinforcement learning (RL) is usually employed to overcome the challenge of sample inefficiency, in which the human expert provides advice for the agent when necessary. The current human-in-the-loop RL (HRL) results mainly focus on discrete action space. In this article, we propose a Q value-dependent policy (QDP)-based HRL (QDP-HRL) algorithm for continuous action space. Considering the cognitive costs of human monitoring, the human expert only selectively gives advice in the early stage of agent learning, where the agent implements human-advised action instead. The QDP framework is adapted to the twin delayed deep deterministic policy gradient algorithm (TD3) in this article for the convenience of comparison with the state-of-the-art TD3. Specifically, the human expert in the QDP-HRL considers giving advice in the case that the difference between the twin Q -networks' output exceeds the maximum difference in the current queue. Moreover, to guide the update of the critic network, the advantage loss function is developed using expert experience and agent policy, which provides the learning direction for the QDP-HRL algorithm to some extent. To verify the effectiveness of QDP-HRL, the experiments are conducted on several continuous action space tasks in the OpenAI gym environment, and the results demonstrate that QDP-HRL greatly improves learning speed and performance.

Unknown distributed incipient thermal fault detection and localization are vital to the safe operation of batteries while they have not been given sufficient attention in existing works compared to the studies on estimation of State of Charge (SoC) as well as State of Health (SoH). In order to fill this gap, a backstepping-based fault localization filter (FLF) is presented. Generally, full-state temperature measurement is required to achieve fault localization, which is impossible in applications. However, with the help of interpolation-based approximation, the required number of sensors decreases from infinity to only a few, which guarantees the usability of FLF. A comprehensive methodology framework, including the FLF design, residual evaluation in a distributed manner, and threshold computation, is introduced to guarantee reliable and robust performance in a real-time pattern. Theoretic analysis as well as experiment validations are presented to for validation.

Fault detection for distributed parameter processes (heat processes, fluid processes, etc.) is vital for safe and efficient operation. On one hand, the existing data-driven methods neglect the evolution dynamics of the processes and cannot guarantee that they work for highly dynamic or transient processes; on the other hand, model-based methods reported so far are mostly based on the backstepping technique, which does not possess enough redundancy for fault detection since only the boundary measurement is considered. Motivated by these considerations, we intend to investigate the robust fault detection problem for distributed parameter processes in a model-based perspective covering both boundary and in-domain measurement cases. A real-time fault detection filter (FDF) is presented, which gets rid of a large amount of data collection and offline training procedures. Rigorous theoretic analysis is presented for guiding the parameters selection and threshold computation. A time-varying threshold is designed such that the false alarm in the transient stage can be avoided. Successful application results on a hot strip mill cooling system demonstrate the potential for real industrial applications.

Constrained multiobjective optimization problems (CMOPs) involve both conflicting objective functions and various constraints. Due to the presence of constraints, CMOPs' Pareto-optimal solutions are very likely lying on constraint boundaries. The experience from the constrained single-objective optimization has shown that to quickly obtain such an optimal solution, the search should surround the boundary of the feasible region from both the feasible and infeasible sides. In this article, we extend this idea to cope with CMOPs and, accordingly, we propose a novel constrained multiobjective evolutionary algorithm with bidirectional coevolution, called BiCo. BiCo maintains two populations, that is: 1) the main population and 2) the archive population. To update the main population, the constraint-domination principle is equipped with an NSGA-II variant to move the population into the feasible region and then to guide the population toward the Pareto front (PF) from the feasible side of the search space. While for updating the archive population, a nondominated sorting procedure and an angle-based selection scheme are conducted in sequence to drive the population toward the PF within the infeasible region while maintaining good diversity. As a result, BiCo can get close to the PF from two complementary directions. In addition, to coordinate the interaction between the main and archive populations, in BiCo, a restricted mating selection mechanism is developed to choose appropriate mating parents. Comprehensive experiments have been conducted on three sets of CMOP benchmark functions and six real-world CMOPs. The experimental results suggest that BiCo can obtain quite competitive performance in comparison to eight state-of-the-art-constrained multiobjective evolutionary optimizers.

Spatiotemporal modeling is critical to the simulation, optimization, and control of the thermal process of a lithium-ion battery, which is a typical kind of distributed parameter system (DPS). Data-driven spatiotemporal modeling methods are of practical interest to construct an analytical model of the thermal process of a lithium-ion battery, since they only need some sampled data rather than the structure descriptions or parameters of a DPS. How to sample data optimally for data-driven spatiotemporal modeling is still an open question. In this article, with the aim of minimizing the spatiotemporal modeling error, we propose a novel evolutionary algorithm to optimally place sensors for data sampling. First, an objective function that can quantify both the spatial error and the temporal error is designed. Additionally, a novel differential evolution algorithm with two kinds of encoding mechanisms (called DETEM) is proposed to optimize the objective function. Numerical simulations and experimental studies have shown that the proposed method is competitive. Besides, both the objective function and DETEM are critical to the proposed method. In summary, the proposed method provides an effective way to obtain the optimal sensor placement for spatiotemporal modeling of the thermal process of a lithium-ion battery.

Lithium-ion batteries are widely used as power sources in industrial applications. Electrochemical models and simulations are crucial to disclose many details that cannot be directly measured through experiments. Parameter identification of an accurate electrochemical model is much more cost-effective than direct and destructive measurement methods. However, the complex structure and strong nonlinearity of electrochemical models will make the parameter identification very difficult. Additionally, time-consuming electrochemical simulations can significantly limit the identification efficiency. This article proposes a surrogate-model-based scheme to achieve high-efficiency parameter identification of an electrochemical battery model. To be specific, the proposed method is implemented by the close integration of an evolutionary algorithm and a surrogate model. A sensitivity-based identification strategy is first designed to alleviate the difficulty of optimization. Then, a surrogate model is developed from historical data to gradually approach the objective function used for parameter evaluations. Finally, an evolutionary algorithm is employed to find promising solutions by minimizing the output of the surrogate model. Simulations and experimental studies demonstrate the effectiveness and high efficiency of the proposed method.

Solving constrained multiobjective optimization problems (CMOPs) is a challenging task since it is necessary to optimize several conflicting objective functions and handle various constraints simultaneously. A promising way to solve CMOPs is to integrate multiobjective evolutionary algorithms (MOEAs) with constraint-handling techniques, and the resultant algorithms are called constrained MOEAs (CMOEAs). At present, many attempts have been made to combine dominance-based and decomposition-based MOEAs with diverse constraint-handling techniques together. However, for another main branch of MOEAs, i.e., indicator-based MOEAs, almost no effort has been devoted to extending them for solving CMOPs. In this article, we make the first study on the possibility and rationality of combining indicator-based MOEAs with constraint-handling techniques together. Afterward, we develop an indicator-based CMOEA framework which can combine indicator-based MOEAs with constraint-handling techniques conveniently. Based on the proposed framework, nine indicator-based CMOEAs are developed. Systemic experiments have been conducted on 19 widely used constrained multiobjective optimization test functions to identify the characteristics of these nine indicator-based CMOEAs. The experimental results suggest that both indicator-based MOEAs and constraint-handing techniques play very important roles in the performance of indicator-based CMOEAs. Some practical suggestions are also given about how to select appropriate indicator-based CMOEAs. Besides, we select a superior approach from these nine indicator-based CMOEAs and compare its performance with five state-of-the-art CMOEAs. The comparison results suggest that the selected indicator-based CMOEA can obtain quite competitive performance. It is thus believed that this article would encourage researchers to pay more attention to indicator-based CMOEAs in the future.

Pareto dominance-based multiobjective optimization has been successfully applied to constrained evolutionary optimization during the last two decades. However, as another famous multiobjective optimization framework, decomposition-based multiobjective optimization has not received sufficient attention from constrained evolutionary optimization. In this paper, we make use of decomposition-based multiobjective optimization to solve constrained optimization problems (COPs). In our method, first of all, a COP is transformed into a biobjective optimization problem (BOP). Afterward, the transformed BOP is decomposed into a number of scalar optimization subproblems. After generating an offspring for each subproblem by differential evolution, the weighted sum method is utilized for selection. In addition, to make decomposition-based multiobjective optimization suit the characteristics of constrained evolutionary optimization, weight vectors are elaborately adjusted. Moreover, for some extremely complicated COPs, a restart strategy is introduced to help the population jump out of a local optimum in the infeasible region. Extensive experiments on three sets of benchmark test functions, namely, 24 test functions from IEEE CEC2006, 36 test functions from IEEE CEC2010, and 56 test functions from IEEE CEC2017, have demonstrated that the proposed method shows better or at least competitive performance against other state-of-the-art methods.

When solving constrained optimization problems by evolutionary algorithms, the core issue is to balance constraints and objective function. This paper is the first attempt to utilize the correlation between constraints and objective function to keep this balance. First of all, the correlation between constraints and objective function is mined and represented by a correlation index. Afterward, a weighted sum updating approach and an archiving and replacement mechanism are proposed to make use of this correlation index to guide the evolution. By the above process, a novel constrained optimization evolutionary algorithm is presented. Experiments on a broad range of benchmark test functions indicate that the proposed method shows better or at least competitive performance against other state-of-the-art methods. Moreover, the proposed method is applied to the gait optimization of humanoid robots.

In this paper, a unified susceptible-exposed-infected-susceptible-aware (SEIS-A) framework is proposed to combine the epidemic spreading process with individuals' self-query behaviors on the Internet. An epidemic spreading prediction model that contains two phases is established based on the SEIS-A framework. To deal with the nonstationary complex characteristic of the time series data of disease density, it is decomposed through the empirical mode decomposition (EMD) method to obtain the intrinsic mode functions (IMFs) in phase I. To enhance the prediction performance, the ensemble learning techniques that use the self-query data as an external input are applied to these IMFs in phase II. Finally, an empirical study on the prediction of weekly consultation rates of hand-foot-and-mouth disease (HFMD) in Hong Kong is conducted to validate the effectiveness of the proposed method. The main advantage of this method is that it outperforms other learning methods on fluctuating complex epidemic spreading data.

Time/space separation based spatiotemporal modeling methods have been proven to be effective and efficient for modeling a class of distributed parameter systems (DPSs). However, these conventional methods may not work satisfactorily for DPSs with time-dependent boundary conditions. A sliding window based dynamic spatiotemporal modeling method is proposed for this kind of DPSs. First, the sliding window is appropriately designed to capture the most recent spatiotemporal data. Then, the conventional Karhunen-Loève method can be used to construct the analytical model. Besides, a more general sliding window method can be achieved by using a forgetting factor to adjust different influence of the current and previous data. This analytical model can be utilized for online performance prediction. Simulation experiments on a benchmark and a battery with unknown boundary cooling have demonstrated the superior performance of the proposed method on the DPSs with time-dependent boundary conditions.

When solving constrained optimization problems (COPs) by evolutionary algorithms, the search algorithm plays a crucial role. In general, we expect that the search algorithm has the capability to balance not only diversity and convergence but also constraints and objective function during the evolution. For this purpose, this paper proposes a composite differential evolution (DE) for constrained optimization, which includes three different trial vector generation strategies with distinct advantages. In order to strike a balance between diversity and convergence, one of these three trial vector generation strategies is able to increase diversity, and the other two exhibit the property of convergence. In addition, to accomplish the tradeoff between constraints and objective function, one of the two trial vector generation strategies for convergence is guided by the individual with the least degree of constraint violation in the population, and the other is guided by the individual with the best objective function value in the population. After producing offspring by the proposed composite DE, the feasibility rule and the ε constrained method are combined elaborately for selection in this paper. Moreover, a restart scheme is proposed to help the population jump out of a local optimum in the infeasible region for some extremely complicated COPs. By assembling the above techniques together, a constrained composite DE is proposed. The experiments on two sets of benchmark test functions with various features, i.e., 24 test functions from IEEE CEC2006 and 18 test functions with 10 dimensions and 30 dimensions from IEEE CEC2010, have demonstrated that the proposed method shows better or at least competitive performance against other state-of-the-art methods.

A multi-task learning based spatiotemporal modeling method is proposed to construct analytical models of distributed thermal processes. Firstly, the time/space separation based framework is utilized to reduce a distributed thermal process into a finite-dimensional system, which is composed of a set of time series. Afterward, the multi-task learning based least squares support vector machine (ML-LS-SVM) is employed to model these time series which are related to each other. Finally, through time/space synthesis, the nonlinear spatiotemporal dynamics can be achieved. Experiments on a curing process have validated the effectiveness of the proposed method. The superiority of ML-LS-SVM over LS-SVM has also been demonstrated experimentally.

When solving constrained optimization problems by evolutionary algorithms, an important issue is how to balance constraints and objective function. This paper presents a new method to address the above issue. In our method, after generating an offspring for each parent in the population by making use of differential evolution (DE), the well-known feasibility rule is used to compare the offspring and its parent. Since the feasibility rule prefers constraints to objective function, the objective function information has been exploited as follows: if the offspring cannot survive into the next generation and if the objective function value of the offspring is better than that of the parent, then the offspring is stored into a predefined archive. Subsequently, the individuals in the archive are used to replace some individuals in the population according to a replacement mechanism. Moreover, a mutation strategy is proposed to help the population jump out of a local optimum in the infeasible region. Note that, in the replacement mechanism and the mutation strategy, the comparison of individuals is based on objective function. In addition, the information of objective function has also been utilized to generate offspring in DE. By the above processes, this paper achieves an effective balance between constraints and objective function in constrained evolutionary optimization. The performance of our method has been tested on two sets of benchmark test functions, namely, 24 test functions at IEEE CEC2006 and 18 test functions with 10-D and 30-D at IEEE CEC2010. The experimental results have demonstrated that our method shows better or at least competitive performance against other state-of-the-art methods. Furthermore, the advantage of our method increases with the increase of the number of decision variables.