A robust correntropy based subspace tracking algorithm in impulsive noise environments

The maximum correntropy criterion (MCC) demonstrates the inherent robustness to outliers in adaptive filtering. By employing the MCC based cost function in projection approximation subspace tracking (PAST) algorithm, the MCC-PAST algorithm is deduced and utilized for the subspace tracking under impulsive noise environments. To handle the fast varying subspaces circumstances, the variable forgetting factor (VFF) technique is developed and incorporated into the MCC-PAST algorithm. To assess the robustness of the proposed MCC-PAST with VFF algorithm, SαS processes are employed to comprehensively model different scenarios of impulsive noises. The simulation results show the proposed MCC-PAST algorithm with VFF performs better than the other two PAST algorithms developed for subspace tracking in impulsive noise environments, namely, the robust PAST algorithm and the robust Kalman filter based algorithm with variable number of measurements (KFVNM), especially when the noise is extremely impulsive or the GSNR (generalized signal to noise ratio) is relatively low.     

A time-varying Newton algorithm for adaptive subspace tracking

We propose a general framework for tracking the zeros of a time-varying gradient vector field on Riemannian manifolds. Thus, a differential equation, called the time-varying Newton flow, is introduced, whose solutions asymptotically converge to a time-varying family of critical points of the corresponding cost function. A discretization of the differential equation leads to a recursive update scheme for the time-varying critical point.     

On an evolutionary approach for constrained optimization problem solving

Over the last few decades, many different evolutionary algorithms have been introduced for solving constrained optimization problems. However, due to the variability of problem characteristics, no single algorithm performs consistently over a range of problems. In this paper, instead of introducing another such algorithm, we propose an evolutionary framework that utilizes existing knowledge to make logical changes for better performance. The algorithmic aspects considered here are: the way of using search operators, dealing with feasibility, setting parameters, and refining solutions. The combined impact of such modifications is significant as has been shown by solving two sets of test problems: (i) a set of 24 test problems that were used for the CEC2006 constrained optimization competition and (ii) a second set of 36 test instances introduced for the CEC2010 constrained optimization competition. The results demonstrate that the proposed algorithm shows better performance in comparison to the state-of-the-art algorithms.     

A double-multiplicative dynamic penalty approach for constrained evolutionary optimization

The present paper proposes a double-multiplicative penalty strategy for constrained optimization by means of genetic algorithms (GAs). The aim of this research is to provide a simple and efficient way of handling constrained optimization problems in the GA framework without the need for tuning the values of penalty factors for any given optimization problem. After a short review on the most popular and effective exterior penalty formulations, the proposed penalty strategy is presented and tested on five different benchmark problems. The obtained results are compared with the best solutions provided in the literature, showing the effectiveness of the proposed approach.     

Blended biogeography-based optimization for constrained optimization

Biogeography-based optimization (BBO) is a new evolutionary optimization method that is based on the science of biogeography. We propose two extensions to BBO. First, we propose a blended migration operator. Benchmark results show that blended BBO outperforms standard BBO. Second, we employ blended BBO to solve constrained optimization problems. Constraints are handled by modifying the BBO immigration and emigration procedures. The approach that we use does not require any additional tuning parameters beyond those that are required for unconstrained problems. The constrained blended BBO algorithm is compared with solutions based on a stud genetic algorithm (SGA) and standard particle swarm optimization 2007 (SPSO 07). The numerical results demonstrate that constrained blended BBO outperforms SGA and performs similarly to SPSO 07 for constrained single-objective optimization problems.     

Biogeography-based optimization for constrained optimization problems

Biogeography-based optimization (BBO) has been recently proposed as a viable stochastic optimization algorithm and it has so far been successfully applied in a variety of fields, especially for unconstrained optimization problems. The present paper shows how BBO can be applied for constrained optimization problems, where the objective is to find a solution for a given objective function, subject to both inequality and equality constraints.     

A new algorithm inspired in the behavior of the social-spider for constrained optimization

During the past decade, solving constrained optimization problems with swarm algorithms has received considerable attention among researchers and practitioners. In this paper, a novel swarm algorithm called the Social Spider Optimization (SSO-C) is proposed for solving constrained optimization tasks. The SSO-C algorithm is based on the simulation of cooperative behavior of social-spiders. In the proposed algorithm, individuals emulate a group of spiders which interact to each other based on the biological laws of the cooperative colony. The algorithm considers two different search agents (spiders): males and females. Depending on gender, each individual is conducted by a set of different evolutionary operators which mimic different cooperative behaviors that are typically found in the colony. For constraint handling, the proposed algorithm incorporates the combination of two different paradigms in order to direct the search towards feasible regions of the search space. In particular, it has been added: (1) a penalty function which introduces a tendency term into the original objective function to penalize constraint violations in order to solve a constrained problem as an unconstrained one; (2) a feasibility criterion to bias the generation of new individuals toward feasible regions increasing also their probability of getting better solutions. In order to illustrate the proficiency and robustness of the proposed approach, it is compared to other well-known evolutionary methods. Simulation and comparisons based on several well-studied benchmarks functions and real-world engineering problems demonstrate the effectiveness, efficiency and stability of the proposed method.     

An improved electromagnetism-like mechanism algorithm for constrained optimization

Many problems in scientific research and engineering applications can be decomposed into the constrained optimization problems. Most of them are the nonlinear programming problems which are very hard to be solved by the traditional methods. In this paper, an electromagnetism-like mechanism (EM) algorithm, which is a meta-heuristic algorithm, has been improved for these problems. Firstly, some modifications are made for improving the performance of EM algorithm. The process of calculating the total force is simplified and an improved total force formula is adopted to accelerate the searching for optimal solution. In order to improve the accuracy of EM algorithm, a parameter called as move probability is introduced into the move formula where an elitist strategy is also adopted. And then, to handle the constraints, the feasibility and dominance rules are introduced and the corresponding charge formula is used for biasing feasible solutions over infeasible ones. Finally, 13 classical functions, three engineering design problems and 22 benchmark functions in CEC’06 are tested to illustrate the performance of proposed algorithm. Numerical results show that, compared with other versions of EM algorithm and other state-of-art algorithms, the improved EM algorithm has the advantage of higher accuracy and efficiency for constrained optimization problems.     

A simple and efficient real-coded genetic algorithm for constrained optimization

This paper presents a simple and efficient real-coded genetic algorithm (RCGA) for constrained real-parameter optimization. Different from some conventional RCGAs that operate evolutionary operators in a series framework, the proposed RCGA implements three specially designed evolutionary operators, named the ranking selection (RS), direction-based crossover (DBX), and the dynamic random mutation (DRM), to mimic a specific evolutionary process that has a parallel-structured inner loop. A variety of benchmark constrained optimization problems (COPs) are used to evaluate the effectiveness and the applicability of the proposed RCGA. Besides, some existing state-of-the-art optimization algorithms in the same category of the proposed algorithm are considered and utilized as a rigorous base of performance evaluation. Extensive comparison results reveal that the proposed RCGA is superior to most of the comparison algorithms in providing a much faster convergence speed as well as a better solution accuracy, especially for problems subject to stringent equality constraints. Finally, as a specific application, the proposed RCGA is applied to optimize the GaAs film growth of a horizontal metal-organic chemical vapor deposition reactor. Simulation studies have confirmed the superior performance of the proposed RCGA in solving COPs.     

Training and testing a self-adaptive multi-operator evolutionary algorithm for constrained optimization

Over the last two decades, many different evolutionary algorithms (EAs) have been introduced for solving constrained optimization problems (COPs). Due to the variability of the characteristics in different COPs, no single algorithm performs consistently over a range of practical problems. To design and refine an algorithm, numerous trial-and-error runs are often performed in order to choose a suitable search operator and the parameters. However, even by trial-and-error, one may not find an appropriate search operator and parameters. In this paper, we have applied the concept of training and testing with a self-adaptive multi-operator based evolutionary algorithm to find suitable parameters. The training and testing sets are decided based on the mathematical properties of 60 problems from two well-known specialized benchmark test sets. The experimental results provide interesting insights and a new way of choosing parameters.     

An angle based evolutionary algorithm with infeasibility information for constrained many-objective optimization

Recently, angle-based approaches have shown promising for unconstrained many-objective optimization problems (MaOPs), but few of them are extended to solve constrained MaOPs (CMaOPs). Moreover, due to the difficulty in searching for feasible solutions in high-dimensional objective space, the use of infeasible solutions comes to be more important in solving CMaOPs. In this paper, an angle based evolutionary algorithm with infeasibility information is proposed for constrained many-objective optimization, where different kinds of infeasible solutions are utilized in environmental selection and mating selection. To be specific, an angle-based constrained dominance relation is proposed for non-dominated sorting, which gives infeasible solutions with good diversity the same priority to feasible solutions for escaping from the locally feasible regions. As for diversity maintenance, an angle-based density estimation is developed to give the infeasible solutions with good convergence a chance to survive for next generation, which is helpful to get across the large infeasible barrier. In addition, in order to utilize the potential of infeasible solutions in creating high-quality offspring, a modified mating selection is designed by considering the convergence, diversity and feasibility of solutions simultaneously. Experimental results on two constrained many-objective optimization test suites demonstrate the competitiveness of the proposed algorithm in comparison with five existing constrained many-objective evolutionary algorithms for CMaOPs. Moreover, the effectiveness of the proposed algorithm on a real-world problem is showcased.     

A new approach for solving singular systems in topology optimization using Krylov subspace methods

In topology optimization, elements without any contribution to the improvement of the objective function vanish by decrease of density of the design parameter. This easily causes a singular stiffness matrix. To avoid the numerical breakdown caused by this singularity, conventional optimization techniques employ additional procedures. These additional procedures, however, raise some problems. On the other hand, convergence of Krylov subspace methods for singular systems have been studied recently. Through subsequent studies, it has been revealed that the conjugate gradient method (CGM) does not converge to the local optimal solution in some singular systems but in those satisfying certain condition, while the conjugate residual method (CRM) yields converged solutions in any singular systems. In this article, we show that a local optimal solution for topology optimization is obtained by using the CRM and the CGM as a solver of the equilibrium equation in the structural analysis, even if the stiffness matrix becomes singular. Moreover, we prove that the CGM, without any additional procedures, realizes convergence to a local optimal solution in that case. Computer simulation shows that the CGM gives almost the same solutions obtained by the CRM in the case of the two-bar truss problem.     

A novel adaptive V-BLAST algorithm based on subspace tracking and Hermitian matrix perturbation theorem

A novel vertical Bell laboratories layered space-time(V-BLAST)system with adaptive successive interference cancellation(SIC)detector based on subspace tracking(SST)and Hermitian matrix perturbation theorem is proposed in this paper,and the corresponding optimal symbol detection order operation is obtained.Moreover,asymptotic limit theorems for the detectors are established.The final simulation results verify that the symbol error probability(SEP)performance,the immunity to channel estimation errors and the algorithm convergence rate are superior to that of the conventional V-BLAST detection algorithm when channel estimation errors exist.     

An evolutionary algorithm with directed weights for constrained multi-objective optimization

When solving constrained multi-objective optimization problems (CMOPs), keeping infeasible individuals with good objective values and small constraint violations in the population can improve the performance of the algorithms, since they provide the information about the optimal direction towards Pareto front. By taking the constraint violation as an objective, we propose a novel constraint-handling technique based on directed weights to deal with CMOPs. This paper adopts two types of weights, i.e. feasible and infeasible weights distributing on feasible and infeasible regions respectively, to guide the search to the promising region. To utilize the useful information contained in infeasible individuals, this paper uses infeasible weights to maintain a number of well-diversified infeasible individuals. Meanwhile, they are dynamically changed along with the evolution to prefer infeasible individuals with better objective values and smaller constraint violations. Furthermore, 18 test instances and 2 engineering design problems are used to evaluate the effectiveness of the proposed algorithm. Several numerical experiments indicate that the proposed algorithm outperforms four compared algorithms in terms of finding a set of well-distributed non-domination solutions.     

一种子空间辨识的广义预测控制算法

针对广义预测控制(GPC)模型中输入输出数据可能存在噪声和系统先验结构信息未知导致的难于辨识问题,提出了一种子空间辨识的广义预测控制算法。该算法采用变遗忘因子的子空间辨识方法,按照预测优化值与参考输出值的误差构造变遗忘因子,调整采集数据权重,进行在线辨识以提高灵敏度和控制效果。实验结果验证了所提出算法的有效性。