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This paper is concerned with the problem of distributed Nash equilibrium computation in aggregative games. Note that the traditional computation algorithms are designed based on time-scheduled communication strategy, which may lead to high communication consumption of the whole network. To reduce the consumption, this paper proposes a novel distributed algorithm with an event-triggered mechanism, where the communication between any two agents is only carried out when an edge-based event condition is triggered. In the convergence analysis of the proposed algorithm, an important event-related error variable is firstly defined. Then, based on a zero-sum property of this event-related error, two key relations on the agents' estimates in the proposed algorithm are provided. Further, by using these relations, it is proven that the agents' estimates can achieve a Nash equilibrium under a proper event-triggering condition. Finally, examples on the demand response of power systems are presented to verify the theoretical findings. [ABSTRACT FROM AUTHOR]

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]

This paper presents a novel Differential Evolution algorithm for protein folding optimization that is applied to a three-dimensional AB off-lattice model. The proposed algorithm includes two new mechanisms. A local search is used to improve convergence speed and to reduce the runtime complexity of the energy calculation. For this purpose, a local movement is introduced within the local search. The designed evolutionary algorithm has fast convergence speed and, therefore, when it is trapped into the local optimum or a relatively good solution is located, it is hard to locate a better similar solution. The similar solution is different from the good solution in only a few components. A component reinitialization method is designed to mitigate this problem. Both the new mechanisms and the proposed algorithm were analyzed on well-known amino acid sequences that are used frequently in the literature. Experimental results show that the employed new mechanisms improve the efficiency of our algorithm and that the proposed algorithm is superior to other state-of-the-art algorithms. It obtained a hit ratio of 100% for sequences up to 18 monomers, within a budget of 10 11 solution evaluations. New best-known solutions were obtained for most of the sequences. The existence of the symmetric best-known solutions is also demonstrated in the paper. [ABSTRACT FROM AUTHOR]

The performance of differential evolution (DE) has been significantly influenced by trial vector generation strategies and control parameters. Various powerful trial vector generation strategies with adaptive parameter adjustment methods such that the population generation is guided by the elites have been proposed. This paper aims to strengthen the performance of DE by compositing these powerful trial vector generation strategies, making it possible to obtain the guidance of each individual from multiple elites concurrently and independently. In this manner, the deleterious behavior in which an individual is misguided by various local optimal solutions into unpromising areas could be restrained to a certain extent. An adaptive multiple-elites-guided composite differential evolution algorithm with a shift mechanism (abbreviated as AMECoDEs) has been proposed in this paper. This algorithm concurrently employs two elites-guided trial vector generation strategies for each individual to generate two candidate solutions accordingly, and the best one is adopted to participate in the selection. Moreover, a novel shift mechanism is established to handle stagnation and premature convergence issues. AMECoDEs has been tested on the CEC2014 benchmark functions. Experimental results show that AMECoDEs outperforms various classic state-of-the-art DE variants and is better than or at least comparable to various recently proposed DE methods. [ABSTRACT FROM AUTHOR]

This paper studies a class of distributed optimization algorithms by a set of agents, where each agent only has access to its own local convex objective function, and the goal of the agents is to jointly minimize the sum of all the local functions. The communications among agents are described by a sequence of time-varying directed graphs which are assumed to be uniformly strongly connected. A column stochastic mixing matrices is employed in the algorithm which exactly steers all the agents to asymptotically converge to a global and consensual optimal solution even under the assumption that the step-sizes are uncoordinated. Two fairly standard conditions for achieving the geometrical convergence rate are established under the assumption that the objective functions are strong convexity and have Lipschitz continuous gradient. The theoretical analysis shows that the distributed algorithm is capable of driving the whole network to geometrically converge to an optimal solution of the convex optimization problem as long as the uncoordinated step-sizes do not exceed some upper bound. We also give an explicit analysis for the convergence rate of our algorithm through a different approach. Finally, simulation results illustrate the feasibility of the proposed algorithm and the effectiveness of the theoretical analysis throughout this paper. [ABSTRACT FROM AUTHOR]

This paper develops a particle swarm optimisation (PSO) based framework for multi-objective optimisation (MOO). As a part of development, a new PSO method, named self-adaptive PSO (SAPSO), is first proposed. Since the convergence of SAPSO determines the quality of the obtained Pareto front, this paper analytically investigates the convergence of SAPSO and provides a parameter selection principle that guarantees the convergence. Leveraging the proposed SAPSO, this paper then designs a SAPSO-based MOO framework, named SAMOPSO. To gain a well-distributed Pareto front, we also design an external repository that keeps the non-dominated solutions. Next, a circular sorting method, which is integrated with the elitist-preserving approach, is designed to update the external repository in the developed MOO framework. The performance of the SAMOPSO framework is validated through 12 benchmark test functions and a real-word MOO problem. For rigorous validation, the performance of the proposed framework is compared with those of four well-known MOO algorithms. The simulation results confirm that the proposed SAMOPSO outperforms its contenders with respect to the quality of the Pareto front over the majority of the studied cases. The non-parametric comparison results reveal that the proposed method is significantly better than the four algorithms compared at the confidence level of 90% over the 12 test functions. [ABSTRACT FROM AUTHOR]

Particle swarm optimizations (PSOs) are drawing extensive attention from both research and engineering fields due to their simplicity and powerful global search ability. However, there are two issues needing to be improved: one is that the classical PSO converges slowly; the other is that classical PSO tends to result in premature convergence, especially for multi-modal problems. This paper attempts to address these two issues. Firstly, to improve the convergent efficiency, this paper proposes an asymptotic predicting model of the globally-optimal solution, which is used to predict the global optimum based on extracting the features reflecting the evolutionary trend. The predicted global optimum is then taken as the third exemplar, in a way similar to the individual historical best solution and the swarm historical best solution in guiding the evolutionary process of other particles. To reduce the probability that the population is trapped into a local optimum due to the premature phenomenon, this paper proposes an adaptive mutation strategy, which is used to help the trapped particles to escape away from the local optimum by using the extended non-uniform mutation operator. Finally, we combine the two entities to develop a globally-optimal prediction-based adaptive mutation particle swarm optimization (GPAM-PSO). In numerical experimental parts, we compare the proposed GPAM-PSO with 11 existing PSO variants by using 22 benchmark problems of 30-dimensions and 100-dimensions, respectively. Numerical experiments demonstrate that the proposed GPAM-PSO could improve the accuracy and efficiency remarkably, which means that the combination of the globally-optimal prediction-based search and the adaptive mutation strategy could accelerate the convergence and reduce premature phenomenon effectively. Generally speaking, GPAM-PSO performs most efficiently and robustly. Moreover, the performance on an engineering problem demonstrates the practical application of the proposed GPAM-PSO algorithm. [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]

This paper puts forward a comprehensive study of the design of global stopping criteria for multi-objective optimization. In this study we propose a global stopping criterion, which is terms as MGBM after the authors surnames. MGBM combines a novel progress indicator, called mutual domination rate (MDR) indicator, with a simplified Kalman filter, which is used for evidence-gathering purposes. The MDR indicator, which is also introduced, is a special-purpose progress indicator designed for the purpose of stopping a multi-objective optimization. As part of the paper we describe the criterion from a theoretical perspective and examine its performance on a number of test problems. We also compare this method with similar approaches to the issue. The results of these experiments suggest that MGBM is a valid and accurate approach. [ABSTRACT FROM AUTHOR]

The main objective of this paper is to propose an effective evolutionary method for solving the problem of working paths optimization in survivable MPLS network. The paper focuses on existing network, in which only network flow can be optimized to provide network survivability using the local repair strategy. The problem is NP-complete, the solution space of the test cases is large and many genes are required to code the potential solution. Recently, the MuPPetS method (Multi-Population Pattern Searching Algorithm for Flow Assignment) was proposed and seems to be a promising tool for tackling high-dimensional, hard optimization problems. The MuPPetS is a linkage learning method that minimizes the negative effects of typical EA bottlenecks, e.g., preconvergence and significant effectiveness dropdown caused by an increasing number of genes in the chromosome. In comparison to other evolutionary methods, the MuPPetS was shown to be effective and capable of solving GA-hard problems. Therefore, the proposed MuPPetS-FuN method (Multi-Population Pattern Searching Algorithm for Flow Assignment in Non-bifurcated Commodity Flow) is based on MuPPetS. The additional objective of this paper is to propose changes to general MuPPetS framework to increase its effectiveness via better subpopulation number control strategy. [ABSTRACT FROM AUTHOR]

This paper proposes an enhanced Particle Swarm Optimisation (PSO) algorithm and examines its performance. In the proposed PSO approach, PSO is combined with Evolutionary Game Theory to improve convergence. One of the main challenges of such stochastic optimisation algorithms is the difficulty in the theoretical analysis of the convergence and performance. Therefore, this paper analytically investigates the convergence and performance of the proposed PSO algorithm. The analysis results show that convergence speed of the proposed PSO is superior to that of the Standard PSO approach. This paper also develops another algorithm combining the proposed PSO with the Standard PSO algorithm to mitigate the potential premature convergence issue in the proposed PSO algorithm. The combined approach consists of two types of particles, one follows Standard PSO and the other follows the proposed PSO. This enables exploitation of both diversification of the particles’ exploration and adaptation of the search direction. [ABSTRACT FROM AUTHOR]

This paper proposes using the opposition-based learning (OBL) strategy in the shuffled frog leaping (SFL). The SFL divides a population into several memeplexes and then improves each memeplex in an evolutionary process. The OBL by comparing the fitness of an individual to its opposite and retaining the fitter one in the population accelerates search process. The objective of this paper is to introduce new versions of the SFL which employ on one hand the OBL to accelerate the SFL without making premature convergence and on the other hand use the OBL strategy to diversify search moves of SFL. Four versions of SFL algorithm are proposed by incorporating the OBL and the SFL. All algorithms similarly use the opposition-based population initialization to achieve fitter initial individuals and their difference is in applying opposition-based generation jumping. Experiments are performed on parameter identification problems. The obtained results demonstrate that incorporating the opposition-based strategy and SFL performed in a proper way is a good idea to enhance performance of SFL. Two versions of opposition-based SFL outperform their pure competitor i.e., SFL in terms of all aspects on all problems but two other versions of SFL obtained a worse performance than the pure SFL. Also some performance comparisons of the proposed algorithms with some other algorithms reported in the literature confirm a significantly better performance of our proposed algorithms. Also in final part of the comparison study, a comparison of the proposed algorithm in this study in respect to other algorithms on CEC05 functions demonstrates a completely comparable performance of proposed algorithm. [ABSTRACT FROM AUTHOR]

When optimizing many-objective problems (MaOP), the same strategy might behave differently when facing problems with different features. Therefore, obtaining problem features helps to obtain high-quality solutions. However, in practice, the problem features are unknown during the optimization process. In this case, learning to adjust strategies to match the problem features is a challenging work. In this paper, a learning-based algorithm is proposed, aimed to enhance the generalization ability. On the basis of a decomposition-based many-objective optimization framework, a learning automaton (LA) is included in the algorithm. The LA adjusts the evolutionary strategies of the algorithm to adapt to the problem characteristics, according to the feedback information during the optimizing procedure. An external archive is employed to store the Pareto non-dominant solutions. Based on the external archive, a reference vector adjustment strategy is designed to enhance the capability of solving problems with a degenerate or discrete Pareto front (PF). To validate the performance of the proposed algorithm, a comparison experiment is conducted on a novel authority test suite. Five state-of-the-art algorithms are selected as peer algorithms. The results of the experiment indicate that the proposed algorithm obtains satisfactory performance in determining the convergence and the approximation of the PF. [ABSTRACT FROM AUTHOR]

In this paper, the universal adaptive control problem for a class of uncertain nonlinear systems is solved by the output feedback control approach. Firstly, a homogenous high-gain observer is proposed to estimate the system states based on the homogenous theory. Then, by using adding one power integrator method, a homogeneous controller is designed. It can be shown that all signals of the whole system are bounded and at the same time the system states globally asymptotically converge to the origin. In the end, we extend the proposed method to a class of upper-triangular nonlinear systems. Two examples are provided to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, (1) a new fuzzy model is presented to simulate two different chaotic systems with different numbers of nonlinear terms and (2) a new adaptive approach and a new control Lyapunov function are proposed to synchronize these two different fuzzy chaotic systems and speed up the convergence of errors. By using this new model, the numbers of fuzzy rules of chaotic systems can be reduced from to and only 2 subsystems are needed, where N is the number of nonlinear terms. The fuzzy systems become much simpler. In addition, through the new fuzzy model, the new fuzzy systems are much simpler than T–S fuzzy systems (when nonlinear systems are complicated) and can be used to any other kind of application in fuzzy logic control or fuzzy modeling. Mathieu–Van der Pol system (which is called M–V system in this paper) and Quantum cellular neural networks nanosystem (which is called Q-CNN system in this paper) are used for illustrations in numerical simulation results to show the effectiveness and feasibility of our new adaptive approach and new control Lyapunov function. The T–S fuzzy modeling and traditional adaptive control are also given in Appendices B and C for comparison. [Copyright &y& Elsevier]

Abstract: This paper proposes a neural network approach for efficiently solving general nonlinear convex programs with second-order cone constraints. The proposed neural network model was developed based on a smoothed natural residual merit function involving an unconstrained minimization reformulation of the complementarity problem. We study the existence and convergence of the trajectory of the neural network. Moreover, we show some stability properties for the considered neural network, such as the Lyapunov stability, asymptotic stability, and exponential stability. The examples in this paper provide a further demonstration of the effectiveness of the proposed neural network. This paper can be viewed as a follow-up version of [20,26] because more stability results are obtained. [Copyright &y& Elsevier]

Abstract: Most real world multi-objective problems (MOPs) have a complicated solution space. Facing such problems, a direction vectors based co-evolutionary multi-objective optimization algorithm (DVCMOA) that introduces the decomposition idea from MOEA/D to co-evolutionary algorithms is proposed in this paper. It is novel in the sense that DVCMOA applies the concept of direction vectors to co-evolutionary algorithms. DVCMOA first divides the entire population into several subpopulations on the basis of the initial direction vectors in the objective space. Then, it solves MOPs through the co-evolutionary interaction among the subpopulations in which individuals are classified according to their direction vectors. Finally, it explores the less developed regions to maintain the relatively uniform distribution of the solution space. In this way, DVCMOA has advantages in convergence, diversity and uniform distribution of the non-dominated solution set, which are explained through comparison with other state-of-the-art multi-objective optimization evolutionary algorithms (MOEAs) in this paper. DVCMOA is shown to be effective on 6 multi-objective 0–1 knapsack problems. [Copyright &y& Elsevier]

Abstract: To overcome the main drawbacks of (μ + λ)-constrained differential evolution ((μ + λ)-CDE) [45], this paper proposes an improved version of (μ + λ)-CDE, named ICDE, to solve constrained optimization problems (COPs). ICDE mainly consists of an improved (μ + λ)-differential evolution (IDE) and a novel archiving-based adaptive tradeoff model (ArATM). Therein, IDE employs several mutation strategies and the binomial crossover of differential evolution (DE) to generate the offspring population. Moreover, a new mutation strategy named “current-to-rand/best/1” is proposed by making use of the current generation number in IDE. Since the population may undergo three situations during the evolution (i.e., the infeasible situation, the semi-feasible situation, and the feasible situation), like (μ + λ)-CDE, ArATM designs one constraint-handling mechanism for each situation. However, unlike (μ + λ)-CDE, in the constraint-handling mechanism of the infeasible situation, the hierarchical nondominated individual selection scheme is utilized, and an individual archiving technique is proposed to maintain the diversity of the population. Furthermore, in the constraint-handling mechanism of the semi-infeasible situation, the feasibility proportion of the combined population consisting of the parent population and the offspring population is used to convert the objective function of each individual. It is noteworthy that ICDE adopts a fixed tolerance value for the equality constraints. In addition, in this paper two criteria are used to compute the degree of constraint violation of each individual in the population, according to the difference among the violations of different constraints. By combining IDE with ArATM, ICDE has the capability to maintain a good balance between the diversity and the convergence of the population during the evolution. The performance of ICDE has been tested on 24 well-known benchmark test functions collected for the special session on constrained real-parameter optimization of the 2006 IEEE Congress on Evolutionary Computation (IEEE CEC2006). The experimental results demonstrate that ICDE not only overcomes the main drawbacks of (μ + λ)-CDE but also obtains very competitive performance compared with other state-of-the-art methods for constrained optimization in the community of constrained evolutionary optimization. [Copyright &y& Elsevier]

Abstract: The research on optimal design of infinite-impulse response (IIR) filters based on optimization techniques has gained much attention in recent years. However, due to the limited performance of the applied optimization techniques, the orders of the filters, which can be obtained, are very low in the previous research. Memetic algorithms (MAs) are widely recognized to have better convergence capability than their conventional counterparts. However, the universality of the MAs, e.g. the ability of solving diverse kinds of digital IIR filter designs, is still limited. In this paper, we design a Two-Stage ensemble Memetic Algorithm (TSMA) framework to more appropriately synthesize the strengths of the evolutionary global search and local search techniques. In the first optimization stage, a competition is held among the candidate local search techniques. Its major idea is to choose the best local search technique and to obtain good initial state. Inheriting the good information of the first stage, the second optimization stage is to implement effective adaptive MA to pursue high-quality solution. The experimental studies presented in this paper contain three aspects: (1) the benefits of the TSMA framework are experimentally investigated by comparing TSMA with its sub-optimizers and recent effective evolutionary algorithms (EAs) on 26 test functions; then (2) TSMA is compared with 4 MAs on the CEC05 functions to comprehensively show the advantages of TSMA; and (3) the TSMA and 6 state-of-the-art algorithms are applied to design high-order digital infinite-impulse response (IIR) filters. The experimental results definitely demonstrate the excellent effectiveness, efficiency and reliability of TSMA on both function optimization and digital IIR filter design tasks. [Copyright &y& Elsevier]

Penalty boundary intersection (PBI) is one popular method in decomposition based evolutionary multi-objective algorithms, where the penalty factor is crucial for striking a balance between convergence and diversity in a high-dimensional objective space. Meanwhile, the distribution of the obtained solutions highly depends on the setting of the weight vectors. This paper proposes an adaptive decomposition-based evolutionary algorithm for many-objective optimization, which introduces one adaptation mechanism for PBI-based decomposition and the other for adjusting the weight vector. The former assigns a specific penalty factor for each subproblem by using the distribution information of both population and the weight vectors, while the latter adjusts the weight vectors based on the objective ranges to handle problems with different scales on the objectives. We have compared the proposed algorithm with seven state-of-the-art many-objective evolutionary algorithms on a number of benchmark problems. The empirical results demonstrate the superiority of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Highlights • We study the consensus formation and convergence speed in the SNDG model. • We show the rule to determine agents' weights to form a consensus. • We show the rule to determine the convergence speed when reaching a consensus. Abstract In this paper, we investigate how the agent's self-confidence level and the node degree influence the consensus opinion formation and the consensus convergence speed in the social network DeGroot model. We find that (1) the higher self-confidence will increase the agent's importance degree to determine the consensus opinion, but will also slow down the convergence speed for all agents to be able to obtain consensus, and (2) it is conducive to accelerating the convergence speed to be able to reach a consensus where all agents can manage to balance self-confidence levels and node degrees in the social network. [ABSTRACT FROM AUTHOR]

Abstract In this paper, we present a new insight into the simultaneous policy update algorithm (SPUA) for solving H ∞ control problems. From the perspective of practicability, a checkable criterion is presented for the initialization of SPUAs such that the initial guess can be chosen with clear rules and lie within a local domain of convergence. To further get a better convergence property, a novel initialization is developed such that the starting matrix does not need to lie in a neighborhood of the solution of H ∞ control problems in some cases and its convergence is established rigorously by mathematical induction principle. Subsequently, an improved SPUA is proposed, and its model-free variant based on reinforcement learning (RL) is also able to learn the solution online without any system dynamics. Finally, numerical results illustrate the effectiveness of the proposed methods. [ABSTRACT FROM AUTHOR]

Abstract This paper studies the decentralized tracking control problem for a class of interconnected stochastic nonlinear systems defined on a directed graph, where the interconnections are allowed to include the states of each subsystems. The main contributions are that a new strictly decentralized control method is proposed to acquire the desired tracking performance, and a modified compensation mechanism is presented to address the state-dependent interconnections. Furthermore, by using quartic Lyapunov functions and graph theory, it is proved that the signals of the resulting closed-loop system are globally bounded in probability, and the tracking errors converge to a compact set, whose radius can be adjusted by choosing different controller design parameters. Finally, two examples are used to illustrate the effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract: Let X denote a locally compact metric space and φ : X → X be a continuous map. In the 1970s Zadeh presented an extension principle helping us to fuzzify the dynamical system (X, φ), i.e., to obtain a map Φ for the space of fuzzy sets on X. We extend an idea mentioned in [P. Diamond, A. Pokrovskii, Chaos, entropy and a generalized extension principle, Fuzzy Sets Syst. 61 (1994) 277–283] to generalize Zadeh’s original extension principle. In this paper we study basic properties of so-called g-fuzzifications, such as their continuity properties. We also show that, for any g-fuzzification: (i) a uniformly convergent sequence of uniformly continuous maps on X induces a uniformly convergent sequence of fuzzifications on the space of fuzzy sets and (ii) a conjugacy (resp., a semi-conjugacy) between two discrete dynamical systems can be extended to a conjugacy (resp., a semi-conjugacy) between fuzzified dynamical systems. Throughout this paper we consider different topological structures in the space of fuzzy sets, namely, the sendograph, endograph and levelwise topologies. [Copyright &y& Elsevier]

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]

Abstract: Motivated by the recent success of diverse approaches based on differential evolution (DE) to solve constrained numerical optimization problems, in this paper, the performance of this novel evolutionary algorithm is evaluated. Three experiments are designed to study the behavior of different DE variants on a set of benchmark problems by using different performance measures proposed in the specialized literature. The first experiment analyzes the behavior of four DE variants in 24 test functions considering dimensionality and the type of constraints of the problem. The second experiment presents a more in-depth analysis on two DE variants by varying two parameters (the scale factor F and the population size NP), which control the convergence of the algorithm. From the results obtained, a simple but competitive combination of two DE variants is proposed and compared against state-of-the-art DE-based algorithms for constrained optimization in the third experiment. The study in this paper shows (1) important information about the behavior of DE in constrained search spaces and (2) the role of this knowledge in the correct combination of variants, based on their capabilities, to generate simple but competitive approaches. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents an information theory that is based on meanings and relationships between information. It first introduces the foundation of our approach, a binary relation contain between two pieces of information, based on inference between the two pieces of information. Then, based on the contain relation, it introduces two basic operations union and intersection on a collection (i.e., set) of information. This paper lays the foundation of our approach by introducing the core concept, informalogical space. An informalogical space is a collection of information that satisfies certain conditions represented in terms of the contain relation, and the union and intersection operations. An informalogical space is similar to a topological space in a symbolic sense, but is different in nature. This paper also introduces an information net in an informalogical space. An information net is a generalization of information sequence, just as a net is a generalization of sequence in general topology. This paper builds a convergence theory for information nets that is similar in a symbolic sense to the Moore–Smith convergence theory in general topology. Then, this paper applies the results for information nets to information sequences. [Copyright &y& Elsevier]

Abstract: Fuzzy matrices have been proposed to represent fuzzy relations on finite universes. Since Thomason’s paper in 1977 showing that powers of a max–min fuzzy matrix either converge or oscillate with a finite period, conditions for limiting behavior of powers of a fuzzy matrix have been studied. It turns out that the limiting behavior depends on the algebraic operations employed, which usually in the literature includes max–min/max-product/max-Archimedean t-norm/max t-norm/max-arithmetic mean operations, respectively. In this paper, we consider the powers of a fuzzy matrix with convex combination of max–min and max-arithmetic mean operations. We show that the powers of such a fuzzy matrix are always convergent. [Copyright &y& Elsevier]

Abstract: Optimization in dynamic environments is important in real-world applications, which requires the optimization algorithms to be able to find and track the changing optimum efficiently over time. Among various algorithms for dynamic optimization, particle swarm optimization algorithms (PSOs) are attracting more and more attentions in recent years, due to their ability of keeping good balance between convergence and diversity maintenance. To tackle the challenges of dynamic optimization, several strategies have been proposed to enhance the performance of PSO, and have gained success on various dynamic optimization problems. But there still exist some issues in dynamic optimization which need to be studied carefully, i.e. the robustness of the algorithm to problems of various dynamic features. In this paper, a new multi-strategy ensemble particle swarm optimization (MEPSO) for dynamic optimization is proposed. In MEPSO, all particles are divided into two parts, denoted as part I and part II, respectively. Two new strategies, Gaussian local search and differential mutation, are introduced into these two parts, respectively. Experimental analyses reveal that the mechanisms used in part I can enhance the convergence ability of the algorithm, while mechanisms used in part II can extend the searching area of the particle population to avoid being trapped into the local optimum, and can enhance the ability of catching up with the changing optimum in dynamic environments. The whole algorithm has few parameters that need to be tuned, and all of them are not sensitive to problems. We compared MEPSO with other PSOs, including MQSO, PHPSO and Standard PSO with re-initialization, on moving peaks Benchmark and dynamic Rastrigin function. The experimental results show that MEPSO has pretty good performance on almost all testing problems adopted in this paper, and outperforms other algorithms when the dynamic environment is unimodal and changes severely, or has a great number of local optima as dynamic Rastrigin function does. [Copyright &y& Elsevier]

Many interactive image segmentation methods design energy functions based on the local relationship of neighboring pixels, which is insufficient at capturing the abundant information of an image, and these methods are susceptible to many problems, such as sensitivity to seeds and under-segmentation of boundaries. To solve these problems, this paper explores utilizing the global relationship for interactive image segmentation. To effectively obtain the global information of the image, we first propose a robust affinity diffusion (RAD) method to propagate the local affinity graph. Compared with the existing diffusion-based approaches, the advantage of RAD is that it can converge to an effective limit value, which makes the diffusion process more computationally efficient and easier to control. The segmentation model is then constructed based on this convergent global graph. To efficiently utilize the global information, the energy function is designed by the multiplication of the global affinity matrix and a prior probability vector. The use of global information can significantly improve the segmentation performance. Experiments on challenging data sets demonstrate that RAD can obtain better results than state-of-the-art methods. [ABSTRACT FROM AUTHOR]

In this paper, we develop a quick and effective position control strategy based on the differential evolution (DE) algorithm for a planar three-link passive-active-active (PAA) underactuated system with first-order nonholonomic constraint. Due to the existence of the constraint, when the angular velocities of the two active links are proportional, the planar PAA system is transformed from a first-order nonholonomic system to a holonomic system like an Acrobot. Making full use of the angular constraint of the like-Acrobot, we employ the DE algorithm to calculate the target angles of all links and the target ratio between the angular velocities of the two active links. After that, one continuous controller for one active link is designed to ensure the target ratio in the whole control process; meantime, the other continuous controller for the other active link is designed to make its angle asymptotically converge to the corresponding target value. In this way, the angles of all links can asymptotically converge to the corresponding target values according to the angular constraint, and thus the position control of the system is realized using the continuous control method. Finally, the simulation results demonstrate the quickness and effectiveness of our proposed control method. [ABSTRACT FROM AUTHOR]

In this paper, a new multi-objective optimization algorithm in a multi-scale framework with faster convergence characteristics is presented, referred to as the Pareto-Aware DIviding RECTangles ( PA-DIRECT ) method. PA-DIRECT follows the Multi-scale Search Optimization (MSO) framework and considers Pareto-optimality of the sampled points in the objective space during its search. The importance of Pareto awareness is highlighted in PA-DIRECT through the use of two selection strategies for Potentially Optimal Hyper-rectangles (POHs), on the (a) approximate Pareto front and (b) dominated fronts. With the aim of performing sampling conservatively, both strategies are embedded with the concept of diversification through the use of a modified Hypervolume measure that accounts for diversity in (a) and the number of dominating points in (b). Further, a new Pareto-aware global score assignment, aligned to the notion of Pareto-awareness, is introduced. PA-DIRECT has been benchmarked against MO-DIRECT and other state-of-the-art algorithms selected from different techniques of multi-objective optimization solvers using a bi-objective test suite on the Comparing Continuous Optimisers (COCO) platform. The study results substantiate the efficacy of PA-DIRECT in providing a high-quality approximate set, especially for multi-modal problems. [ABSTRACT FROM AUTHOR]

Inspired by the natural phenomenon that honey bees follow the elite group in the foraging process, we propose a novel artificial bee colony algorithm named ECABC based on elite group guidance and the combined breadth-depth search strategy in this paper. Firstly, by simulating the behavior that bees follow the elite group, a novel neighborhood search equation is proposed. According to the equation, with the center of the elite group as the starting point of the search, under the guidance of the global optimum, neighborhood search is performed. Secondly, a combined search strategy is designed as follows: the stochastic breadth-first search strategy for employed bees and the stochastic depth-first search strategy for onlooker bees. Thirdly, the random selection method of elite bees is adopted to replace the probability selection method of onlooker bees. Besides, the influencing parameters of the optimization results are studied and the optimum parameters allowing the best comprehensive performance are obtained. In addition, the proposed algorithm is experimentally verified with 22 benchmark functions and then compared with other improved artificial bee colony algorithms. The comparison results show that the ECABC can effectively improve the convergence speed, convergence precision, and robustness. [ABSTRACT FROM AUTHOR]

Many optimization problems in reality have become more and more complex, which promote the research on the improvement of different optimization algorithms. The particle swarm optimization (PSO) algorithm has been proved to be an effective tool to solve various kinds of optimization problems. However, for the basic PSO, the updating strategy is mainly aims to learn the global best, and it often suffers premature convergence as well as performs poorly on many complex optimization problems, especially for multimodal problems. A hybrid PSO algorithm which employs an adaptive learning strategy (ALPSO) is developed in this paper. In ALPSO, we employ a self-learning based candidate generation strategy to ensure the exploration ability, and a competitive learning based prediction strategy to guarantee exploitation of the algorithm. To balance the exploration ability and the exploitation ability well, we design a tolerance based search direction adjustment mechanism. The experimental results on 40 benchmark test functions demonstrate that, compared with five representative PSO algorithms, ALPSO performs much better than the others in more cases, on both convergence accuracy and convergence speed. [ABSTRACT FROM AUTHOR]

In this paper, we propose a novel tensor completion model using framelet regularization and low-rank matrix factorization. An effective block successive upper-bound minimization (BSUM) algorithm is designed to solve the proposed optimization model. The convergence of our algorithm is theoretically guaranteed, and under some mild conditions, our algorithm converges to the coordinate-wise minimizers. Extensive experiments are conducted on the synthetic data and real data, and the results demonstrate the effectiveness and the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

Abstract The ant colony optimization (ACO) algorithm is a type of classical swarm intelligence algorithm that is especially suitable for combinatorial optimization problems. To further improve the convergence speed without affecting the solution quality, in this paper, a novel strengthened pheromone update mechanism is designed that strengthens the pheromone on the edges, which had never been done before, utilizing dynamic information to perform path optimization. In addition, to enhance the global search capability, a novel pheromone-smoothing mechanism is designed to reinitialize the pheromone matrix when the ACO algorithm's search process approaches a defined stagnation state. The improved algorithm is analyzed and tested on a set of benchmark test cases. The experimental results show that the improved ant colony optimization algorithm performs better than compared algorithms in terms of both the diversity of the solutions obtained and convergence speed. [ABSTRACT FROM AUTHOR]

External archive can be used to improve the performance of a multi-objective evolutionary algorithm. Various archiving approaches have been developed but with some drawbacks. These drawbacks such as computation-inefficiency, retreating and shrinking, have not yet been well addressed. In this paper, we propose an efficient decomposition-based archiving approach (DAA) inspired from the decomposition strategy for dealing with multi-objective optimization. In DAA, the whole objective space is uniformly divided into a number of subspaces according to a set of weight vectors. At each generation, only one non-dominated solution lying in a subspace is chosen to be used for updating the external archive in consideration of its diversity. A normalized distance-based method, incorporated with the Pareto dominance, is proposed to decide which subspace a new solution should fall into, and whether this solution should replace existing one in this subspace or not. Empirical results on a diverse set of benchmark test problems show that DAA is more efficient than a number of state-of-the-art archiving methods in terms of the diversity of the obtained non-dominated solutions; and DAA can accelerate the convergence speed of the evolutionary search for most test problems. [ABSTRACT FROM AUTHOR]

Most multi-objective immune algorithms (MOIAs) adopt clonal selection to speed up convergence, as this operator only clones the best individuals during the search process. However, this approach somehow deteriorates the population diversity, which may cause a MOIA to be trapped in a local optimum and could also lead to premature convergence when tackling some complicated multi-objective optimization problems (MOPs). In order to overcome this problem, an adaptive immune-inspired multi-objective algorithm (AIMA) is presented in this paper, in which multiple differential evolution (DE) strategies having distinct advantages are embedded into a conventional MOIA. Our proposed approach strengthens the exploration capabilities of a MOIA while also improving its population diversity. At each generation, based on the current search stage, an adaptive selection method is designed to choose an appropriate DE strategy for evolution. The core idea is to effectively combine the advantages of three DE strategies when solving different MOPs. A number of comparative experiments are conducted on the well-known and frequently-used WFG and DTLZ test problems. Our experimental results validate the superiority of our proposed AIMA, as it performs better than some state-of-the-art multi-objective optimization algorithms and some state-of-the-art MOIAs. [ABSTRACT FROM AUTHOR]

In this paper we replace the product of the masses in the Gravitational search algorithm introduced by [17] by other bivariate functions with specific properties. We analyze the properties of these functions to guarantee convergence in the algorithm and we discuss an application to justify our theoretical study and the need of using functions other than the product. [ABSTRACT FROM AUTHOR]

In the past two decades, multi-objective optimization has attracted increasing interests in the evolutionary computation community, and a variety of multi-objective optimization algorithms have been proposed on the basis of different population based meta-heuristics, where the family of multi-objective particle swarm optimization is among the most representative ones. While the performance of most existing multi-objective particle swarm optimization algorithms largely depends on the global or personal best particles stored in an external archive, in this paper, we propose a competitive mechanism based multi-objective particle swarm optimizer, where the particles are updated on the basis of the pairwise competitions performed in the current swarm at each generation. The performance of the proposed competitive multi-objective particle swarm optimizer is verified by benchmark comparisons with several state-of-the-art multi-objective optimizers, including three multi-objective particle swarm optimization algorithms and three multi-objective evolutionary algorithms. Experimental results demonstrate the promising performance of the proposed algorithm in terms of both optimization quality and convergence speed. [ABSTRACT FROM AUTHOR]

In this paper, a novel two-archive method is proposed for solving many-objective optimization problems. Our aim is to exploit the advantages of using two separate archives to balance the convergence and diversity. To this end, two updating strategies based on the aggregation-based framework are presented and incorporated into the two-archive method. In addition, we further extend this method by eliminating the restricted neighbourhood models. The proposed algorithms have been tested extensively on a number of well-known benchmark problems with 3–20 objectives. Experimental results reveal that the proposed algorithms work well on the many-objective optimization problems with different characteristics. [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]

The classical Back-Propagation (BP) scheme with gradient-based optimization in training Artificial Neural Networks (ANNs) suffers from many drawbacks, such as the premature convergence, and the tendency of being trapped in local optimums. Therefore, as an alternative for the BP and gradient-based optimization schemes, various Evolutionary Algorithms (EAs), i.e., Particle Swarm Optimization (PSO), Genetic Algorithm (GA), Simulated Annealing (SA), and Differential Evolution (DE), have gained popularity in the field of ANN weight training. This study applied a new efficient and effective Shuffled Complex Evolutionary Global Optimization Algorithm with Principal Component Analysis – University of California Irvine (SP-UCI) to the weight training process of a three-layer feed-forward ANN. A large-scale numerical comparison is conducted among the SP-UCI-, PSO-, GA-, SA-, and DE-based ANNs on 17 benchmark, complex, and real-world datasets. Results show that SP-UCI-based ANN outperforms other EA-based ANNs in the context of convergence and generalization. Results suggest that the SP-UCI algorithm possesses good potential in support of the weight training of ANN in real-word problems. In addition, the suitability of different kinds of EAs on training ANN is discussed. The large-scale comparison experiments conducted in this paper are fundamental references for selecting proper ANN weight training algorithms in practice. [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]

In this paper, we propose a novel vector coevolving particle swarm optimization algorithm (VCPSO). In VCPSO, the full dimension of each particle is first randomly partitioned into several sub-dimensions. Then, we randomly assign either one of our newly designed scalar operators or learning operators to update the values in each sub-dimension. The scalar operators are designed to enhance the population diversity and avoid premature convergence. In addition, the learning operators are designed to enhance the global and local search ability. The proposed algorithm is compared with several other classical swarm optimizers on thirty-three benchmark functions. Comprehensive experimental results show that VCPSO displays a better or comparable performance compared to the other algorithms in terms of solution accuracy and statistical results. [ABSTRACT FROM AUTHOR]

In this paper, a new variant of feedforward neural networks has been proposed for a class of nonsmooth optimization problems. The penalty term of the presented neural networks stems from the Group Lasso method which selects hidden variables in a grouped manner. To deal with the non-differentiability of the original penalty term ( l 1 − l 2 norm) and avoid oscillations, smoothing techniques have been used to approximate the objective function. It is assumed that the training samples are supplied to the networks in a specific incremental way during training, that is, in each cycle samples are supplied in a fixed order. Then, under suitable assumptions on learning rate, penalization coefficients and smoothing parameters, the weak and strong convergence of the training process for the smoothing neural networks have been proved. The convergence analysis shows that the gradient of the smoothing error function approaches zero and the weight sequence converges to a fixed point, respectively. We demonstrate how the smoothing approximation parameter can be updated in the training procedure so as to guarantee the convergence of the procedure to a Clarke stationary point of the original optimization problem. In addition, we have proved that the original nonsmoothing algorithm with l 1 − l 2 norm penalty converges consistently to the same optimum solution with the corresponding smoothed algorithm. Numerical simulations demonstrate the convergence and effectiveness of the proposed training algorithm. [ABSTRACT FROM AUTHOR]

It is prevalent that the Pareto-based dominant framework is inefficient in non-dominated sorting because the performance sharply deteriorates when there are numerous weak dominance relations. In order to address this issue, the paper presents a novel ranking strategy called Global Margin Ranking (GMR) which deploys the position information of individuals in objective space to gain the margin of dominance throughout the population. The method not only considers the distribution of population, but also incorporates the associated information of individuals, without incurring user-defined parameters. Moreover, in view of the challenges faced by Multi-objective Particle Swarm Optimization (MOPSO) in selection of gBest and pBest , we present an innovative strategy for selecting gBest and pBest by integrating the GMR and the individual’s density information. We compare the GMR method with a variety of other ranking methods in terms of the distribution of ranks, the ranking landscape and convergence of the evolutionary process. The relatively extensive experimental results on some benchmark functions show that MOPSO/GMR performs better than those specialized MOEAs. [ABSTRACT FROM AUTHOR]

This paper focuses on developing new algorithms for distributed cooperative learning based on zero-gradient-sum (ZGS) optimization in a network setting. Specifically, the feedforward neural network with random weights (FNNRW) is introduced to train on data distributed across multiple learning agents, and each agent runs the program on a subset of the entire data. In this scheme, there is no requirement for a fusion center, due to, e.g., practical limitations, security, or privacy reasons. The centralized FNNRW problem is reformulated into an equivalent separable form with consensus constraints among nodes and is solved by the ZGS-based distributed optimization strategy, which theoretically guarantees convergence to the optimal solution. The proposed method is more effective than the existing methods using the decentralized average consensus (DAC) and alternating direction method of multipliers (ADMM) strategies. It is simple and requires less computational and communication resources, which is well suited for potential applications, such as wireless sensor networks, artificial intelligence, and computational biology, involving datasets that are often extremely large, high-dimensional and located on distributed data sources. We show simulation results on both synthetic and real-world datasets. [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]

This paper proposes a multi-scale search algorithm for solving global optimization problems given a finite number of function evaluations. We refer to this algorithm as the Naive Multi-scale Search Optimization ( NMSO ). NMSO looks for the optimal solution by optimistically partitioning the search space over multiple scales in a hierarchical fashion. Based on a weak assumption about the function smoothness, we present a theoretical analysis on its finite-time and asymptotic convergence. An empirical assessment of the algorithm has been conducted on the noiseless Black-Box Optimization Benchmarking (BBOB) testbed and compared with the state-of-the-art optimistic as well as stochastic algorithms. Moreover, the efficacy of NMSO has been validated on the black-box optimization competition within the GECCO’15 conference where it has secured the third place out of twenty-eight participating algorithms. Overall, NMSO is suitable for problems with limited function evaluations, low-dimensionality search space, and objective functions that are separable or multi-modal. Otherwise, it is comparable with the top performing algorithms. [ABSTRACT FROM AUTHOR]