# Population Structure And Particle Swarm Performance Pdf

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*The slave swarms execute PSO or its variants independently to maintain the diversity of particles, while the master swarm enhances its particles based on its own knowledge and also the knowledge of the particles in the slave swarms. In the simulation part, several benchmark functions are performed, and the performance of the proposed algorithm is compared to the standard PSO SPSO to demonstrate its efficiency. Unable to display preview.*

- Human Behavior-Based Particle Swarm Optimization
- Multi-population Cooperative Particle Swarm Optimization
- A Performance Class-Based Particle Swarm Optimizer

## Human Behavior-Based Particle Swarm Optimization

One of the main concerns with Particle Swarm Optimization PSO is to increase or maintain diversity during search in order to avoid premature convergence. In this study, a Performance Class-Based learning PSO PCB-PSO algorithm is proposed, that not only increases and maintains swarm diversity but also improves exploration and exploitation while speeding up convergence simultaneously.

In the PCB-PSO algorithm, each particle belongs to a class based on its fitness value and particles might change classes at evolutionary stages or search step based on their updated position.

The particles are divided into an upper, middle and lower. In the upper class are particles with top fitness values, the middle are those with average while particles in the bottom class are the worst performing in the swarm. The number of particles in each group is predetermined.

Each class has a unique learning strategy designed specifically for a given task. The upper class is designed to converge towards the best solution found, Middle class particles exploit the search space while lower class particles explore.

The Algorithm is tested on a set of 8 benchmark functions which have generally proven to be difficult to optimize. The algorithm is able to be on par with some cutting edge PSO variants and outperforms other swarm and evolutionary algorithms on a number of functions.

On complex multimodal functions, it is able to outperform other PSO variants showing its ability to escape local optima solutions. Optimization is one of the key features in obtaining good performance in systems. In fact optimization problems can be found everywhere in real life from transportation to even dieting. The original PSO algorithm has a topology fully connected network where all particles learn from their personal best historical search position and the global best particle in the swarm.

This learning structure is the main reason why the original PSO algorithm is inefficient and ca easily be trapped into a local minima as all particles are guided by one global leader. Several other topological structures have been introduce to enhanced performance e.

These topologies use different ways to update the velocity and position of particles in the swarm. Comprehensive learning PSO CLPSO tries to solve the problem of premature convergence by using different learning topologies on different dimensions to ensure diversity is maintained [ 5 ].

Exploration, the ability of the swarm to search its entire environment global search and exploitation, the ability for particles to thoroughly search their neighborhood local search are two important features of any PSO or search algorithm.

To ensure swarm stability, stability based adaptive inertia weight SAIW uses a performance based approach to determine each particles inertia weight [ 6 ]. There are several other balanced Algorithms that are specifically designed to ensure both exploration and exploitation [ 8 , 9 , 10 ].

Introduces a new paradigm of PSO learning that enhances exploration, exploitation and convergence speed simultaneously. Deals with the problem of premature convergence by making some particles continue exploration and exploitation while others converge to a given minima or optima. The problem of swarm diversity is dealt with by continuous exploration of the search space by lower class particles. Introduces flexibility by allowing a given behavior to be prioritized by simply assigning more or all particles to a given class.

The rest of the paper is organized as follows: The original PSO algorithm and some learning topologies are reviewed in Sect. Finally, in Sect. A choice of each value is problem dependent and determines the convergence speed, exploitation and exploration ability of the swarm. Therefore, the choice of values should be harmonious. In a simple PSO algorithm, w can be between 0. Illustrates the classification of particles based on fitness with their corresponding classes and population sizes search process of the PCB-PSO.

Illustrates the learning mechanisms of each class with their source of information indicated by arrows. The proposed Algorithm shows superior performance in comparison to the other variants on the multimodal functions F6—F8. This shows the agility of the algorithms and its ability to escape the local optima while still managing to push for faster convergence.

On unimodal functions, F1—F5 the performance is on par with other PSO variants but outperforms the other swarm and evolutionary algorithms. In unimodal functions, there is only one minima but our algorithm was still set to continuously explore and exploit other regions.

If we set the whole population to UC, the algorithm will work towards faster convergence and we will expect achieve better quality results. In this study, a novel learning paradigm for PSO is introduce to balance exploration, exploitation and convergence while maintaining diversity of the swarm. The algorithm uses only the social and cognitive components of PSO for learning which further simplifies the algorithm.

Particles Learn according to the class they fall in and these gives flexibility and robustness to the algorithm as different learning methods are in cooperated at the same time. The algorithm further introduces dynamism by varying class population at given intervals during the search.

The algorithm is tested on a number of benchmark functions, compared with other swarm and evolutionary optimization algorithms including other advance PSO techniques, and see the superiority of the proposed algorithm. In future work, this algorithm will be tested on more functions like the or CEC suit. It will also be used to solve a real world problem.

Skip to main content Skip to sections. This service is more advanced with JavaScript available. Advertisement Hide. International Conference on Swarm Intelligence. Conference paper First Online: 13 July Download conference paper PDF. In this study, a novel PSO algorithm called PCB-PSO is proposed, with a new learning topology to ensure exploration and exploitation while also ensuring a high convergence speed therefore avoiding premature convergence.

The upper class consist of particles with superior performance while the lower class consist of the poorest performing members. The middle class is made-up of members considered not to be performing poorly and not having superior performance. Particles in the same group have a common learning strategy or topology, which is different from those in the other groups.

Lower class particles are designed to enhance exploration while the middle class particles are designed for exploitation. Upper class particles are designed for fast convergence. The intuition here is that if a particle is performing poorly, it has to do more exploration and if its performance is good, it focuses on converging faster, and if its performing neither poorly nor well, then it should exploit its neighborhood.

The main contributions of this study can be listed as follows: 1. PSO is a population based stochastic swarm and evolutionary computational algorithm. In PSO, a population of particles, with each having a position and velocity component, is use to find the solution to an optimization problem. Each particle is a solution and the search space is the set of all solutions to the given problem. The particles or solutions are evolved by updating the velocity and position after every iteration.

A particles update is done using its personal best experience and the best experience of the entire swarm. This update is designed to guide the particles towards the global best solution and eventually and eventually towards the optimal solution. The update of velocity and position of each particle are done using Eqs. The particles continue to evolve until a termination criterion is met usually the maximum iteration pre-determined before start of search.

In this section, an efficient variant of PSO called PCB-PSO is proposed to simultaneously tackle the problems of premature convergence, exploration, exploitation and diversity while also converging faster to the global minima. The algorithm introduces a new learning topology and the major difference from the base PSO is as follows 1 Particles in the swarm belong to one of three groups based of their fitness value. The population size of each class is predetermined and will be discussed in the later section.

The intuition here is that, classifying particles into three groups can allow us to design a learning strategy for each group of the swarm to simultaneously explore, exploit and converge while maintaining diversity throughout the search. This is opposed to the base PSO where all the particles learn from a global leader making them to move towards one region of the search space. UC particles, which, have good performance and are most likely to find the optimal solution are designed to enhance convergence speed.

LC particles, which are poorly performing in the swarm, roam the search area exploring new solutions and maintaining diversity of the swarm. MC particles, which are performing neither poorly nor well, are designed for exploitation since they move in areas between UC and MC particles Fig. Open image in new window. The population of each class is determined in three simple steps. First, a class is chosen and the proportion of the total population N to belong to that class is assigned to determine the population of the given class.

Finally, the last remainder of the population falls into the last class. Note that we can start with any class. UC and LC particles have probabilities associated to them. This associated probability is a measure of how likely a particle is chosen to be learned from by another particle in the learning strategy of a given class, which will be discussed later.

For UC particles, the probability is proportional to the fitness value meaning the higher the value, the higher the probability while for LC particles; the probability is inversely proportional to the fitness value. MC particles learn from both UC and LC members and so we want the best particles in UC to be less likely to learn from and the best particles in LC to be more likely to learn from so as to keep them exploiting regions between MC and LC.

The probability of a UC particle is calculated using Eq. In PSO particles are updated by directing them towards the global best solution of the swarm and the personal best solution of the given particle with a velocity. This might be problematic if the solution found is not actually the best solution in the search space then particles will fail to explore other search regions missing other potentially better solutions.

This problem has been solved by introducing different learning strategies and parameter modification. The simplest way is to vary the inertia weight and acceleration coefficients throughout the search to enhance exploration in the early stages and exploitation in the late stages.

We leverage this idea but ensure both exploration and exploitation are carried-out throughout the search by introducing a new topology structure. This ensures a thorough search of the solution space making it less likely to miss a global best solution.

The velocity component is not used in this algorithm because in higher dimensions, the inertia weight is required to be less than 0. Instead of using the recommended small value of the inertia weight, we focus on tuning acceleration of the social and cognitive component, which further simplifies the position update equation by eliminating the inertia weight and velocity. Hence, in this algorithm, we do not need to calculate the velocity component of a particle.

In PCB-PSO, the update mechanism of each class is design for a given property of exploration, exploitation and convergence of the particles. Three different update mechanisms are designed for the three classes. Each update strategy is unique to a given class.

UC Update Mechanism. These are the best performing particles in the swarm and so are close to the best solution found at any period during the search. The update equation for UC is as shown in Eq.

## Multi-population Cooperative Particle Swarm Optimization

Particle Swarm Optimization PSO is a search method which utilizes a set of agents that move through the search space to find the global minimum of an objective function. The trajectory of each particle is determined by a simple rule incorporating the current particle velocity and exploration histories of the particle and its neighbors. Since its introduction by Kennedy and Eberhart in , PSO has attracted many researchers due to its search efficiency even for a high dimensional objective function with multiple local optima. The dynamics of PSO search has been investigated and numerous variants for improvements have been proposed. This paper reviews the progress of PSO research so far, and the recent achievements for application to large-scale optimization problems. Already have an account?

Time-series forecasting of pollutant concentration levels using particle swarm optimization and artificial neural networks. Francisco S. Fernandes I ; Paulo S. Ferreira III. This study evaluates the application of an intelligent hybrid system for time-series forecasting of atmospheric pollutant concentration levels. The proposed method consists of an artificial neural network combined with a particle swarm optimization algorithm.

PDF | The effects of various population topologies on the particle swarm algorithm were systematically investigated. Random graphs were.

## A Performance Class-Based Particle Swarm Optimizer

The particle swarm optimization PSO algorithm, in which individuals collaborate with their interacted neighbors like bird flocking to search for the optima, has been successfully applied in a wide range of fields pertaining to searching and convergence. Here we employ the scale-free network to represent the inter-individual interactions in the population, named SF-PSO. In contrast to the traditional PSO with fully-connected topology or regular topology, the scale-free topology used in SF-PSO incorporates the diversity of individuals in searching and information dissemination ability, leading to a quite different optimization process.

Abstract: Population structure strongl y affects the dynamic behavior and performance of the particle swarm. Most of PSOs use one of two simple soc iometric pr inciples for defining th e. One connects all the members of the swarm to one another. This strategy is often called gbest and.

*Metrics details. Different mixtures of ion concentrations and temperatures generate almost identical backscattered signals, hindering the discrimination between plasma parameters.*

One of the main concerns with Particle Swarm Optimization PSO is to increase or maintain diversity during search in order to avoid premature convergence. In this study, a Performance Class-Based learning PSO PCB-PSO algorithm is proposed, that not only increases and maintains swarm diversity but also improves exploration and exploitation while speeding up convergence simultaneously. In the PCB-PSO algorithm, each particle belongs to a class based on its fitness value and particles might change classes at evolutionary stages or search step based on their updated position. The particles are divided into an upper, middle and lower.

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