Browsing by Author "Liu, Xiaohui"
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Item Open Access Bi-goal evolution for many-objective optimization problems(Elsevier, 2015-11) Li, M.; Yang, Shengxiang; Liu, XiaohuiThis paper presents a meta-objective optimization approach, called Bi-Goal Evolution (BiGE), to deal with multi-objective optimization problems with many objectives. In multi-objective optimization, it is generally observed that 1) the conflict between the proximity and diversity requirements is aggravated with the increase of the number of objectives and 2) the Pareto dominance loses its effectiveness for a high-dimensional space but works well on a low-dimensional space. Inspired by these two observations, BiGE converts a given multi-objective optimization problem into a bi-goal (objective) optimization problem regarding proximity and diversity, and then handles it using the Pareto dominance relation in this bi-goal domain. Implemented with estimation methods of individuals' performance and the classic Pareto nondominated sorting procedure, BiGE divides individuals into different nondominated layers and attempts to put well-converged and well-distributed individuals into the first few layers. From a series of extensive experiments on four groups of well-defined continuous and combinatorial optimization problems with 5, 10 and 15 objectives, BiGE has been found to be very competitive against five state-of-the-art algorithms in balancing proximity and diversity. The proposed approach is the first step towards a new way of addressing many-objective problems as well as indicating several important issues for future development of this type of algorithms.Item Open Access A constrained optimization approach to dynamic state estimation for power systems including PMU and missing measurements(IEEE, 2015-07-24) Hu, Liang; Wang, Zidong; Liu, Xiaohui; Rahman, I.In this brief, a hybrid filter algorithm is developed to deal with the state estimation (SE) problem for power systems by taking into account the impact from the phasor measurement units (PMUs). Our aim is to include PMU measurements when designing the dynamic state estimators for power systems with traditional measurements. Also, as data dropouts inevitably occur in the transmission channels of traditional measurements from the meters to the control center, the missing measurement phenomenon is also tackled in the state estimator design. In the framework of extended Kalman filter (EKF) algorithm, the PMU measurements are treated as inequality constraints on the states with the aid of the statistical criterion, and then the addressed SE problem becomes a constrained optimization one based on the probability-maximization method. The resulting constrained optimization problem is then solved using the particle swarm optimization algorithm together with the penalty function approach. The proposed algorithm is applied to estimate the states of the power systems with both traditional and PMU measurements in the presence of probabilistic data missing phenomenon. Extensive simulations are carried out on the IEEE 14-bus test system and it is shown that the proposed algorithm gives much improved estimation performances over the traditional EKF method.Item Metadata only Diversity comparison of Pareto front approximations in many-objective optimization(IEEE Press, 2014-04-03) Li, Miqing; Yang, Shengxiang; Liu, XiaohuiDiversity assessment of Pareto front approximations is an important issue in the stochastic multiobjective optimization community. Most of the diversity indicators in the literature were designed to work for any number of objectives of Pareto front approximations in principle, but in practice many of these indicators are infeasible or not workable when the number of objectives is large. In this paper, we propose a diversity comparison indicator (DCI) to assess the diversity of Pareto front approximations in many-objective optimization. DCI evaluates relative quality of different Pareto front approximations rather than provides an absolute measure of distribution for a single approximation. In DCI, all the concerned approximations are put into a grid environment so that there are some hyperboxes containing one or more solutions. The proposed indicator only considers the contribution of different approximations to nonempty hyperboxes. Therefore, the computational cost does not increase exponentially with the number of objectives. In fact, the implementation of DCI is of quadratic time complexity, which is fully independent of the number of divisions used in grid. Systematic experiments are conducted using three groups of artificial Pareto front approximations and seven groups of real Pareto front approximations with different numbers of objectives to verify the effectiveness of DCI. Moreover, a comparison with two diversity indicators used widely in many-objective optimization is made analytically and empirically. Finally, a parametric investigation reveals interesting insights of the division number in grid and also offers some suggested settings to the users with different preferences.Item Open Access Dynamic state estimation of power systems with quantization effects: a recursive filter approach(IEEE, 2015-01-07) Hu, Liang; Wang, Zidong; Liu, XiaohuiIn this paper, a recursive filter algorithm is developed to deal with the state estimation problem for power systems with quantized nonlinear measurements. The measurements from both the remote terminal units and the phasor measurement unit are subject to quantizations described by a logarithmic quantizer. Attention is focused on the design of a recursive filter such that, in the simultaneous presence of nonlinear measurements and quantization effects, an upper bound for the estimation error covariance is guaranteed and subsequently minimized. Instead of using the traditional approximation methods in nonlinear estimation that simply ignore the linearization errors, we treat both the linearization and quantization errors as norm-bounded uncertainties in the algorithm development so as to improve the performance of the estimator. For the power system with such kind of introduced uncertainties, a filter is designed in the framework of robust recursive estimation, and the developed filter algorithm is tested on the IEEE benchmark power system to demonstrate its effectiveness.Item Metadata only ETEA: A Euclidean minimum spanning tree-based evolutionary algorithm for multiobjective optimization(MIT Press, 2014-05) Li, Miqing; Yang, Shengxiang; Zheng, Jinhua; Liu, XiaohuiThe Euclidean minimum spanning tree (EMST), widely used in a variety of domains, is a minimum spanning tree of a set of points in space where the edge weight between each pair of points is their Euclidean distance. Since the generation of an EMST is entirely determined by the Euclidean distance between solutions (points), the properties of EMSTs have a close relation with the distribution and position information of solutions. This paper explores the properties of EMSTs and proposes an EMST-based evolutionary algorithm (ETEA) to solve multi-objective optimization problems (MOPs). Unlike most EMO algorithms that focus on the Pareto dominance relation, the proposed algorithm mainly considers distance-based measures to evaluate and compare individuals during the evolutionary search. Specifically, in ETEA, four strategies are introduced: (1) An EMST-based crowding distance (ETCD) is presented to estimate the density of individuals in the population; (2) A distance comparison approach incorporating ETCD is used to assign the fitness value for individuals; (3) A fitness adjustment technique is designed to avoid the partial overcrowding in environmental selection; (4) Three diversity indicators—the minimum edge, degree, and ETCD—with regard to EMSTs are applied to determine the survival of individuals in archive truncation. From a series of extensive experiments on 32 test instances with different characteristics, ETEA is found to be competitive against five state-of-the-art algorithms and its predecessor in providing a good balance among convergence, uniformity, and spread.Item Open Access Event-Based Input and State Estimation for Linear Discrete Time-Varying Systems(Taylor & Francis, 2017-02-01) Hu, Liang; Wang, Zidong; Han, Quing-long; Liu, XiaohuiIn this paper, the joint input and state estimation problem is considered for linear discrete-time stochastic systems. An event-based transmission scheme is proposed with which the current measurement is released to the estimator only when the difference from the previously transmitted one is greater than a prescribed threshold. The purpose of this paper is to design an event-based recursive input and state estimator such that the estimation error covariances have guaranteed upper bounds at all times. The estimator gains are calculated by solving two constrained optimisation problems and the upper bounds of the estimation error covariances are obtained in form of the solution to Riccati-like difference equations. Special efforts are made on the choices of appropriate scalar parameter sequences in order to reduce the upper bounds. In the special case of linear time-invariant system, sufficient conditions are acquired under which the upper bound of the error covariance of the state estimation is asymptomatically bounded. Numerical simulations are conducted to illustrate the effectiveness of the proposed estimation algorithm.Item Metadata only Evolutionary algorithms with segment-based search for multiobjective optimization problems(IEEE Press, 2013-10-10) Li, Miqing; Yang, Shengxiang; Li, Ke; Liu, XiaohuiThis paper proposes a variation operator, called segment-based search (SBS), to improve the performance of evolutionary algorithms on continuous multiobjective optimization problems. SBS divides the search space into many small segments according to the evolutionary information feedback from the set of current optimal solutions. Two operations, micro-jumping and macro-jumping, are implemented upon these segments in order to guide an efficient information exchange among “good” individuals. Moreover, the running of SBS is adaptive according to the current evolutionary status. SBS is activated only when the population evolves slowly, depending on general genetic operators (e.g., mutation and crossover). A comprehensive set of 36 test problems is employed for experimental verification. The influence of two algorithm settings (i.e., the dimensionality and boundary relaxation strategy) and two probability parameters in SBS (i.e., the SBS rate and micro-jumping proportion) are investigated in detail. Moreover, an empirical comparative study with three representative variation operators is carried out. Experimental results show that the incorporation of SBS into the optimization process can improve the performance of evolutionary algorithms for multiobjective optimization problems.Item Open Access Multi-line distance minimization: A visualized many-objective test problem suite(IEEE, 2017-01-18) Li, Miqing; Grosam, Crina; Yang, Shengxiang; Liu, Xiaohui; Yao, XinStudying the search behavior of evolutionary manyobjective optimization is an important, but challenging issue. Existing studies rely mainly on the use of performance indicators which, however, not only encounter increasing difficulties with the number of objectives, but also fail to provide the visual information of the evolutionary search. In this paper, we propose a class of scalable test problems, called multi-line distance minimization problem (ML-DMP), which are used to visually examine the behavior of many-objective search. Two key characteristics of the ML-DMP problem are: 1) its Pareto optimal solutions lie in a regular polygon in the two-dimensional decision space, and 2) these solutions are similar (in the sense of Euclidean geometry) to their images in the high-dimensional objective space. This allows a straightforward understanding of the distribution of the objective vector set (e.g., its uniformity and coverage over the Pareto front) via observing the solution set in the two-dimensional decision space. Fifteen well-established algorithms have been investigated on three types of 10 ML-DMP problem instances. Weakness has been revealed across classic multi-objective algorithms (such as Pareto-based, decompositionbased and indicator-based algorithms) and even state-of-the-art algorithms designed especially for many-objective optimization. This, together with some interesting observations from the experimental studies, suggests that the proposed ML-DMP may also be used as a benchmark function to challenge the search ability of optimization algorithms.Item Open Access Pareto or Non-Pareto: Bi-Criterion Evolution in Multi-Objective Optimization(IEEE, 2015-12-04) Li, Miqing; Yang, Shengxiang; Liu, XiaohuiIt is known that Pareto dominance has its own weaknesses as the selection criterion in evolutionary multi-objective optimization. Algorithms based on Pareto dominance can suffer from slow convergence to the optimal front, inferior performance on problems with many objectives, etc. Non-Pareto criterion, such as decomposition-based criterion and indicator-based criterion, has already shown promising results in this regard, but its high selection pressure may lead the algorithm to prefer some specific areas of the problem’s true Pareto front, especially when the front is highly irregular. In this paper, we propose a bi-criterion evolution framework of Pareto criterion and non-Pareto criterion, which attempts to make use of their strengths and compensates for each other’s weaknesses. The proposed framework consists of two parts, Pareto criterion evolution and non-Pareto criterion evolution. The two parts work collaboratively, with an abundant exchange of information to facilitate each other’s evolution. Specifically, the non-Pareto criterion evolution leads the Pareto criterion evolution forward and the Pareto criterion evolution compensates the possible diversity loss of the non-Pareto criterion evolution. The proposed framework keeps the freedom on the implementation of the non-Pareto criterion evolution part, thus making it applicable for any non-Pareto-based algorithm. In the Pareto criterion evolution, two operations, population mainte- nance and individual exploration, are presented. The former is to maintain a set of representative nondominated individuals, and the latter is to explore some promising areas which are undeveloped (or not well-developed) in the non-Pareto criterion evolution. Experimental results have shown the effectiveness of the proposed framework. The bi-criterion evolution works well on seven groups of 42 test problems with various characteristics, including those where Pareto-based algorithms or non-Pareto- based algorithms struggle.Item Embargo A Performance Comparison Indicator for Pareto Front Approximations in Many-Objective Optimization(ACM Press, 2015-07) Yang, Shengxiang; Li, Miqing; Liu, XiaohuiIncreasing interest in simultaneously optimizing many objectives (typically more than three objectives) of problems leads to the emergence of various many-objective algorithms in the evolutionary multi-objective optimization field. However, in contrast to the development of algorithm design, how to assess many-objective algorithms has received scant concern. Many performance indicators are designed in principle for any number of objectives, but in practice are invalid or infeasible to be used in many-objective optimization. In this paper, we explain the di culties that popular performance indicators face and propose a performance comparison indicator (PCI) to assess Pareto front approximations obtained by many-objective algorithms. PCI evaluates the quality of approximation sets with the aid of a reference set constructed by themselves. The points in the reference set are divided into many clusters, and the proposed indicator estimates the minimum moves of solutions in the approximation sets to weakly dominate these clusters. PCI has been verified both by an analytic comparison with several well-known indicators and by an empirical test on four groups of Pareto front approximations with different numbers of objectives and problem characteristics.Item Open Access Recent Advances on State Estimation for Power Grids with Unconventional Measurements(IET, 2017-12) Hu, Liang; Wang, Zidong; Liu, Xiaohui; Vasilakos, A. V.; Alsaadi, F. E.State estimation problem for power systems has long been a fundamental issue that demands a variety of methodologies depending on the system settings. With the recent introduction of advanced devices of phasor measurement units (PMUs) and dedicated communication networks, the infrastructure of power grids has been greatly improved. Coupled with the infrastructure improvements are three emerging issues for the state estimation problems, namely, the coexistence of both traditional and PMU measurements, the incomplete information resulting from delayed, asynchronous and missing measurements due to communication constraints, and the cyber-attacks on the communication channels. In this study, the authors aim to survey some recent advances on the state estimation methods which tackle the above three issues in power grids. Traditional state estimation methods applied in power grids are first introduced. Latest results on state estimation with mixed measurements and incomplete measurements are then discussed in great detail. In addition, the techniques developed to ensure the cyber-security of the state estimation schemes for power grids are highlighted. Finally, some concluding remarks are given and some possible future research directions are pointed out.Item Metadata only Shift-based density estimation for Pareto-based algorithms in many-objective optimization(IEEE Press, 2013-05-16) Li, Miqing; Yang, Shengxiang; Liu, XiaohuiIt is commonly accepted that Pareto-based evolutionary multiobjective optimization (EMO) algorithms encounter difficulties in dealing with many-objective problems. In these algorithms, the ineffectiveness of the Pareto dominance relation for a high-dimensional space leads diversity maintenance mechanisms to play the leading role during the evolutionary process, while the preference of diversity maintenance mechanisms for individuals in sparse regions results in the final solutions distributed widely over the objective space but distant from the desired Pareto front. Intuitively, there are two ways to address this problem: 1) modifying the Pareto dominance relation and 2) modifying the diversity maintenance mechanism in the algorithm. In this paper, we focus on the latter and propose a shift-based density estimation (SDE) strategy. The aim of our study is to develop a general modification of density estimation in order to make Pareto-based algorithms suitable for many-objective optimization. In contrast to traditional density estimation which only involves the distribution of individuals in the population, SDE covers both the distribution and convergence information of individuals. The application of SDE in three popular Pareto-based algorithms demonstrates its usefulness in handling many-objective problems. Moreover, an extensive comparison with five state-of-the-art EMO algorithms reveals its competitiveness in balancing convergence and diversity of solutions. These findings not only show that SDE is a good alternative to tackle many-objective problems, but also present a general extension of Pareto-based algorithms in many-objective optimization.Item Open Access State estimation under false data injection attacks: Security analysis and system protection(Elsevier, 2017-10-23) Hu, Liang; Wang, Zidong; Han, Quing-Long; Liu, XiaohuiThe security issue in the state estimation problem is investigated for a networked control system (NCS). The communication channels between the sensors and the remote estimator in the NCS are vulnerable to attacks from malicious adversaries. The false data injection attacks are considered. The aim of this paper to find the so-called insecurity conditions under which the estimation system is insecure in the sense that there exist malicious attacks that can bypass the anomaly detector but still lead to unbounded estimation errors. In particular, a new necessary and sufficient condition for the insecurity is derived in the case that all communication channels are compromised by the adversary. Moreover, a specific algorithm is proposed for generating attacks with which the estimation system is insecure. Furthermore, for the insecure system, a system protection scheme through which only a few (rather than all) communication channels require protection against false data injection attacks is proposed. A simulation example is utilized to demonstrate the effectiveness of the proposed conditions/algorithms in the secure estimation problem for a flight vehicle.Item Open Access A test problem for visual investigation of high-dimensional multi-objective search(IEEE Press, 2014-09-22) Li, Miqing; Yang, Shengxiang; Liu, XiaohuiAn inherent problem in multiobjective optimization is that the visual observation of solution vectors with four or more objectives is infeasible, which brings major difficulties for algorithmic design, examination, and development. This paper presents a test problem, called the Rectangle problem, to aid the visual investigation of high-dimensional multiobjective search. Key features of the Rectangle problem are that the Pareto optimal solutions 1) lie in a rectangle in the two-variable decision space and 2) are similar (in the sense of Euclidean geometry) to their images in the four-dimensional objective space. In this case, it is easy to examine the behavior of objective vectors in terms of both convergence and diversity, by observing their proximity to the optimal rectangle and their distribution in the rectangle, respectively, in the decision space. Fifteen algorithms are investigated. Underperformance of Pareto-based algorithms as well as most state-of-the-art many-objective algorithms indicates that the proposed problem not only is a good tool to help visually understand the behavior of multiobjective search in a high-dimensional objective space but also can be used as a challenging benchmark function to test algorithms' ability in balancing the convergence and diversity of solutions.