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

An adaptive particle swarm optimization (APSO) that features better search efficiency than classical particle swarm optimization (PSO) is presented. More importantly, it can perform a global search over the entire search space with faster convergence speed. The APSO consists of two main steps. First, by evaluating the population distribution and particle fitness, a real-time evolutionary state estimation procedure is performed to identify one of the following four defined evolutionary states, including exploration, exploitation, convergence, and jumping out in each generation. It enables the automatic control of inertia weight, acceleration coefficients, and other algorithmic parameters at run time to improve the search efficiency and convergence speed. Then, an elitist learning strategy is performed when the evolutionary state is classified as convergence state. The strategy will act on the globally best particle to jump out of the likely local optima. The APSO has comprehensively been evaluated on 12 unimodal and multimodal benchmark functions. The effects of parameter adaptation and elitist learning will be studied. Results show that APSO substantially enhances the performance of the PSO paradigm in terms of convergence speed, global optimality, solution accuracy, and algorithm reliability. As APSO introduces two new parameters to the PSO paradigm only, it does not introduce an additional design or implementation complexity.

/pdf/adaptive-particle-swarm-optimization-2lys782m7h.pdf

Adaptive Particle Swarm Optimization

This paper reviews recent studies on the Particle Swarm Optimization PSO algorithm. The review has been focused on high impact recent articles that have analyzed and/or modified PSO algorithms. This paper also presents some potential areas for future study.

Book review: particle swarm optimization for single objective continuous space problems: A review

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.

/pdf/particle-swarm-optimization-technique-system-and-challenges-1t22wy4m1r.pdf

Particle Swarm Optimization: Technique, System and Challenges

Function evaluations (FEs) of many real-world optimization problems are time or resource consuming, posing a serious challenge to the application of evolutionary algorithms (EAs) to solve these problems. To address this challenge, the research on surrogate-assisted EAs has attracted increasing attention from both academia and industry over the past decades. However, most existing surrogate-assisted EAs (SAEAs) either still require thousands of expensive FEs to obtain acceptable solutions, or are only applied to very low-dimensional problems. In this paper, a novel surrogate-assisted particle swarm optimization (PSO) inspired from committee-based active learning (CAL) is proposed. In the proposed algorithm, a global model management strategy inspired from CAL is developed, which searches for the best and most uncertain solutions according to a surrogate ensemble using a PSO algorithm and evaluates these solutions using the expensive objective function. In addition, a local surrogate model is built around the best solution obtained so far. Then, a PSO algorithm searches on the local surrogate to find its optimum and evaluates it. The evolutionary search using the global model management strategy switches to the local search once no further improvement can be observed, and vice versa. This iterative search process continues until the computational budget is exhausted. Experimental results comparing the proposed algorithm with a few state-of-the-art SAEAs on both benchmark problems up to 30 decision variables as well as an airfoil design problem demonstrate that the proposed algorithm is able to achieve better or competitive solutions with a limited budget of hundreds of exact FEs.

Committee-Based Active Learning for Surrogate-Assisted Particle Swarm Optimization of Expensive Problems

A recurrent neural network is presented for solving systems of quadratic programming problems with equality constraints involving complex-valued coefficients. The proposed recurrent neural network is asymptotically stable and able to generate optimal solutions to quadratic programs with equality constraints. An opamp based analogue circuit realization of the recurrent neural network is described. An illustrative example is also discussed to demonstrate the performance and characteristics of the analogue neural network.

A recurrent neural network for solving complex-valued quadratic programming problems with equality constraints

A lower order discrete-time recurrent neural network is presented in this paper for solving higher quadratic programming It bases on the orthogonal decomposition method and solves high order quadratic programs, especially for the case that the number of decision variables is close to the number of its constraints The proposed recurrent neural network is globally exponential stability and converges to the optimal solutions of the higher quadratic programming The condition for the neural network to globally converge to the optimal solution of the quadratic program is given An illustrative example and the simulation results are presented to illustrate its performance

A lower order discrete-time recurrent neural network for solving high order quadratic problems with equality constraints

In this paper, first of all, we introduce the normal particle swarm optimization algorithms (PSO), for this kind of algorithms, there are problems like it easily stuck at a local minimum point and its convergence speed is slow. To overcome this, an improved particle swarm optimization algorithms is presented for improving global and local search ability of PSO. That is, the rate of particle convergence changing was introduced in this new algorithm and the inertia weight was formulated as a function of this factor according to its impact on the search performance of the swarm to adjust its convergence speed and jump over local minimum points. To show effectiveness of this method, the simulations of four benchmark examples are carried out by the proposed method, as a result, this indicates that the proposed method is very useful.

http://ieeexplore.ieee.org/iel5/6016074/6024900/06024978.pdf

Improved particle swarm optimization algorithms

A discrete-time recurrent neural network is presented in this paper for solving systems of complex-valued linear equations. The network shown in this paper is simple in structure and can converge to the solutions of complex-valued linear equations. The condition for the neural network to globally converge to the complex-valued linear equations is given. An illustrative example is presented to illustrate its performance.

A discrete-time recurrent neural network for solving systems of complex-valued linear equations

Asymptotically stable conditions of linear discrete time delay system and robust stable conditions of the corresponding perturbed system (called this interval system) are setup and proved respectively. Based on the fundamental matrix of the system, equivalent conditions guaranteeing the system asymptotical stability are proposed and the rigorous proof are given. Based on these general conditions, sufficient condition is obtained and some extended results in existed reference are pointed out to be wrong. For the perturbed system, the perturbed range is estimated, in which the perturbed system are robust stability. Some simulated example show that the results obtained in this paper are effective.

Rigorous stability analysis and error correction of existed results of linear discrete time delay system

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