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Health monitoring of current complex systems significantly impacts the total cost of the system. Centralized fault diagnosis architectures are sometimes prohibitive for large-scale interconnected systems, such as distribution systems, telecommunication networks, water distribution networks, or fluid power systems. Confidentiality constraints are also an issue. This article presents a decentralized fault diagnosis method that only requires the knowledge of local models and limited knowledge of their neighboring subsystems. The method, implemented in the decentralized diagnoser design ($D^{3}$) algorithm, is based on structural analysis and can advantageously be applied to high-dimensional systems, linear or nonlinear. Using the concept of isolation on request, a hierarchy is built according to diagnostic objectives. The resulting diagnoser is based on analytical redundancy relations (ARRs) generated along the hierarchy. Their number is optimized via binary integer linear programming (BILP) while still guaranteeing maximal diagnosability at each level. $D^{3}$ proves of lower time complexity than its centralized equivalent. It is successfully applied to a nonlinear combined cycle gas-turbine power plant. [ABSTRACT FROM AUTHOR]

Multiobjective optimization evolutionary algorithms (MOEAs) have received significant achievements in recent years. However, they encounter many difficulties in dealing with many-objective optimization problems (MaOPs) due to the weak selection pressure. One possible way to improve the ability of MOEAs for these MaOPs is to balance the convergence and diversity in the high-dimensional objective space. Based on this consideration, this article proposes a novel generic two-stage (TS) framework for MaOPs. The entire evolutionary search process is divided into two stages: in the first stage, a new subregion dominance and a modified subregion density-based mating selection mainly purse the convergence and in the second stage, a novel level-based Pareto dominance cooperates with the traditional Pareto dominance that mainly promotes diversity. Integrated into NSGA-II, the TS NSGA-II, referred to as TS-NSGA-II, is proposed. To extensively evaluate the performance of our approach, 29 benchmark problems were used as the test suite. The experimental results demonstrate our approach obtained superior or competitive performance compared with eight state-of-the-art many-objective optimization evolutionary algorithms. To study its generality, the proposed TS strategy was also combined with four other advanced methods for MaOPs. The results show that it can also improve the performance of these four methods in terms of convergence and diversity. [ABSTRACT FROM AUTHOR]

Optimization modeling of real-world application problems usually involves noise from various sources. Noisy optimization imposes challenges to optimization methods since the objective values can be different for multiple evaluations. In this article, we propose a novel online population size learning (OPL) technique of evolution strategies for handling noisy optimization problems. By re-evaluating a fraction of the candidates, we measure the strength of noise level of the re-evaluated candidate solutions and adapt the population size according to the noise level. The proposed OPL combines the advantages of both explicit averaging by re-evaluations and the implicit averaging by large population size and overcomes their limitations. We incorporate it with the covariance matrix adaptation evolution strategy (CMA-ES) and obtain OPL-CMA-ES. Compared with the existing noise handling technique, the proposed OPL is much simpler in both concepts and computation. We conduct comprehensive experiments to evaluate the algorithm’s performance on standard problems with Gaussian noise. We further evaluate the performance of OPL-CMA-ES on the black-box optimization benchmarks (BBOBs) noisy testbed, which is a standard platform for comparing black-box optimization algorithms, compared with the state-of-the-art noise-handling algorithms. The experimental results show that OPL-CMA-ES achieves remarkable performance and outperforms the compared variants. [ABSTRACT FROM AUTHOR]

Competitive swarm optimizers (CSOs) have shown very promising search efficiency in large-scale decision space. However, they face difficulties when solving large-scale multi-/many-objective optimization problems (LMOPs), as their winner particles are selected by random pairwise competition based on only a single evaluation criterion, which does not provide diverse guidance for LMOPs. To alleviate this issue, this article proposes a comprehensive competitive learning (CCL) strategy for CSOs using three competition mechanisms to guide the particle search. Specifically, environmental competition classifies winner and loser particles from the swarm, while cognitive competition and social competition select one winner particle as the cognitive component and the social component, respectively, to guide the search for loser particles. This competitive learning strategy aims to enhance the search capability of loser particles and provides diverse search directions for solving LMOPs. When compared with eight competitive optimizers, the experimental results validate the high efficiency and effectiveness of our method in solving nine LMOPs with 2–10 objectives and 100–5000 variables. [ABSTRACT FROM AUTHOR]

Deep learning has been widely applied in many fields. Efficient optimization algorithms contribute a lot to the enhancement of deep learning. However, reverse studies on how deep learning can solve optimization problems, especially mathematical programming, are relatively scarce. In this work, we aim to initiate a discussion on using deep learning to solve parametric mathematical programming, which can be converted to find a mapping from parameter space to solution space. Given that deep convolutional neural networks (DCNNs) have been successfully applied in the field of computer vision, converting a mathematical programming problem into an image representation may provide the solution. This work takes the 0–1 knapsack problem (KP) as an example to build an original image representation method. After modifying the image details, the proposed method is extended to the general 0–1 linear programming (LP) problem, and a deep learning architecture is designed to solve the transferred computer vision problem. The efficiency of the proposed DCNNs method is validated on a large number of problems, and results show that this method can solve the 0–1 LP accurately and efficiently without iteration. The solution speed is 20 times faster than that of traditional optimization solvers. [ABSTRACT FROM AUTHOR]

In this article, a general approach for directed graph clustering and two new density-based clustering objectives are presented. First, using an equivalence between the clustering objective functions and a trace maximization expression, the directed graph clustering objectives are converted into the corresponding weighted kernel $k$ -means problems. Then, a nonspectral algorithm, which covers both the direction and weight information of the directed graphs, is thus proposed. Next, with Rayleigh’s quotient, the upper and lower bounds of clustering objectives are obtained. After that, we introduce a new definition of weak links to characterize the effectiveness of clustering. Finally, illustrative examples are given to demonstrate effectiveness of the results. This article provides a glance at the potential connection between density-based and pattern-based clustering. Compared with other approaches for directed graph clustering, the method proposed in this article naturally avoids the loss of the nonsymmetric edge data because there is no need for any additional symmetrization. [ABSTRACT FROM AUTHOR]

This article presents a new model to handle the cast break problem caused by small daily disruptions in the processing time of the steelmaking and continuous casting (SCC) production process. In this model, the exact distribution of the uncertain parameters is unknown, and support set, mean, and covariance information is used to describe the uncertain processing time. The problem aims to determine the assignments, sequences, and time points of the charges to be processed on corresponding machines. The main goal is to minimize the expected value of the production objective while reducing the number of cast break occurrences. The problem is solved in two steps. First, a subproblem is developed by fixing the sequences and the assignments of the charges. This subproblem is formulated as a distributionally robust chance-constrained (DRCC) model, in which the constraints are established with certain probabilities even when the uncertain processing times are in their worst cases. A dual approximation method is proposed to convert the model into a semidefinite programming problem so that it can be solved by standard solvers. Additionally, a linear programming approximation method is used to accelerate the solving procedure. A Tabu search algorithm incorporated with a speed-up strategy is also designed to determine the assignments and sequences of the charges. Both simulated data generated from different distributions and actual production data are used to test the efficacy of our model. Results of the numerical experiments show that the schedule obtained from the DRCC model is more robust, i.e., it causes fewer cast breaks than the nominal schedule obtained from a deterministic model. [ABSTRACT FROM AUTHOR]

With integer linear programming problems (ILPPs) being formulated and solved, the existing approaches design optimal Petri-net supervisors via nonpure net structures, including self-loops and data inhibitor arcs. Nonpure net structures are powerful for control of Petri-net-modeled discrete-event systems. However, in the existing work, the formulated ILPPs contain a large number of constraints, which is computationally inefficient. In this article, we propose approaches that formulate ILPPs with fewer constraints such that the computational efficiency is significantly improved. To do so, in formulating ILPPs for optimal Petri-net controllers by using self-loops and data inhibitor arcs, we remove the reachability conditions for legal markings. By doing so, an obtained solution may result in some legal markings unreachable. To solve this problem, a novel technique is developed to design an optimal controller by modifying the initial marking and structure of the obtained supervisor. It is shown that, by the reduced ILPPs, one can find the same feasible solutions as that obtained by the existing work. Finally, the proposed approaches are demonstrated by examples. [ABSTRACT FROM AUTHOR]

Convergence, diversity and feasibility are three important issues when solving constrained multiobjective optimization problems (CMOPs). To deal with the balance among convergence, diversity and feasibility well, this article proposes a cooperative multiobjective evolutionary algorithm with propulsive population (CMOEA-PP) for solving CMOPs. CMOEA-PP has two populations, including propulsive population and normal population, and these two populations work cooperatively. Specifically, propulsive population focuses on convergence. Normal population gives priority to feasibility and is obligated to maintain diversity. To cross through the infeasible region and reach the Pareto front (PF), propulsive population does not consider constraints in the early stage and only considers constraints in the later stage. To further accelerate the speed of convergence, propulsive population only searches for corner solutions and center solutions, while normal population searches for the whole PF. As a result, propulsive population can cross through the infeasible region because of the lack of attention to feasibility. In addition, propulsive population also can guide and accelerate the convergence of the evolutionary process. Comprehensive experiment results on several sets of benchmark problems demonstrate that CMOEA-PP is better than existing state-of-the-art competitors. [ABSTRACT FROM AUTHOR]

This article proposes a data-driven multiobjective evolutionary interval type-2 fuzzy-logic system (IT2FLS) learning approach that considers both system performance and rule interpretability. One characteristic of the evolutionary learning framework is that the IT2FLS structure is incrementally generated instead of searching from an initially huge grid-type rule base, which significantly reduces the parameter search space. Another one is that a new constrained objective function is proposed to improve the distinguishability of the generated interval type-2 fuzzy sets (FSs) without restricting them to be evenly distributed. Because of the tradeoff between system performance and interpretability, a new multiobjective ant colony optimization (ACO) algorithm is proposed to optimize the IT2FLS parameters and improve optimization performance. The evolutionary IT2FLS learning approach is applied to control a real wall-following hexapod robot. The approach shows the advantages of model-free design and interpretability and robustness to noise in the evolved type-2 fuzzy rules. Simulations with performance comparisons and experiments in controlling a real robot show the advantages of the learning approach. [ABSTRACT FROM AUTHOR]

This article focuses on the issue of checking critical observability for labeled Petri nets. Critical observability is a property related to the safety concern of cyber-physical systems. With the aim of checking this property of a net system, it is required to detect whether a set of markings consistent with any observed word of the net system is a subset of a set of critical states representing undesirable operations or a set of noncritical states. In this work, we prove a necessary and sufficient condition to check critical observability when the critical state set is described by an arbitrary subset of reachable markings. Then, the result is extended to the case when a critical state set is modeled by all the reachable markings that satisfy disjunctions of generalized mutual exclusion constraints. The proposed method is derived from the solutions of integer linear programming problems and is applicable to net systems with liveness and boundness. Several case studies show the performance of the presented methodology for discrete-event systems. [ABSTRACT FROM AUTHOR]

Solving constrained multiobjective optimization problems brings great challenges to an evolutionary algorithm, since it simultaneously requires the optimization among several conflicting objective functions and the satisfaction of various constraints. Hence, how to adjust the tradeoff between objective functions and constraints is crucial. In this article, we propose a dynamic selection preference-assisted constrained multiobjective differential evolutionary (DE) algorithm. In our approach, the selection preference of each individual is suitably switching from the objective functions to constraints as the evolutionary process. To be specific, the information of objective function, without considering any constraints, is extracted based on Pareto dominance to maintain the convergence and diversity by exploring the feasible and infeasible regions; while the information of constraint is used based on constrained dominance principle to promote the feasibility. Then, the tradeoff in these two kinds of information is adjusted dynamically, by emphasizing the utilization of objective functions at the early stage and focusing on constraints at the latter stage. Furthermore, to generate the promising offspring, two DE operators with distinct characteristics are selected as components of the search algorithm. Experiments on four test suites including 56 benchmark problems indicate that the proposed method exhibits superior or at least competitive performance, in comparison with other well-established methods. [ABSTRACT FROM AUTHOR]

A mixed-integer programming (MIP) problem contains not only constraints but also integer restrictions. Integer restrictions divide the feasible region defined by constraints into multiple discontinuous feasible parts with different sizes. Several popular methods (e.g., rounding and truncation) have been proposed to deal with integer restrictions. Although it is easy for these methods to generate an integer, they tend to converge to an integer which is located in a feasible part with a big size. If the optimal solution is not in this feasible part, they are very likely to converge to a local optimal solution due to the loss of diversity of the population. To overcome this shortcoming, a biobjective optimization-based two-phase method is proposed in this article. In the first phase, a measure function is designed to compute the degree that a solution violates integer restrictions. By employing this measure function as the second objective function and removing integer restrictions, a MIP problem is transformed into a constrained biobjective optimization problem (CBOP). It can be proven that the Pareto optimal solution of the transformed CBOP which satisfies integer restrictions is the optimal solution of the original MIP problem. To solve the transformed CBOP, a new comparison rule is designed. After the first phase, the population can approach the Pareto optimal solution which satisfies integer restrictions. Then, the second phase is implemented to enhance the convergence precision and obtain the optimal solution. In addition, we design 12 test problems to verify the effectiveness of the proposed method. The results demonstrate that the proposed method shows better performance against five state-of-the-art evolutionary algorithms for MIP. [ABSTRACT FROM AUTHOR]

In this article, the issue of positive $\mathcal {L}_{1}$ filter design is investigated for positive nonlinear stochastic switching systems subject to the phase-type semi-Markov jump process. Many complicated factors, such as semi-Markov jump parameters, positivity, T–S fuzzy strategy, and external disturbance, are taken into consideration. Practical systems under positivity constraint conditions and unpredictable structural changes are characterized by positive semi-Markov jump systems (S-MJSs). First, by the key properties of the supplementary variable and the plant transformation technique, phase-type S-MJSs are transformed into Markov jump systems (MJSs), which means that, to an extent, these two kinds of stochastic switching systems are mutually represented. Second, with the help of the normalized membership function, the associated nonlinear MJSs are transformed into the local linear MJSs with specific T–S fuzzy rules. Third, by choosing the linear copositive Lyapunov function (LCLF), stochastic stability (SSY) criteria are given for the corresponding system with $\mathcal {L}_{1}$ performance. Some solvability conditions for positive $\mathcal {L}_{1}$ filter are constructed under a linear programming framework. Finally, an epidemiological model illustrates the effectiveness of the theoretical findings. [ABSTRACT FROM AUTHOR]

Quantum-inspired differential evolution (QDE) is an evolutionary algorithm, which can effectively solve complex optimization problems. However, sometimes, it easily leads to premature convergence and low search ability and falls to local optima. To overcome these problems, based on the MSIQDE (improved QDE with multistrategies) algorithm, an enhanced MSIQDE algorithm based on mixing multiple strategies, namely, EMMSIQDE is proposed in this article. In the EMMSIQDE, a new differential mutation strategy of a difference vector is proposed to enhance the search ability and descent ability. Then, a new multipopulation mutation evolution mechanism is designed to ensure the relative independence of each subpopulation and the population diversity. The feasible solution space transformation strategy is used to achieve the optimal solution by mapping the quantum chromosome from a unit space to solution space. Finally, some multidimensional unimodal and multimodal functions are selected to demonstrate the optimization performance of EMMSIQDE. The results demonstrate that the EMMSIQDE is significantly better than the DE, QDE, QGA, and MSIQDE, and has better optimization ability, scalability, efficiency, and stability. [ABSTRACT FROM AUTHOR]

We investigate a general solution based on reinforcement learning for the agile satellite scheduling problem. The core idea of this method is to determine a value function for evaluating the long-term benefit under a certain state by training from experiences, and then apply this value function to guide decisions in unknown situations. First, the process of agile satellite scheduling is modeled as a finite Markov decision process with continuous state space and discrete action space. Two subproblems of the agile Earth observation satellite scheduling problem, i.e., the sequencing problem and the timing problem are solved by the part of the agent and the environment in the model, respectively. A satisfactory solution of the timing problem can be quickly produced by a constructive heuristic algorithm. The objective function of this problem is to maximize the total reward of the entire scheduling process. Based on the above design, we demonstrate that Q-network has advantages in fitting the long-term benefit of such problems. After that, we train the Q-network by Q-learning. The experimental results show that the trained Q-network performs efficiently to cope with unknown data, and can generate high total profit in a short time. The method has good scalability and can be applied to different types of satellite scheduling problems by customizing only the constraints checking process and reward signals. [ABSTRACT FROM AUTHOR]

This article investigates stochastic stability of positive singular Markovian jump systems (PSMJSs) with mode-dependent derivative-term coefficient. Different from the existing results, the condition on stochastic stability of PSMJSs associated with state jumps behavior at switching instants is given by means of linear co-positive Lyapunuov function. On the basis of it, the conditions on stochastic stability under the cases of partially known transition rates and uncertain transition rates have been presented, respectively. All obtained conditions can be solved by linear programming (LP) technique. Finally, an example is introduced to illustrate the effectiveness and the merits of the results proposed in this article. [ABSTRACT FROM AUTHOR]

This article is concerned with the trajectory optimization problem of a drilling process, which is of significance to drilling efficiency and safety. Due to the difference between an actual trajectory and a planned trajectory, this problem is a multiobjective optimization problem (MOP) with parameter uncertainties. To solve the problem, this study devises a new approach named nondominated sorting genetic Algorithm II using outlier removal (OR-NSGA-II). First, the optimization problem with parameter uncertainties is formulated, including two objective functions: 1) a trajectory length and 2) an expected value of drill-string torque. Then, an outlier-removal mechanism is devised in the sorting process of NSGA-II to reduce the negative effects of parameter uncertainties. Next, the crowding distance calculation in NSGA-II is improved to ensure population diversity. Comparison of simulation results show that our method is effective on the MOP with parameter uncertainties. [ABSTRACT FROM AUTHOR]

This work considers the observability problem in bearings-only tracking (BOT). Although the rank criterion has always been used for observability analysis, the evident drawback that it can only give a qualitative result prevents us from exploiting more information from the observability matrix. In reality, we want to know not only if the system is observable but also the degree of the observability. In order to quantitatively describe the system observability, we propose a series of metrics for BOT. Being derived based on the condition number, the novel metrics can reflect the observability degree as well as evaluate the tracking performance. Besides, the metrics can be extended to be used for sensor trajectory optimization and sensor configuration, which are crucial to enhancing the tracking performance. [ABSTRACT FROM AUTHOR]

Evolutionary algorithms and swarm intelligence algorithms have been widely used for constrained optimization problems for decades and numerous techniques for constraint handling have been proposed. The ${\varepsilon }$ -constrained method is a very effective one. In the literature, the ${\varepsilon }$ value was usually controlled via an exponential function, which is not competent for solving certain types of constrained optimization problems, e.g., whose global optima are located near the boundary of the feasible and infeasible regions. To solve this problem, this article proposes a new adaptive ${\varepsilon }$ control method and incorporate it into a basic differential evolution (DE) algorithm: (DE/rand/1/exp). Based on the information of constraint violation in the current population, the adaptive method controls the value of ${\varepsilon }$ through a simple heuristic rule. Compared with the traditional exponential function-based control methods, the proposed adaptive method can prevent the algorithm from being trapped into local optima while retaining the obtained near-optimal candidate solutions in the infeasible region for generating promising searching paths. Besides, we set the crossover rate (CR) as a more reasonable value for DE/rand/1/exp, which can enhance the efficiency significantly. The well-known 2006 IEEE Congress on Evolutionary Computation (CEC 2006) competition on real-parameter single-objective constrained optimization benchmark is adopted to evaluate the effectiveness of the proposed adaptive ${\varepsilon }$ -constrained DE. Fifteen constrained engineering optimization problems are collected from the literature to test the proposed algorithm. Moreover, the adaptive ${\varepsilon }$ control method is extended to an adaptive algorithm to solve the benchmark problems from CEC 2017. The comparison results confirm the superiority of the proposed method. [ABSTRACT FROM AUTHOR]

Community detection has long been a fundamental problem in network analysis. A great deal of previous research has regarded community detection as an optimization process, where a variety of internal quality metrics are typically treated as objective functions, such as modularity (${Q}$) and weighted community clustering (WCC). However, purely optimizing a predefined quality metric probably results in an extreme unbalance in the scale of the detected communities, e.g., few giant communities with many very small communities. To reveal the true mesoscopic structure inside a big network under the suitable number of communities, we propose a novel community detection framework called LL-GMR, which is a local learning framework based on generalized metric with neighboring regularization. LL-GMR is qualified for both nonoverlapping and overlapping detection tasks. In LL-GMR, we propose a generalized representation and illustrate that it can be instantiated into 12 well-known internal quality metrics. When the generalized metric is used as an objective function, we encode node-level and community-level neighborhood information into two regularization terms to alleviate the dilemma of unbalanced communities. The experimental results show that our LL-GMR consistently outperforms other state-of-the-art community detection approaches in terms of discovering ground-truth communities in six real-life networks. [ABSTRACT FROM AUTHOR]

In this article, the issue of $\mathscr {L}_{1}$ control design is addressed for a class of delayed stochastic jump systems subject to semi-Markov jump parameters. The stochastic jump systems in the presence of positivity constraints are described by positive semi-Markov jump systems (S-MJSs). By constructing new linear Lyapunov functional dependent double integral, some sojourn-time-dependent sufficient conditions are established to realize the corresponding stochastic stability with a prescribed $\mathscr {L}_{1}$ -gain performance index. Then, a switching controller via gain matrix decomposition is designed to achieve positivity and stochastic stabilization with a prescribed $\mathscr {L}_{1}$ -gain performance, which can be solved with the help of linear programming approach. Finally, the virus mutation treatment model verifies the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

A social cost minimization problem is addressed in this article. In the considered problem, a network of agents work collaboratively to minimize the social cost function, which is defined as the sum of the agents’ local objective functions. The engaged agents are supposed to be equipped with an undirected and connected communication graph. Different from most of the existing works, the social cost function in the considered problem is allowed to be nonconvex and possibly admits local extrema. To avoid local extrema and achieve the global minimization of the social cost function, an extremum-seeking-based approach is proposed by introducing a dynamic average consensus protocol to the sinusoidal-dither-signal-based extremum seeking scheme. The dynamic average consensus protocol is leveraged in the proposed extremum-seeker for information sharing and the sinusoidal probing signal is utilized for information extraction. For the avoidance of local extrema, the amplitude of the dither signal is designed to be adaptive. Through Lyapunov stability analysis, it is shown that the proposed method enables the decision variable to converge to a neighborhood of the global minimum point if the conditions on the network connectivity, the existence of unique global minimum and achievability of the global minimum are satisfied. The theoretical result is verified via simulating a numerical example. [ABSTRACT FROM AUTHOR]

Recent studies have examined minimum cost consensus models from the moderator’s perspective. However, current dual models aimed at deriving a maximum return have been limited to special cases. A further problem has been the return allocation to the individuals. With this in mind, this article presents two general dual consensus models, the first of which is a minimum cost consensus model, and the second of which allows the different individuals to have different tolerance levels. In both models the individual opinions and the group opinion are connected using a weighted average operator. To understand the economic significance of these models, some properties, such as the weak duality property, the optimality property, and the strong duality property are given. The relationships between the individual opinions, the unit costs, and the unit returns are also proven, and the core return allocation problem is addressed. It was found that in both cases, the costs the moderator needed to pay to a given individual were precisely equal to the returns the individual deserved. Numerical case studies were used to illustrate the proposed models, with the simulation results providing insights into the practical use of these optimization consensus models. [ABSTRACT FROM AUTHOR]

A kind of facilities for wafer fabrication, cluster tools (CTs) need to close down to an idle state from time to time because of periodical maintenance and switches from one type of lots to another, which is called a normal close-down process (NCDP). It is crucial to optimize such a transient process since it tends to occur more and more frequently due to customization. Also, process modules (PMs) in CTs are known to be failure-prone. Once a PM failure occurs, a tool needs to close down to an idle state as well, which is different from NCDP and is called a failure close-down process (FCDP). With wafer residency time constraints (WRTCs) being imposed, close-down process optimization for such a tool is challenging, since one needs to not only finish this process as soon as possible but also meet WRTCs during this transient process. In order to tackle this problem, this article first introduces steady state scheduling problems. Then, with a presented backward robot task sequence, a linear programming model is first proposed to optimize NCDP. To deal with the PM failures, efficient PM failure response policies are formulated for the cases in which a PM fails. Then, four linear programs are proposed to optimize an FCDP. Finally, industrial case studies are given to show the usefulness of the proposed approaches. [ABSTRACT FROM AUTHOR]

This article is concerned with the exponential stability and ℓ1-gain performance analysis of discrete-time switched positive systems (DTSPSs) under mode-dependent average dwell time (MDADT) switching. A novel linear copositive Lyapunov function, which is both quasi-time-dependent and mode-dependent, is designed for the stability and performance analysis. Stability conditions are developed such that the considered DTSPS is exponentially stable and also attains an attenuation performance. The solved conditions for the controllers design are presented in terms of linear programming (LP), and are both quasi-time-dependent and mode-dependent. Two examples are organized to validate the effectiveness of the proposed scheme finally. [ABSTRACT FROM AUTHOR]

A distributed optimization problem (DOP) with affine equality and convex inequality constraints is studied in this article. First, the consensus constraint of the considered DOP is relaxed and a related approximate DOP (ADOP) is presented. It is proved that the optimal solutions of the ADOP (i.e., the near-optimal solutions of the original DOP) are able to approach the optimal solutions of the original DOP. A continuous-time algorithm is proposed for the ADOP and it is demonstrated that the state solution of the presented algorithm converges to the critical point set of the ADOP with general locally Lipschitz continuous objective functions. This means the presented algorithm is efficient for distributed nonconvex optimization problems. Particularly, when the objective functions are convex ones, the state solution of the presented algorithm is further proved to converge to a near-optimal solution of the original DOP. One illustrative example and an application on load sharing problems are shown to validate the effectiveness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

As a newly emerging multivariate statistical process monitoring method, non-negative matrix factorization (NMF) and its variants avoid the positive and negative cancellations between the extracted features because of the purely additive combination of non-negative components. Thus, they make a good match with this reality that the negative values of both observations and decomposed components are physically meaningless in many kinds of industrial processes. However, these methods are effective only for linearly separable problems and are not suitable for dealing with nonlinear process monitoring. In this article, the kernel-based method is integrated into the projective NMF (KPNMF) to improve the accuracy of fault detection, and the appropriate multiplicative update method is proven to be convergent. Furthermore, inspired by the false nearest neighbors (FNNs) method, a new dimensionality reduction approach (KPNMF-FNN) is presented to further reduce the original variables for determining the smallest dimension regression vector needed. Compared with the traditional methods, the proposed approach can greatly reduce the time and storage space required on the premise of maintaining a high fault detection rate and low false alarm rate. The experimental results on the Tennessee Eastman benchmark process and the pumping unit system show that the proposed algorithms have excellent performance and can effectively detect faults under the circumstances of retaining only the top 60% of the original variables. [ABSTRACT FROM AUTHOR]

In this article, the problem of the distributed convex optimization is investigated, where the target is to collectively minimize a sum of local convex functions over an unbalanced directed multiagent network. Each agent in the network possesses only its private local objective function, and the sum of all local objective functions constitutes the global objective function. We particularly consider the scenario, where the underlying interaction network is strongly connected and the relevant weight matrix is row stochastic. To collectively figure out the optimization problem, a distributed accelerated convergence algorithm where agents utilize uncoordinated step-sizes is presented by incorporating consensus of multiagent networks into distributed inexact gradient tracking technique. Most of the existing methods require all agents to possess the out-degree information of their in-neighbors, which is impractical and hardly inevitable as interpreted in this article. By utilizing the small-gain theorem, we prove that if the maximum step-size is positive and sufficiently small (constrained by a specific upper bound), the proposed algorithm, termed as SGT-FROST, converges geometrically to the optimal solution given that the objective functions are smooth and strongly convex. A certain convergence rate is also shown. Simulations confirm the findings in this article. [ABSTRACT FROM AUTHOR]

This article focuses on the research of a general time-varying nonlinear optimization (TVNO) problem solving especially in a noise-disturbance environment. For addressing this problem more efficiently, a new noise-enduring and finite-time convergent design formula is suggested to establish a novel zeroing neural network (NZNN). In contrast to the initial zeroing neural network or the noising-enduring zeroing neural network, which either only achieves finite-time convergence or only suppresses external disturbances, the merit of the proposed NZNN model is able to find an error-free optimal solution in a finite time under various different types of external noises. In addition, the detailed mathematical analyses about finite-time convergence and noise endurance are given to prove the excellent characteristics of the NZNN model. Numerical comparative results are provided to demonstrate the accuracy, efficiency, and advantages of the NZNN model for TVNO under various types of external disturbances. Robotic tracking example further validates the applicability of the NZNN model especially in a noise-disturbance environment. [ABSTRACT FROM AUTHOR]

Non-negative latent factor (NLF) models well represent high-dimensional and sparse (HiDS) matrices filled with non-negative data, which are frequently encountered in industrial applications like recommender systems. However, current NLF models mostly adopt Euclidean distance in their objective function, which represents a special case of a β-divergence function. Hence, it is highly desired to design a β-divergence-based NLF (β-NLF) model that uses a β-divergence function, and investigate its performance in recommender systems as β varies. To do so, we first model β-NLF’s learning objective with a β-divergence function. Subsequently, we deduce a general single latent factor-dependent, non-negative and multiplicative update scheme for β-NLF, and then design an efficient β-NLF algorithm. The experimental results on HiDS matrices from industrial applications indicate that by carefully choosing the value of β, β-NLF outperforms an NLF model with Euclidean distance in terms of accuracy for missing data prediction without increasing computational time. The research outcomes show the necessity of using an optimal β-divergence function in order to achieve the best performance of an NLF model on HiDS matrices. Hence, the proposed model has both theoretical and application significance. [ABSTRACT FROM AUTHOR]