Hybrid particle swarm optimization with chaotic search for solving integer and mixed integer programming problems

A novel chaotic search method is proposed,and a hybrid algorithm combining particle swarm optimization(PSO) with this new method,called CLSPSO,is put forward to solve 14 integer and mixed integer programming problems.The performances of CLSPSO are compared with those of other five hybrid algorithms combining PSO with chaotic search methods.Experimental results indicate that in terms of robustness and final convergence speed,CLSPSO is better than other five algorithms in solving many of these problems.Furthermore,CLSPSO exhibits good performance in solving two high-dimensional problems,and it finds better solutions than the known ones.A performance index(PI) is introduced to fairly compare the above six algorithms,and the obtained values of(PI) in three cases demonstrate that CLSPSO is superior to all the other five algorithms under the same conditions.

Support vector machine forecasting method improved by chaotic particle swarm optimization and its application

By adopting the chaotic searching to improve the global searching performance of the particle swarm optimization (PSO), and using the improved PSO to optimize the key parameters of the support vector machine (SVM) forecasting model, an improved SVM model named CPSO-SVM model was proposed. The new model was applied to predicting the short term load, and the improved effect of the new model was proved. The simulation results of the South China Power Market’s actual data show that the new method can effectively improve the forecast accuracy by 2.23% and 3.87%, respectively, compared with the PSO-SVM and SVM methods. Compared with that of the PSO-SVM and SVM methods, the time cost of the new model is only increased by 3.15 and 4.61 s, respectively, which indicates that the CPSO-SVM model gains significant improved effects.

Hybrid particle swarm optimization with differential evolution and chaotic local search to solve reliability-redundancy allocation problems

In order to solve reliability-redundancy allocation problems more effectively, a new hybrid algorithm named CDEPSO is proposed in this work, which combines particle swarm optimization （PSO） with differential evolution （DE） and a new chaotic local search. In the CDEPSO algorithm, DE provides its best solution to PSO if the best solution obtained by DE is better than that by PSO, while the best solution in the PSO is performed by chaotic local search. To investigate the performance of CDEPSO, four typical reliability-redundancy allocation problems were solved and the results indicate that the convergence speed and robustness of CDEPSO is better than those of PSO and CPSO （a hybrid algorithm which only combines PSO with chaotic local search）. And, compared with the other six improved meta-heuristics, CDEPSO also exhibits more robust performance. In addition, a new performance was proposed to more fairly compare CDEPSO with the same six improved recta-heuristics, and CDEPSO algorithm is the best in solving these problems.

A Chaotic Local Search-Based Particle Swarm Optimizer for Large-Scale Complex Wind Farm Layout Optimization

Wind energy has been widely applied in power generation to alleviate climate problems.The wind turbine layout of a wind farm is a primary factor of impacting power conversion efficiency due to the wake effect that reduces the power outputs of wind turbines located in downstream.Wind farm layout optimization(WFLO)aims to reduce the wake effect for maximizing the power outputs of the wind farm.Nevertheless,the wake effect among wind turbines increases significantly as the number of wind turbines increases in the wind farm,which severely affect power conversion efficiency.Conventional heuristic algorithms suffer from issues of low solution quality and local optimum for large-scale WFLO under complex wind scenarios.Thus,a chaotic local search-based genetic learning particle swarm optimizer(CGPSO)is proposed to optimize large-scale WFLO problems.CGPSO is tested on four larger-scale wind farms under four complex wind scenarios and compares with eight state-of-the-art algorithms.The experiment results indicate that CGPSO significantly outperforms its competitors in terms of performance,stability,and robustness.To be specific,a success and failure memories-based selection is proposed to choose a chaotic map for chaotic search local.It improves the solution quality.The parameter and search pattern of chaotic local search are also analyzed for WFLO problems.

Image Thresholding Using Two-Dimensional Tsallis Cross Entropy Based on Either Chaotic Particle Swarm Optimization or Decomposition

The segmentation effect of Tsallis entropy method is superior to that of Shannon entropy method, and the computation speed of two-dimensional Shannon cross entropy method can be further improved by optimization. The existing two-dimensional Tsallis cross entropy method is not the strict two-dimensional extension. Thus two new methods of image thresholding using two-dimensional Tsallis cross entropy based on either Chaotic Particle Swarm Optimization (CPSO) or decomposition are proposed. The former uses CPSO to find the optimal threshold. The recursive algorithm is adopted to avoid the repetitive computation of fitness function in iterative procedure. The computing speed is improved greatly. The latter converts the two-dimensional computation into two one-dimensional spaces, which makes the computational complexity further reduced from O(L2) to O(L). The experimental results show that, compared with the proposed recently two-dimensional Shannon or Tsallis cross entropy method, the two new methods can achieve superior segmentation results and reduce running time greatly.

Particle Swarm Optimization Algorithm Based on Chaotic Sequences and Dynamic Self-Adaptive Strategy

To deal with the problems of premature convergence and tending to jump into the local optimum in the traditional particle swarm optimization, a novel improved particle swarm optimization algorithm was proposed. The self-adaptive inertia weight factor was used to accelerate the converging speed, and chaotic sequences were used to tune the acceleration coefficients for the balance between exploration and exploitation. The performance of the proposed algorithm was tested on four classical multi-objective optimization functions by comparing with the non-dominated sorting genetic algorithm and multi-objective particle swarm optimization algorithm. The results verified the effectiveness of the algorithm, which improved the premature convergence problem with faster convergence rate and strong ability to jump out of local optimum.

Particle Swarm Optimization with Directed Mutation

In the standard particle swarm optimization(SPSO),the big problem is that it suffers from premature convergence,that is,in complex optimization problems,it may easily get trapped in local optima.In order to mitigate premature convergence problem,this paper presents a new algorithm,which is called particle swarm optimization(PSO) with directed mutation,or DMPSO.The main idea of this algorithm is to "let the best particle(the smallest fitness of the particle swarm) become more excellent and the worst particle(the largest fitness of the particle swarm) try to be excellent".The new algorithm is tested on a set of eight benchmark functions,and compared with those of other four PSO variants.The experimental results illustrate the effectiveness and efficiency of the DMPSO.The comparisons show that DMPSO significantly improves the performance of PSO and searching accuracy.

CPSO: Chaotic Particle Swarm Optimization for Cluster Analysis

Background:To solve the cluster analysis better,we propose a new method based on the chaotic particle swarm optimization(CPSO)algorithm.Methods:In order to enhance the performance in clustering,we propose a novel method based on CPSO.We first evaluate the clustering performance of this model using the variance ratio criterion(VRC)as the evaluation metric.The effectiveness of the CPSO algorithm is compared with that of the traditional particle swarm optimization(PSO)algorithm.The CPSO aims to improve the VRC value while avoiding local optimal solutions.The simulated dataset is set at three levels of overlapping:non-overlapping,partial overlapping,and severe overlapping.Finally,we compare CPSO with two other methods.Results:By observing the comparative results,our proposed CPSO method performs outstandingly.In the conditions of non-overlapping,partial overlapping,and severe overlapping,our method has the best VRC values of 1683.2,620.5,and 275.6,respectively.The mean VRC values in these three cases are 1683.2,617.8,and 222.6.Conclusion:The CPSO performed better than other methods for cluster analysis problems.CPSO is effective for cluster analysis.

Improved particle swarm optimization algorithm for fuzzy multi-class SVM

An improved particle swarm optimization（PSO） algorithm is proposed to train the fuzzy support vector machine（FSVM） for pattern multi-classification.In the improved algorithm,the particles studies not only from itself and the best one but also from the mean value of some other particles.In addition,adaptive mutation was introduced to reduce the rate of premature convergence.The experimental results on the synthetic aperture radar（SAR） target recognition of moving and stationary target acquisition and recognition（MSTAR） dataset and character recognition of MNIST database show that the improved algorithm is feasible and effective for fuzzy multi-class SVM training.

Seepage safety monitoring model for an earth rock dam under influence of high-impact typhoons based on particle swarm optimization algorithm

Extreme hydrological events induced by typhoons in reservoir areas have presented severe challenges to the safe operation of hydraulic structures. Based on analysis of the seepage characteristics of an earth rock dam, a novel seepage safety monitoring model was constructed in this study. The nonlinear influence processes of the antecedent reservoir water level and rainfall were assumed to follow normal distributions. The particle swarm optimization （PSO） algorithm was used to optimize the model parameters so as to raise the fitting accuracy. In addition, a mutation factor was introduced to simulate the sudden increase in the piezometric level induced by short-duration heavy rainfall and the possible historical extreme reservoir water level during a typhoon. In order to verify the efficacy of this model, the earth rock dam of the Siminghu Reservoir was used as an example. The piezometric level at the SW1-2 measuring point during Typhoon Fitow in 2013 was fitted with the present model, and a corresponding theoretical expression was established. Comparison of fitting results of the piezometric level obtained from the present statistical model and traditional statistical model with monitored values during the typhoon shows that the present model has a higher fitting accuracy and can simulate the uprush feature of the seepage pressure during the typhoon perfectly.

Design of Radial Basis Function Network Using Adaptive Particle Swarm Optimization and Orthogonal Least Squares

This paper presents a two-level learning method for designing an optimal Radial Basis Function Network (RBFN) using Adaptive Velocity Update Relaxation Particle Swarm Optimization algorithm (AVURPSO) and Orthogonal Least Squares algorithm (OLS) called as OLS-AVURPSO method. The novelty is to develop an AVURPSO algorithm to form the hybrid OLS-AVURPSO method for designing an optimal RBFN. The proposed method at the upper level finds the global optimum of the spread factor parameter using AVURPSO while at the lower level automatically constructs the RBFN using OLS algorithm. Simulation results confirm that the RBFN is superior to Multilayered Perceptron Network (MLPN) in terms of network size and computing time. To demonstrate the effectiveness of proposed OLS-AVURPSO in the design of RBFN, the Mackey-Glass Chaotic Time-Series as an example is modeled by both MLPN and RBFN.

Dynamic Self-Adaptive Double Population Particle Swarm Optimization Algorithm Based on Lorenz Equation

In order to improve some shortcomings of the standard particle swarm optimization algorithm, such as premature convergence and slow local search speed, a double population particle swarm optimization algorithm based on Lorenz equation and dynamic self-adaptive strategy is proposed. Chaotic sequences produced by Lorenz equation are used to tune the acceleration coefficients for the balance between exploration and exploitation, the dynamic self-adaptive inertia weight factor is used to accelerate the converging speed, and the double population purposes to enhance convergence accuracy. The experiment was carried out with four multi-objective test functions compared with two classical multi-objective algorithms, non-dominated sorting genetic algorithm and multi-objective particle swarm optimization algorithm. The results show that the proposed algorithm has excellent performance with faster convergence rate and strong ability to jump out of local optimum, could use to solve many optimization problems.

Quantum particle swarm optimization for micro-grid system with consideration of consumer satisfaction and benefit of generation side

Considering comprehensive benefit of micro-grid system and consumers,we establish a mathematical model with the goal of the maximum consumer satisfaction and the maximum benefit of power generation side in the view of energy management.An improved multi-objective local mutation adaptive quantum particle swarm optimization(MO-LM-AQPSO)algorithm is adopted to obtain the Pareto frontier of consumer satisfaction and the benefit of power generation side.The optimal solution of the non-dominant solution is selected with introducing the power shortage and power loss to maximize the benefit of power generation side,and its reasonableness is verified by numerical simulation.Then,translational load and time-of-use electricity price incentive mechanism are considered and reasonable peak-valley price ratio is adopted to guide users to actively participate in demand response.The simulation results show that the reasonable incentive mechanism increases the benefit of power generation side and improves the consumer satisfaction.Also the mechanism maximizes the utilization of renewable energy and effectively reduces the operation cost of the battery.

Immunity clone algorithm with particle swarm evolution

Combining the clonal selection mechanism of the immune system with the evolution equations of particle swarm optimization, an advanced algorithm was introduced for functions optimization. The advantages of this algorithm lies in two aspects. Via immunity operation, the diversity of the antibodies was maintained, and the speed of convergent was improved by using particle swarm evolution equations. Simulation programme and three functions were used to check the effect of the algorithm. The advanced algorithm were compared with clonal selection algorithm and particle swarm algorithm. The results show that this advanced algorithm can converge to the global optimum at a great rate in a given range, the performance of optimization is improved effectively.

基于自适应变异粒子群算法的风光储微网调度

为克服传统粒子群算法在求解时容易形成局部最优,求解精度低的不足,提出了一种基于自适应变异粒子群优化的微电网调度求解方法。惯性权重采用自适应正态分布递减,随着迭代次数的增加更新粒子位置的移动策略,并且在算法后期引入变异环节。为验证算法的有效性,文章与其他算法进行收敛性能对比,并对两种典型天气情况下的微网运行成本模型仿真求解,得到最优调度。算例结果表明,改进算法能够对粒子全局最优搜索优化,效果优于其他算法,可合理调配分布式电源出力时段,具有良好的可行性。

Dynamics analysis of chaotic maps: From perspective on parameter estimation by meta-heuristic algorithm

Chaotic encryption is one of hot topics in cryptography, which has received increasing attention. Among many encryption methods, chaotic map is employed as an important source of pseudo-random numbers(PRNS). Although the randomness and the butterfly effect of chaotic map make the generated sequence look very confused, its essence is still the deterministic behavior generated by a set of deterministic parameters. Therefore, the unceasing improved parameter estimation technology becomes one of potential threats for chaotic encryption, enhancing the attacking effect of the deciphering methods. In this paper, for better analyzing the cryptography, we focus on investigating the condition of chaotic maps to resist parameter estimation. An improved particle swarm optimization(IPSO) algorithm is introduced as the estimation method. Furthermore, a new piecewise principle is proposed for increasing estimation precision. Detailed experimental results demonstrate the effectiveness of the new estimation principle, and some new requirements are summarized for a secure chaotic encryption system.

Clustering algorithm based on density function and nichePSO

This paper introduces niching particle swarm optimiza- tion （nichePSO） into clustering analysis and puts forward a cluster- ing algorithm which uses nichePSO to optimize density functions. Firstly, this paper improves main swarm training models and in- creases their ability of space searching. Secondly, the radius of sub-swarms is defined adaptively according to the actual clus- tering problem, which can be useful for the niches＇ forming and searching. At last, a novel method that distributes samples to the corresponding cluster is proposed. Numerical results illustrate that this algorithm based on the density function and nichePSO could cluster unbalanced density datasets into the correct clusters auto- matically and accurately.

Predicting of Power Quality Steady State Index Based on Chaotic Theory Using Least Squares Support Vector Machine

An effective power quality prediction for regional power grid can provide valuable references and contribute to the discovering and solving of power quality problems. So a predicting model for power quality steady state index based on chaotic theory and least squares support vector machine (LSSVM) is proposed in this paper. At first, the phase space reconstruction of original power quality data is performed to form a new data space containing the attractor. The new data space is used as training samples for the LSSVM. Then in order to predict power quality steady state index accurately, the particle swarm algorithm is adopted to optimize parameters of the LSSVM model. According to the simulation results based on power quality data measured in a certain distribution network, the model applies to several indexes with higher forecasting accuracy and strong practicability.

Particle Swarm Optimization with Adaptive Mutation

A new adaptive mutation particle swarm optimizer,which is based on the variance of the population's fitness,is presented in this paper.During the running time,the mutation probability for the current best particle is determined by two factors:the variance of the population's fitness and the current optimal solution.The ability of particle swarm optimization(PSO)algorithm to break away from the local optimum is greatly improved by the mutation.The experimental results show that the new algorithm not only has great advantage of convergence property over genetic algorithm and PSO,but can also avoid the premature convergence problem effectively.