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This paper considers the constrained consensus problem over multi-cluster networks. It is assumed that the agents’ states are constrained by different sets, where each constraint set is privately known by the corresponding agent. Within this framework, a hierarchical projection-based consensus algorithm is presented to solve the considered problem. Technically, the consensus analysis of the proposed algorithm consists of the following three aspects: First, by using the property of the projection operator, the limiting behaviors of the agents’ states generated by the algorithm are investigated. Then, based on the limiting behaviors, it is proven that the agents’ states in the whole network achieve a constrained consensus. Furthermore, by introducing an important auxiliary variable that relates to the agents’ states, the linear convergence of the proposed algorithm is proved. Compared with the existing results, this paper generalizes the constrained consensus methods under single-cluster networks to the multi-cluster ones. Finally, simulations are given to verify the theoretical results. [ABSTRACT FROM AUTHOR]

Many-objective problems refer to the optimization problems containing more than three conflicting objectives. To obtain a representative set of well-distributed non-dominated solutions close to Pareto front in the objective space remains a challenging problem. Many papers have proposed different Multi-Objective Evolutionary Algorithms to solve the lack of the convergence and diversity in many-objective problems. One of the more promising approaches uses a set of reference points to discriminate the solutions and guide the search process. However, this approach was incorporated mainly in Multi-Objective Evolutionary Algorithms, and there are just some few promising adaptations of Particle Swarm Optimization approaches for effectively tackling many-objective problems regarding convergence and diversity. Thus, this paper proposes a practical and efficient Many-Objective Particle Swarm Optimization algorithm for solving many-objective problems. Our proposal uses a set of reference points dynamically determined according to the search process, allowing the algorithm to converge to the Pareto front, but maintaining the diversity of the Pareto front. Our experimental results demonstrate superior or similar performance when compared to other state-of-art algorithms. [ABSTRACT FROM AUTHOR]

Abstract This paper develops a novel algorithm to solve real-world constrained optimization problems, which hybridizes multiobjective optimization techniques with an ϵ-constrained method. First, a constrained optimization problem at hand is transformed into a bi-objective optimization problem. By the transformation, the advantage of multiobjective optimization techniques can be utilized in the constrained optimization area to balance population diversity and convergence. Meanwhile, the ϵ-constrained method is applied, which keeps the population evolving toward feasible region of the constrained optimization problem. In our proposed algorithm, the differential evolution is employed as a search engine to create offspring at each generation. Further, different combinations of mutation operators have been developed to improve the search ability and the population convergence at different stages. The performance of our approach is evaluated on 64 benchmark test functions from three popular test suits. Experimental results demonstrate that our proposed approach is capable of obtaining high-quality solutions on the majority of benchmark test functions, when compared with some other state-of-the-art constrained optimization algorithms. [ABSTRACT FROM AUTHOR]

“ Fuzzy Theoretic Approach to Signals and Systems ” assumes all system variables and parameters as uncertain (i.e. being characterized by membership functions), develops a mathematical theory for analytically determining the membership functions on system variables and parameters, derives algorithms for estimating the parameters of membership functions, and establishes robustness and convergence properties of the estimation algorithms. The membership functions are analytically determined via solving a variational optimization problem that maximizes the “ over-uncertainties-averaged-log-membership ” of the observed data around an initial guess. This paper develops the analytical fuzzy theory for the particular case of a multi-input single-output static system affected by noises. The theory facilitates designing an adaptive filtering algorithm. The robustness of the adaptive filtering algorithm is proved theoretically via a mathematical analysis. Numerical experiments further demonstrate the robustness of the filtering algorithm. A comparison of the algorithm with the state-of-art methods is made using the practical biomedical applications related to the modeling and analysis of heart rate signals for assessing the physiological state of an individual. [ABSTRACT FROM AUTHOR]

Various real-world applications can be formulated as feature selection problems, which have been known to be NP-hard. In this paper, we propose an effective feature selection method based on firefly algorithm (FFA), called return-cost-based binary FFA (Rc-BBFA). The proposed method has the capability of preventing premature convergence and is particularly efficient attributed to the following three aspects. An indicator based on the return-cost is first defined to measure a firefly’s attractiveness from other fireflies. Then, a Pareto dominance-based strategy is presented to seek the attractive one for each firefly. Finally, a binary movement operator based on the return-cost attractiveness and the adaptive jump is developed to update the position of a firefly. The experimental results on a series of public datasets show that the proposed method is competitive in comparison with other feature selection algorithms, including the traditional algorithms, the GA-based algorithm, the PSO-based algorithm, and the FFA-based algorithms. [ABSTRACT FROM AUTHOR]

Dissimilarity measures play a key role in exploring the inherent cluster structure of the data for any partitional clustering algorithm. Commonly used dissimilarity functions for clustering purpose are so far confined to the Euclidean, exponential and Mahalanobish distances. In this article we develop generalized algorithms to solve the partitional clustering problems formulated with a general class of Inner Product Induced Norm (IPIN) based dissimilarity measures. We provide an in-depth mathematical analysis of the underlying optimization framework and analytically address the issue of existence of a solution and its uniqueness. In absence of a closed form solution, we develop a fast stochastic gradient descent algorithm and the Minimization by Incremental Surrogate Optimization (MISO) algorithm (in case of constrained optimization) with exponential convergence rate to obtain the solution. We carry out a convergence analysis of the fuzzy and k -means clustering algorithms with the IPIN based dissimilarity measures and also establish how these algorithms guarantee convergence to a stationary point. In addition, we investigate the nature of the stationary point. Novelty of the paper lies in the introduction of a generalized class of divergence measures, development of fuzzy and k -means clustering algorithms with the general class of divergence measures and a thorough convergence analysis of the developed algorithms. [ABSTRACT FROM AUTHOR]

Structure learning is a very important problem in the field of Bayesian networks (BNs). It is also an active research area for more than 2 decades; therefore, many approaches have been proposed in order to find an optimal structure based on training samples. In this paper, a Particle Swarm Optimization (PSO)-based algorithm is proposed to solve the BN structure learning problem; named BNC-PSO ( B ayesian N etwork C onstruction algorithm using PSO ). Edge inserting/deleting is employed in the algorithm to make the particles have the ability to achieve the optimal solution, while a cycle removing procedure is used to prevent the generation of invalid solutions. Then, the theorem of Markov chain is used to prove the global convergence of our proposed algorithm. Finally, some experiments are designed to evaluate the performance of the proposed PSO-based algorithm. Experimental results indicate that BNC-PSO is worthy of being studied in the field of BNs construction. Meanwhile, it can significantly increase nearly 15% in the scoring metric values, comparing with other optimization-based algorithms. [ABSTRACT FROM AUTHOR]

In this paper, a dynamic mentoring scheme along with a self-regulation scheme have been incorporated in the standard Particle Swarm Optimization (PSO) algorithm to empower the searching particles with human-like characteristics. The algorithm is referred to as a Dynamic Mentoring and Self-Regulation based Particle Swarm Optimization (DMeSR-PSO) algorithm. Based on their experiences, the particles are divided into three groups, viz., the mentor group, the mentee group and the independent learner group where the number of particles in each group is dynamically changing in every iteration. In human learning psychology, mentoring is regarded as a powerful and effective learning process and independent learners are the ones who do not need mentoring and are capable of performing self-regulation of their own knowledge. Therefore, the particles in each of the above three groups have different learning strategies for their velocity updates where the mentors are equipped with a strong self-belief based search, the mentees are taking guidance from the mentors and the independent learners employ self-perception strategy. The DMeSR-PSO algorithm has been extensively evaluated using the simple unimodal and multimodal benchmark functions from CEC2005, more complex shifted and rotated benchmark functions fromCEC2013 and also based on eight real- world problems from CEC2011. The results have been compared with six state-of-the-art PSO variants and five meta-heuristic algorithms for the CEC2005 problems. Further, a comparative analysis on CEC2013 benchmark functions with different PSO variants has also been presented. Finally, DMeSR-PSO's performance on the real-world problems is compared with the top two algorithms from the CEC2011 competition. The results indicate that the proposed learning strategies help DMeSR-PSO to achieve faster convergence and provide better solutions in most of the problems with a 95% confidence level, yielding an effective optimization algorithm for real-world applications. [ABSTRACT FROM AUTHOR]

Abstract: This paper is concerned with a finite-time particle swarm optimization algorithm for odor source localization. First, a continuous-time finite-time particle swarm optimization (FPSO) algorithm is developed based on the continuous-time model of the particle swarm optimization (PSO) algorithm. Since the introduction of a nonlinear damping item, the proposed continuous-time FPSO algorithm can converge over a finite-time interval. Furthermore, in order to enhance its exploration capability, a tuning parameter is introduced into the proposed continuous-time FPSO algorithm. The algorithm’s finite-time convergence is analyzed by using the Lyapunov approach. Second, the discrete-time FPSO algorithm is obtained by using a given dicretization scheme. The corresponding convergence condition is derived by using a linear matrix inequality (LMI) approach. Finally, the features and performance of the proposed FPSO algorithm are illustrated by using two ill-posed functions and twenty-five benchmark functions, respectively. In numerical simulation results, the problem of odor source localization is presented to validate the effectiveness of the proposed FPSO algorithm. [Copyright &y& Elsevier]

Abstract: Recently, Gandomi and Alavi proposed a meta-heuristic optimization algorithm, called Krill Herd (KH). This paper introduces the chaos theory into the KH optimization process with the aim of accelerating its global convergence speed. Various chaotic maps are considered in the proposed chaotic KH (CKH) method to adjust the three main movements of the krill in the optimization process. Several test problems are utilized to evaluate the performance of CKH. The results show that the performance of CKH, with an appropriate chaotic map, is better than or comparable with the KH and other robust optimization approaches. [Copyright &y& Elsevier]