Xingjuan Cai

Particle swarm optimization with FUSS and RWS for high dimensional functions

Abstract High dimensional optimization problems play an important role in many complex engineering area. Though many variants of particle swarm optimization (PSO) have been proposed, however, most of them are tested and compared with dimension no larger than 300. Since numerical problem with high-dimension maintains a large linkage and correlation among different variables, and the number of local optimum increases significantly with different dimensions, this paper proposes a novel variant of PSO aiming to provide a balance between exploration and exploitation capability. Firstly, the fitness uniform selection strategy (FUSS) with a weak selection pressure is incorporated into the standard PSO. Secondly, “random walk strategy” (RWS) with four different form, is designed to further enhance the exploration capability to escaping from a local optimum. Finally, the proposed PSO combined with FUSS and RWS is applied to seven famous high dimensional benchmark with the dimension up to 3000. Simulation results demonstrate good performance of the new method in solving high dimensional multi-modal problems when compared with two other variants of the PSO.

Predicted-velocity particle swarm optimization using game-theoretic approach

In standard particle swarm optimization, velocity information only provides a moving direction of each particle of the swarm, though it also can be considered as one point if there is no limitation restriction. Predicted-velocity particle swarm optimization is a new modified version using velocity and position to search the domain space equality. In some cases, velocity information may be effectively, but fails in others. This paper presents a game-theoretic approach for designing particle swarm optimization with a mixed strategy. The approach is applied to design a mixed strategy using velocity and position vectors. The experimental results show the mixed strategy can obtain the better performance than the best of pure strategy.

A new stochastic algorithm to direct orbits of chaotic systems

In this paper, a new stochastic optimisation algorithm is introduced to simulate the plant growing process. It employs the photosynthesis operator and phototropism operator to mimic photosynthesis and phototropism phenomena. For the plant growing process, photosynthesis is a basic mechanism to provide the energy from sunshine, while phototropism is an important character to guide the growing direction. In our algorithm, each individual is called a branch, and the sampled points are regarded as the branch growing trajectory. Phototropism operator is designed to introduce the fitness function value, as well as to decide the growing direction. To test the performance, it is used to solve the directing orbits of chaotic systems, simulation results show this new algorithm increases the performance significantly when compared with other four optimisation algorithms.

Particle swarm optimization using lévy probability distribution

Velocity threshold is an important parameter to affect the performance of particle swarm optimization. In this paper, a novel velocity threshold automation strategy is proposed by incorporated with Levy probability distribution. Different from Gaussian and Cauchy distribution, it has an infinite second moment and is likely to generate an offspring that is far away from its parent. Therefore, this method employs a larger capability of the global exploration by providing a large velocity scale for each particle. Simulation results show the proposed strategy is effective and efficient.

Self-adaptive PID-Controlled Particle Swarm Optimization

As a new version of particle swarm optimization (PSO), PID-controlled PSO introduces the concept of controller into the algorithm structure. However, with the introduction of PID controller, three additional parameters are incorporated into the algorithm. Thus, how to provide a proper selection of these parameters is an important problem to affect the algorithm efficiency. In this paper, the relationships among these parameters are conducted by the stability theory. Further, a self-adaptive parameter selection strategy is proposed. Simulation results show the proposed strategy is effective.

Stochastic Dynamic Step Length Particle Swarm Optimization

Stochastic particle swarm optimization is a novel variant of particle swarm optimization that convergent to the global optimum with probability one. However, the local search capability is not always well in some cases, therefore, in this paper, a technique, dynamic step length, is incorporated into the structure of stochastic particle swarm optimization aiming to further improve the performance. In this modification, each particle will adjust its velocity according to its performance. In other words, if it finds a better region, it will make a local search, otherwise, a global search pattern is given. By the way, to combining the advantages between the standard version (with better exploitation capability) and the stochastic version (with better exploration capability), the first half period is used with the standard version incorporated with dynamic step length, while in later generations, the stochastic version with dynamic step length is used to escape from a local optimum. Simulation results show this strategy may provide well balance between exploration and exploitation capabilities, and improve the performance significantly.

Particle Swarm Optimization with Dynamic Step Length

Particle swarm optimization (PSO) is a robust swarm intelligent technique inspired from birds flocking and fish schooling. Though many effective improvements have been proposed, however, the premature convergence is still its main problem. Because each particles movement is a continuous process and can be modelled with differential equation groups, a new variant, particle swarm optimization with dynamic step length (PSO-DSL), with additional control coefficient- step length, is introduced. Then the absolute stability theory is introduced to analyze the stability character of the standard PSO, the theoretical result indicates the PSO with constant step length can not always be stable, this may be one of the reason for premature convergence. Simulation results show the PSO-DSL is effective.

Self-learning Particle Swarm Optimization Based on Environmental Feedback

Particle swarm optimization (PSO) simulates the behaviors of birds ocking and poundsh schooling. However, its biological background does not concern the environmental affection. Inspired by the interaction between environment and individuals, a new version - self-learning particle swarm optimization based on environmental feedback (SL-PSO), is proposed, in which two self-learning strategies are designed so that each particle adjusts its moving direction according to the feedback information from the environment. Furthermore, a mutation operator is introduced to avoid premature convergence phenomenon. Simulation results show the proposed algorithm is effective and efpoundcient.

Integral-Controlled Particle Swarm Optimization

Particle swarm optimization (PSO) is a novel population-based stochastic optimization algorithm. However, it gets easily trapped into local optima when dealing with multi-modal high-dimensional problems. To overcome this shortcoming, two integral controllers are incorporated into the methodology of PSO, and the integral-controlled particle swarm optimization (ICPSO) is introduced. Due to the additional accelerator items, the behavior of ICPSO is more complex, and provides more chances to escaping from a local optimum than the standard version of PSO. However, many experimental results show the performance of ICPSO is not always well because of the particles’ un-controlled movements. Therefore, a new variant, integral particle swarm optimization with dispersed accelerator information (IPSO-DAI) is designed to improve the computational efficiency. In IPSO-DAI, a predefined predicted velocity index is introduced to guide the moving direction. If the average velocity of one particle is superior to the index value, it will choice a convergent manner, otherwise, a divergent manner is employed. Furthermore, the choice of convergent manner or divergent manner for each particle is associated with its performance to fit different living experiences. Simulation results show IPSO-DAI is more effective than other three variants of PSO especially for multi-modal numerical problems. The IPSO-DAI is also applied to directing the orbits of discrete chaotic dynamical systems by adding small bounded perturbations, and achieves the best performance among four different variants of PSO.

Stochastic velocity threshold inspired by evolutionary programming

Particle swarm optimization (PSO) is a new robust swarm intelligence technique, which has exhibited good performance on well-known numerical test problems. Though many improvements published aims to increase the computational efficiency, there are still many works need to do. Inspired by evolutionary programming theory, this paper proposes a self-adaptive particle swarm optimization in which the velocity threshold dynamically changes during the course of a simulation, and two further techniques are designed to avoid badly adjusted by the self-adaption. Six benchmark functions are used to testify the new algorithm, and the results show the new adaptive PSO clearly leads to better performance, although the performance improvements were found to be dependent on problems.