Particle swarm optimization (PSO) is a population-based stochastic optimization algorithm motivated by intelligent collective behavior of some animals such as flocks of birds or schools of fish. Since presented in 1995, it has experienced a multitude of enhancements. As researchers have learned about the technique, they derived new versions aiming to different demands, developed new applications in a host of areas, published theoretical studies of the effects of the various parameters and proposed many variants of the algorithm. This paper introduces its origin and background and carries out the theory analysis of the PSO. Then, we analyze its present situation of research and application in algorithm structure, parameter selection, topology structure, discrete PSO algorithm and parallel PSO algorithm, multi-objective optimization PSO and its engineering applications. Finally, the existing problems are analyzed and future research directions are presented.

Particle swarm optimization algorithm: an overview

Particle swarm optimization (PSO) is a stochastic population-based algorithm motivated by intelligent collective behavior of some animals. The most important advantages of the PSO are that PSO is easy to implement and there are few parameters to adjust. The inertia weight (w) is one of PSO's parameters originally proposed by Shi and Eberhart to bring about a balance between the exploration and exploitation characteristics of PSO. Since the introduction of this parameter, there have been a number of proposals of different strategies for determining the value of inertia weight during a course of run. This paper presents the first comprehensive review of the various inertia weight strategies reported in the related literature. These approaches are classified and discussed in three main groups: constant, time-varying and adaptive inertia weights. A new adaptive inertia weight approach is also proposed which uses the success rate of the swarm as its feedback parameter to ascertain the particles' situation in the search space. The empirical studies on fifteen static test problems, a dynamic function and a real world engineering problem show that the proposed particle swarm optimization model is quite effective in adapting the value of w in the dynamic and static environments.

A novel particle swarm optimization algorithm with adaptive inertia weight

Particle Swarm Optimization (PSO) is a biologically inspired computational search and optimization method developed in 1995 by Eberhart and Kennedy based on the social behaviors of birds flocking or fish schooling. A number of basic variations have been developed due to improve speed of convergence and quality of solution found by the PSO. On the other hand, basic PSO is more appropriate to process static, simple optimization problem. Modification PSO is developed for solving the basic PSO problem. The observation and review 46 related studies in the period between 2002 and 2010 focusing on function of PSO, advantages and disadvantages of PSO, the basic variant of PSO, Modification of PSO and applications that have implemented using PSO. The application can show which one the modified or variant PSO that haven’t been made and which one the modified or variant PSO that will be developed.

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Particle Swarm Optimization: Technique, System and Challenges

Particle swarm optimization (PSO) is one of the well-known population-based techniques used in global optimization and many engineering problems. Despite its simplicity and efficiency, the PSO has problems as being trapped in local minima due to premature convergence and weakness of global search capability. To overcome these disadvantages, the PSO is combined with Levy flight in this study. Levy flight is a random walk determining stepsize using Levy distribution. Being used Levy flight, a more efficient search takes place in the search space thanks to the long jumps to be made by the particles. In the proposed method, a limit value is defined for each particle, and if the particles could not improve self-solutions at the end of current iteration, this limit is increased. If the limit value determined is exceeded by a particle, the particle is redistributed in the search space with Levy flight method. To get rid of local minima and improve global search capability are ensured via this distribution in the basic PSO. The performance and accuracy of the proposed method called as Levy flight particle swarm optimization (LFPSO) are examined on well-known unimodal and multimodal benchmark functions. Experimental results show that the LFPSO is clearly seen to be more successful than one of the state-of-the-art PSO (SPSO) and the other PSO variants in terms of solution quality and robustness. The results are also statistically compared, and a significant difference is observed between the SPSO and the LFPSO methods. Furthermore, the results of proposed method are also compared with the results of well-known and recent population-based optimization methods.

A novel particle swarm optimization algorithm with Levy flight

This paper presents "A novel adaptive inertia weight with stability condition for particle swarm optimization (SAIW)". This approach determines the inertia weight in different dimensions for each particle on: (1) its performance and (2) distance from its best position, and by considering the stability condition, the acceleration parameters of PSO are adaptively determined. Presents an adaptive method for finding inertia weight in different dimensions for each particle.The success of the particle and displacement in particle's best position are used as the feedback.Stability analysis of proposed model indicates that its performance is usually optimal.The results clearly show the superiority of the proposed model over the existing methods. Particle swarm optimization (PSO) is a stochastic population-based algorithm motivated by intelligent collective behavior of birds. The performance of the PSO algorithm highly depends on choosing appropriate parameters. Inertia weight is a parameter of this algorithm which was first proposed by Shi and Eberhart to bring about a balance between the exploration and exploitation characteristics of PSO. This paper presents an adaptive approach which determines the inertia weight in different dimensions for each particle, based on its performance and distance from its best position. Each particle will then have different roles in different dimensions of the search environment. By considering the stability condition and an adaptive inertia weight, the acceleration parameters of PSO are adaptively determined. The corresponding approach is called stability-based adaptive inertia weight (SAIW). The proposed method and some other models for adjusting the inertia weight are evaluated and compared. The efficiency of SAIW is validated on 22 static test problems, moving peaks benchmarks (MPB) and a real-world problem for a radar system design. Experimental results indicate that the proposed model greatly improves the PSO performance in terms of the solution quality as well as convergence speed in static and dynamic environments.

A novel stability-based adaptive inertia weight for particle swarm optimization

A modified particle swarm optimizer with dynamic adaptation

The fuzzy system is an important method for intelligent modelling of electric load forecasting, and how to enhance the learning and data mining ability of fuzzy system is crucial for its practical application and the improvement of the load-forecasting accuracy. In this study, a PSO-based improved Wang-Mendel (WM) method is proposed, which is a new combined modelling method based on fuzzy system and evolutionary algorithm. This method adopts a modified Particle swarm optimization (PSO) algorithm to optimize the fuzzy rule centroid of data covered area and thus obtains complete fuzzy rule set through extrapolating. The electric load-forecasting model based on this proposed method is described, and a case study on short-term load forecast illustrates that this method effectively enhances the forecast accuracy of WM method, has a fast convergence rate, and is independent of the forecasting objects.

An improved WM method based on PSO for electric load forecasting

The fuzzy logic method is a useful way in spatial load forecasting (SLF) simulation. However, the randomness is not fully considered in its key step. This paper proposes a new SLF model for distribution network, which brings in Cloud theory. The knowledge representation based on cloud model is adopted to integrate fuzziness and randomness of qualitative concept. The uncertainty reasoning based on it is used to calculate the preference score of the partitioned small area. The randomness of land–use decision is indicated by hyper-entropy obtained from each rule confidence and the digital characters of each cloud model. The small area redevelopment criteria based on this model are provided. Furthermore, the linear multi-objective programming is introduced and improved for the whole-optimal land distribution in which the economic effect and redevelopment are considered. Finally, this model is implemented and the analysis for a real instance is described.

Application of Uncertainty Reasoning Based on Cloud Theory in Spatial Load Forecasting

The middle-term electric load forecasting is an existing difficult work and often has a large error. To address the problem, this paper proposes a novel cloud theory based time-series predictive method for middle-term electric load forecasting. In this method, the time series of daily maximum load is partitioned into two parts, historical dataset and current tendency dataset, backward cloud algorithm is applied to the two datasets to form the historical cloud and the current cloud, and the corresponding rule sets are mined. Then the historical cloud and current cloud is integrated to created predictive cloud through synthesized cloud. Finally, via cloud reasoning, the forecast result can be obtained. This predictive method effectively integrates quasi-periodical regularity and current tendency of time-series data, and has a simple computing model. The case study shows that the proposed method is accurate and practical.

Xueming Yang

Papers

A modified particle swarm optimizer with dynamic adaptation

An improved WM method based on PSO for electric load forecasting

Application of Uncertainty Reasoning Based on Cloud Theory in Spatial Load Forecasting

A Novel Cloud Theory Based Time-series Predictive Method for Middle-term Electric Load Forecasting