Identification and control of nonlinear systems by a dissimilation particle swarm optimization-based Elman neural network

In this paper, we first present a learning algorithm for dynamic recurrent Elman neural networks based on a dissimilation particle swarm optimization. The proposed algorithm computes concurrently both the evolution of network structure, weights, initial inputs of the context units, and self-feedback coefficient of the modified Elman network. Thereafter, we introduce and discuss a novel control method based on the proposed algorithm. More specifically, a dynamic identifier is constructed to perform speed identification and a controller is designed to perform speed control for Ultrasonic Motors (USM). Numerical experiments show that the novel identifier and controller based on the proposed algorithm can both achieve higher convergence precision and speed than other state-of-the-art algorithms. In particular, our experiments show that the identifier can approximate the USM's nonlinear input–output mapping accurately. The effectiveness of the controller is verified using different kinds of speeds of constant, step, and sinusoidal types. Besides, a preliminary examination on a randomly perturbation also shows the robust characteristics of the two proposed models.     

A rank based particle swarm optimization algorithm with dynamic adaptation

The particle swarm optimization (PSO) technique is a powerful stochastic evolutionary algorithm that can be used to find the global optimum solution in a complex search space. This paper presents a variation on the standard PSO algorithm called the rank based particle swarm optimizer, or PSO_rank, employing cooperative behavior of the particles to significantly improve the performance of the original algorithm. In this method, in order to efficiently control the local search and convergence to global optimum solution, the γ best particles are taken to contribute to the updating of the position of a candidate particle. The contribution of each particle is proportional to its strength. The strength is a function of three parameters: strivness, immediacy and number of contributed particles. All particles are sorted according to their fitness values, and only the γ best particles will be selected. The value of γ decreases linearly as the iteration increases. A time-varying inertia weight decreasing non-linearly is introduced to improve the performance. PSO_rank is tested on a commonly used set of optimization problems and is compared to other variants of the PSO algorithm presented in the literature. As a real application, PSO_rank is used for neural network training. The PSO_rank strategy outperformed all the methods considered in this investigation for most of the functions. Experimental results show the suitability of the proposed algorithm in terms of effectiveness and robustness.     

An augmented Lagrangian fish swarm based method for global optimization

This paper presents an augmented Lagrangian methodology with a stochastic population based algorithm for solving nonlinear constrained global optimization problems. The method approximately solves a sequence of simple bound global optimization subproblems using a fish swarm intelligent algorithm. A stochastic convergence analysis of the fish swarm iterative process is included. Numerical results with a benchmark set of problems are shown, including a comparison with other stochastic-type algorithms.     

Balanced fuzzy particle swarm optimization

In the present study an extension of particle swarm optimization (PSO) algorithm which is in conformity with actual nature is introduced for solving combinatorial optimization problems. Development of this algorithm is essentially based on balanced fuzzy sets theory. The classical fuzzy sets theory cannot distinguish differences between positive and negative information of membership functions, while in the new method both kinds of information “positive and negative” about membership function are equally important. The balanced fuzzy particle swarm optimization algorithm is used for fundamental optimization problem entitled traveling salesman problem (TSP). For convergence inspecting of new algorithm, method was used for TSP problems. Convergence curves were represented fast convergence in restricted and low iterations for balanced fuzzy particle swarm optimization algorithm (BF-PSO) comparison with fuzzy particle swarm optimization algorithm (F-PSO).     

Artificial Bee Colony training of neural networks: comparison with back-propagation

The Artificial Bee Colony (ABC) is a swarm intelligence algorithm for optimization that has previously been applied to the training of neural networks. This paper examines more carefully the performance of the ABC algorithm for optimizing the connection weights of feed-forward neural networks for classification tasks, and presents a more rigorous comparison with the traditional Back-Propagation (BP) training algorithm. The empirical results for benchmark problems demonstrate that using the standard “stopping early” approach with optimized learning parameters leads to improved BP performance over the previous comparative study, and that a simple variation of the ABC approach provides improved ABC performance too. With both improvements applied, the ABC approach does perform very well on small problems, but the generalization performances achieved are only significantly better than standard BP on one out of six datasets, and the training times increase rapidly as the size of the problem grows. If different, evolutionary optimized, BP learning rates are allowed for the two layers of the neural network, BP is significantly better than the ABC on two of the six datasets, and not significantly different on the other four.     

Hybrid co-evolutionary particle swarm optimization and noising metaheuristics for the delay constrained least cost path problem

This paper presents a co-evolutionary particle swarm optimization (PSO) algorithm, hybridized with noising metaheuristics, for solving the delay constrained least cost (DCLC) path problem, i.e., shortest-path problem with a delay constraint on the total “cost” of the optimal path. The proposed algorithm uses the principle of Lagrange relaxation based aggregated cost. It essentially consists of two concurrent PSOs for solving the resulting minimization-maximization problem. The main PSO is designed as a hybrid PSO-noising metaheuristics algorithm for efficient global search to solve the minimization part of the DCLC-Lagrangian relaxation by finding multiple shortest paths between a source-destination pair. The auxiliary/second PSO is a co-evolutionary PSO to obtain the optimal Lagrangian multiplier for solving the maximization part of the Lagrangian relaxation problem. For the main PSO, a novel heuristics-based path encoding/decoding scheme has been devised for representation of network paths as particles. The simulation results on several networks with random topologies illustrate the efficiency of the proposed hybrid algorithm for the constrained shortest path computation problems.     

A hybrid glowworm swarm optimization algorithm to solve constrained multimodal functions optimization

In this paper, a novel hybrid glowworm swarm optimization (HGSO) algorithm is proposed. The HGSO algorithm embeds predatory behaviour of artificial fish swarm algorithm (AFSA) into glowworm swarm optimization (GSO) algorithm and combines the GSO with differential evolution on the basis of a two-population co-evolution mechanism. In addition, to overcome the premature convergence, the local search strategy based on simulated annealing is applied to make the search of GSO approach the true optimum solution gradually. Finally, several benchmark functions show that HGSO has faster convergence efficiency and higher computational precision, and is more effective for solving constrained multi-modal function optimization problems.     

An evolutionary game based particle swarm optimization algorithm

Particle swarm optimization (PSO) is an evolutionary algorithm used extensively. This paper presented a new particle swarm optimizer based on evolutionary game (EGPSO). We map particles’ finding optimal solution in PSO algorithm to players’ pursuing maximum utility by choosing strategies in evolutionary games, using replicator dynamics to model the behavior of particles. And in order to overcome premature convergence a multi-start technique was introduced. Experimental results show that EGPSO can overcome premature convergence and has great performance of convergence property over traditional PSO.     

An improved particle swarm optimizer for parametric optimization of flexible satellite controller

Parametric optimization of flexible satellite controller is an essential for almost all modern satellites. Particle swarm algorithm is a global optimization algorithm but it suffers from two major shortcomings, that of, premature convergence and low searching accuracy. To solve these problems, this paper proposes an improved particle swarm optimization (IPSO) which substitute “poorly-fitted-particles” with a cross operation. Based on decision possibility, the cross operation can interchange local optima between three particles. Thereafter the swarm is split in two halves, and random number (s) get generated by crossing the dimension of particle from both halves. This produces a new swarm. Now the new swarm and old swarm are mixed, and based on relative fitness a half of the particles are selected for the next generation. As a result of the cross operation, IPSO can easily jump out of local optima, has improved searching accuracy and accelerates the convergence speed. Some test functions with different dimensions are used to analyze the performance of IPSO algorithm. Simulation results show that the IPSO has more advantages than standard PSO and Genetic Algorithm PSO (GAPSO). In that it has a more stable performance and lower level of complexity. Thus the IPSO is applied for parametric optimization of flexible satellite control, for a satellite having solar wings and antennae. Simulation results shows that the IPSO can effectively get the best controller parameters vis-a-vis the other optimization methods.     

基于改进PSO-BP神经网络的贮存可靠性预测

贮存可靠性是军事储备质量监测的重要环节,科学准确地预测贮存可靠度是现代化军事评估的必然要求。针对历史贮存数据,建立可靠度与年限的贮存可靠性预测模型,采用进化策略改进粒子群算法(PSO)优化BP神经网络进行贮存可靠性预测。通过数据扩充提高样本质量和数量,应用改进后的PSO算法优化BP神经网络的初始权值和阈值,提高网络的泛化能力。PSO算法较好的全局搜索能力与BP网络很强的局部搜索能力相结合,能够避免早熟现象,提高算法的收敛速度及预测精度。实验结果表明,改进的PSO-BP网络模型比PSO-BP和BP神经网络获得更好的预测性能。     

Multiobjective big data optimization based on a hybrid salp swarm algorithm and differential evolution

This paper developed a multiobjective Big Data optimization approach based on a hybrid salp swarm algorithm and the differential evolution algorithm. The role of the differential evolution algorithm is to enhance the capability of the feature exploitation of the salp swarm algorithm because the operators of the differential evolution algorithm are used as local search operators. In general, the proposed method contains three stages. In the first stage, the population is generated, and the archive is initialized. The second stage updates the solutions using the hybrid salp swarm algorithm and the differential evolution algorithm, and the final stage determines the nondominated solutions and updates the archive. To assess the performance of the proposed approach, a series of experiments were performed. A set of single-objective and multiobjective problems from the 2015 Big Data optimization competition were tested; the dataset contained data with and without noise. The results of our experiments illustrated that the proposed approach outperformed other approaches, including the baseline nondominated sorting genetic algorithm, on all test problems. Moreover, for single-objective problems, the score value of the proposed method was better than that of the traditional multiobjective salp swarm algorithm. When compared with both algorithms, that is, the adaptive DE algorithm with external archive and the hybrid multiobjective firefly algorithm, its score was the largest. In contrast, for the multiobjective functions, the scores of the proposed algorithm were higher than that of the fireworks algorithm framework.     

A hybrid simplex search and particle swarm optimization for unconstrained optimization

This paper proposes the hybrid NM-PSO algorithm based on the Nelder–Mead (NM) simplex search method and particle swarm optimization (PSO) for unconstrained optimization. NM-PSO is very easy to implement in practice since it does not require gradient computation. The modification of both the Nelder–Mead simplex search method and particle swarm optimization intends to produce faster and more accurate convergence. The main purpose of the paper is to demonstrate how the standard particle swarm optimizers can be improved by incorporating a hybridization strategy. In a suite of 20 test function problems taken from the literature, computational results via a comprehensive experimental study, preceded by the investigation of parameter selection, show that the hybrid NM-PSO approach outperforms other three relevant search techniques (i.e., the original NM simplex search method, the original PSO and the guaranteed convergence particle swarm optimization (GCPSO)) in terms of solution quality and convergence rate. In a later part of the comparative experiment, the NM-PSO algorithm is compared to various most up-to-date cooperative PSO (CPSO) procedures appearing in the literature. The comparison report still largely favors the NM-PSO algorithm in the performance of accuracy, robustness and function evaluation. As evidenced by the overall assessment based on two kinds of computational experience, the new algorithm has demonstrated to be extremely effective and efficient at locating best-practice optimal solutions for unconstrained optimization.     

A dynamic global and local combined particle swarm optimization algorithm

Particle swarm optimization (PSO) algorithm has been developing rapidly and many results have been reported. PSO algorithm has shown some important advantages by providing high speed of convergence in specific problems, but it has a tendency to get stuck in a near optimal solution and one may find it difficult to improve solution accuracy by fine tuning. This paper presents a dynamic global and local combined particle swarm optimization (DGLCPSO) algorithm to improve the performance of original PSO, in which all particles dynamically share the best information of the local particle, global particle and group particles. It is tested with a set of eight benchmark functions with different dimensions and compared with original PSO. Experimental results indicate that the DGLCPSO algorithm improves the search performance on the benchmark functions significantly, and shows the effectiveness of the algorithm to solve optimization problems.     

A multi-start opposition-based particle swarm optimization algorithm with adaptive velocity for bound constrained global optimization

In this paper we present a multi-start particle swarm optimization algorithm for the global optimization of a function subject to bound constraints. The procedure consists of three main steps. In the initialization phase, an opposition learning strategy is performed to improve the search efficiency. Then a variant of the adaptive velocity based on the differential operator enhances the optimization ability of the particles. Finally, a re-initialization strategy based on two diversity measures for the swarm is act in order to avoid premature convergence and stagnation. The strategy uses the super-opposition paradigm to re-initialize particles in the swarm. The algorithm has been evaluated on a set of 100 global optimization test problems. Comparisons with other global optimization methods show the robustness and effectiveness of the proposed algorithm.     

Enhanced speciation in particle swarm optimization for multi-modal problems

In this paper, we present a novel multi-modal optimization algorithm for finding multiple local optima in objective function surfaces. We build from Species-based particle swarm optimization (SPSO) by using deterministic sampling to generate new particles during the optimization process, by implementing proximity-based speciation coupled with speciation of isolated particles, and by including “turbulence regions” around already found solutions to prevent unnecessary function evaluations. Instead of using error threshold values, the new algorithm uses the particle’s experience, geometric mean, and “exclusion factor” to detect local optima and stop the algorithm. The performance of each extension is assessed with leave-it-out tests, and the results are discussed. We use the new algorithm called Isolated-Speciation-based particle swarm optimization (ISPSO) and a benchmark algorithm called Niche particle swarm optimization (NichePSO) to solve a six-dimensional rainfall characterization problem for 192 rain gages across the United States. We show why it is important to find multiple local optima for solving this real-world complex problem by discussing its high multi-modality. Solutions found by both algorithms are compared, and we conclude that ISPSO is more reliable than NichePSO at finding optima with a significantly lower objective function value.     

Particle swarm optimization: Hybridization perspectives and experimental illustrations

Metaheuristic optimization algorithms have become popular choice for solving complex and intricate problems which are otherwise difficult to solve by traditional methods. In the present study an attempt is made to review the hybrid optimization techniques in which one main algorithm is a well known metaheuristic; particle swarm optimization or PSO. Hybridization is a method of combining two (or more) techniques in a judicious manner such that the resulting algorithm contains the positive features of both (or all) the algorithms. Depending on the algorithm/s used we made three classifications as (i) Hybridization of PSO and genetic algorithms (ii) Hybridization of PSO with differential evolution and (iii) Hybridization of PSO with other techniques. Where, other techniques include various local and global search methods. Besides giving the review we also show a comparison of three hybrid PSO algorithms; hybrid differential evolution particle swarm optimization (DE-PSO), adaptive mutation particle swarm optimization (AMPSO) and hybrid genetic algorithm particle swarm optimization (GA-PSO) on a test suite of nine conventional benchmark problems.     

The block diagram method for designing the particle swarm optimization algorithm

In this paper, the block diagram method of the dispersed control system is proposed for designing or improving the normal particle swarm optimization algorithms (PSO), that is, it uses the Jury-test of the control theory to compare the block diagrams getting from existing particle swarm optimization methods and finds out some defects of the existing particle swarm optimization methods, for example, the premature convergence of PSO algorithm, and so on. Thus a new particle swarm algorithm is also proposed for improving these defects, that is, the speed iteration and position iteration formulas of PSO are revised for both adjusting its convergence speed and jumping out of the local minimum points. To show effectiveness of the proposed method, the simulations of 13 benchmark examples are carried out, as a result, it indicates that the proposed method is very useful.     

Particle swarm optimization with age-group topology for multimodal functions and data clustering

This paper proposes particle swarm optimization with age-group topology (PSOAG), a novel age-based particle swarm optimization (PSO). In this work, we present a new concept of age to measure the search ability of each particle in local area. To keep population diversity during searching, we separate particles to different age-groups by their age and particles in each age-group can only select the ones in younger groups or their own groups as their neighbourhoods. To allow search escape from local optima, the aging particles are regularly replaced by new and randomly generated ones. In addition, we design an age-group based parameter setting method, where particles in different age-groups have different parameters, to accelerate convergence. This algorithm is applied to nonlinear function optimization and data clustering problems for performance evaluation. In comparison against several PSO variants and other EAs, we find that the proposed algorithm provides significantly better performances on both the function optimization problems and the data clustering tasks.     

Close formation flight of swarm unmanned aerial vehicles via metric-distance brain storm optimization

Close formation flight of swarm unmanned aerial vehicles (UAVs) has drawn much attention from scholars due to its significant importance in many aspects. In this paper, we focus on an advanced controller design for swarm UAV close formation based on a novel bio-inspired algorithm, i.e., metric-distance brain storm optimization (MDBSO). The proposed method utilizes the brain storm optimization (BSO) which has been extensively adopted in complicated systems with great performances and modifies its basic operators to formulate the formation flight controller design. The original clustering operator in BSO is replaced by a fresh clustering method based on metric distances, while the individual updating operator utilizes Lévy distribution to extend search steps to fit into the metric searching regions. Then the proposed algorithm is applied to optimize the benchmark controller in swarm UAV close formation to enhance the tracking performances under complicated circumstances. Simulation results demonstrate that our approach is more superior in stable configuration of swarm UAV close formations by comparing with several generic methods.     

Improved particle swarm algorithm for hydrological parameter optimization

In this paper, a new method named MSSE-PSO (master-slave swarms shuffling evolution algorithm based on particle swarm optimization) is proposed. Firstly, a population of points is sampled randomly from the feasible space, and then partitioned into several sub-swarms (one master swarm and other slave swarms). Each slave swarm independently executes PSO or its variants, including the update of particles’ position and velocity. For the master swarm, the particles enhance themselves based on the social knowledge of master swarm and that of slave swarms. At periodic stage in the evolution, the master swarm and the whole slave swarms are forced to mix, and points are then reassigned to several sub-swarms to ensure the share of information. The process is repeated until a user-defined stopping criterion is reached. The tests of numerical simulation and the case study on hydrological model show that MSSE-PSO remarkably improves the accuracy of calibration, reduces the time of computation and enhances the performance of stability. Therefore, it is an effective and efficient global optimization method.