Many scientific, engineering and economic problems involve the optimisation of a set of parameters. These problems include examples like minimising the losses in a power grid by finding the optimal configuration of the components, or training a neural network to recognise images of people's faces. Numerous optimisation algorithms have been proposed to solve these problems, with varying degrees of success. The Particle Swarm Optimiser (PSO) is a relatively new technique that has been empirically shown to perform well on many of these optimisation problems. This thesis presents a theoretical model that can be used to describe the long-term behaviour of the algorithm. An enhanced version of the Particle Swarm Optimiser is constructed and shown to have guaranteed convergence on local minima. This algorithm is extended further, resulting in an algorithm with guaranteed convergence on global minima. A model for constructing cooperative PSO algorithms is developed, resulting in the introduction of two new PSO-based algorithms. Empirical results are presented to support the theoretical properties predicted by the various models, using synthetic benchmark functions to investigate specific properties. The various PSO-based algorithms are then applied to the task of training neural networks, corroborating the results obtained on the synthetic benchmark functions. / Thesis (PhD)--University of Pretoria, 2007. / Computer Science / Unrestricted

Evolutionary algorithms and swarm intelligence techniques have been shown to successfully solve optimization problems where the goal is to find a single optimal solution. In multimodal domains where the goal is the locate multiple solutions in a single search space, these techniques fail. Niching algorithms extend existing global optimization algorithms to locate and maintain multiple solutions concurrently. In this thesis, strategies are developed that utilize the unique characteristics of the particle swarm optimization algorithm to perform niching. Shrinking topological neighborhoods and optimization with multiple subswarms are used to identify and stably maintain niches. Solving systems of equations and multimodal functions are used to demonstrate the effectiveness of the new algorithms. / Dissertation (MS)--University of Pretoria, 2005. / Computer Science / unrestricted

This thesis describes the development and experimental results of a system to explore cloning of facial expressions between dissimilar face models, so new faces can be animated using the animations from existing faces. The system described in this thesis uses fuzzy membership functions and subtractive clustering to represent faces and expressions in an intermediate space. This intermediate space allows expressions for face models with different resolutions to be compared. The algorithm is trained for each pair of faces using particle swarm optimization, which selects appropriate weights and radii to construct the intermediate space. These techniques allow the described system to be more flexible than previous systems, since it does not require prior knowledge of the underlying implementation of the face models to function.

Optimization forms an intrinsic part of the design and implementation of modern systems, such as industrial systems, communication networks, and the configuration of electric or electronic components. Population-based single-solution optimization algorithms such as Particle Swarm Optimization (PSO) have been shown to perform well when a number of optimal or suboptimal solutions exist. However, some problems require algorithms that locate all or most of these optimal and suboptimal solutions. Such algorithms are known as niching or speciation algorithms. Several techniques have been proposed to extend the PSO paradigm so that multiple optima can be located and maintained within a convoluted search space. A significant number of these implementations are subswarm-based, that is, portions of the swarm are optimized separately. Niches are formed to contain these subswarms, a process that often requires user-specified parameters, as the sizes and placing of the niches are unknown. This thesis presents a new niching technique that uses the vector dot product of the social and cognitive direction vectors to determine niche boundaries. Thus, a separate niche radius is calculated for each niche, a process that requires minimal knowledge of the search space. This strategy differs from other techniques using niche radii where a niche radius is either required to be set in advance, or calculated from the distances between particles. The development of the algorithm is traced and tested extensively using synthetic benchmark functions. Empirical results are reported using a variety of settings. An analysis of the algorithm is presented as well as a scalability study. The performance of the algorithm is also compared to that of two other well-known PSO niching algorithms. To conclude, the vector-based PSO is extended to locate and track multiple optima in dynamic environments. / Thesis (PhD)--University of Pretoria, 2010. / Computer Science / unrestricted

The purpose of this thesis was to identify the optimal design parameters for a jet nozzle which obtains a local maximum shear stress while maximizing the average shear stress on the floor of a fluid filled system. This research examined how geometric parameters of a jet nozzle, such as the nozzle's angle, height, and orifice, influence the shear stress created on the bottom surface of a tank. Simulations were run using a Computational Fluid Dynamics (CFD) software package to determine shear stress values for a parameterized geometric domain including the jet nozzle. A response surface was created based on the shear stress values obtained from 112 simulated designs. A multi-objective optimization software utilized the response surface to generate designs with the best combination of parameters to achieve maximum shear stress and maximum average shear stress. The optimal configuration of parameters achieved larger shear stress values over a commercially available design.

This dissertation presents an analysis of the angle modulated particle swarm optimisation (AMPSO) algorithm. AMPSO is a technique that enables one to solve binary optimisation problems with particle swarm optimisation (PSO), without any modifications to the PSO algorithm. While AMPSO has been successfully applied to a range of optimisation problems, there is little to no understanding of how and why the algorithm might fail. The work presented here includes in-depth theoretical and emprical analyses of the AMPSO algorithm in an attempt to understand it better. Where problems are identified, they are supported by theoretical and/or empirical evidence. Furthermore, suggestions are made as to how the identified issues could be overcome. In particular, the generating function is identified as the main cause for concern. The generating function in AMPSO is responsible for generating binary solutions. However, it is shown that the increasing frequency of the generating function hinders the algorithm’s ability to effectively exploit the search space. The problem is addressed by introducing methods to construct different generating functions, and to quantify the quality of arbitrary generating functions. In addition to this, a number of other problems are identified and addressed in various ways. The work concludes with an empirical analysis that aims to identify which of the various suggestions made throughout this dissertatioin hold substantial promise for further research. / Dissertation (MSc)--University of Pretoria, 2017. / Computer Science / MSc / Unrestricted

Particle swarm optimisation (PSO) is a stochastic, population-based optimisation algorithm. PSO has been applied successfully to a variety of domains. This thesis examines the behaviour of PSO when applied to high dimensional optimisation problems. Empirical experiments are used to illustrate the problems exhibited by the swarm, namely that the particles are prone to leaving the search space and never returning. This thesis does not intend to develop a new version of PSO speci cally for high dimensional problems. Instead, the thesis investigates why PSO fails in high dimensional search spaces. Four di erent types of approaches are examined. The rst is the application of velocity clamping to prevent the initial velocity explosion and to keep particles inside the search space. The second approach selects values for the acceleration coe cients and inertia weights so that particle movement is restrained or so that the swarm follows particular patterns of movement. The third introduces coupling between problem variables, thereby reducing the swarm's movement freedom and forcing the swarm to focus more on certain subspaces within the search space. The nal approach examines the importance of initialisation strategies in controlling the swarm's exploration to exploitation ratio. The thesis shows that the problems exhibited by PSO in high dimensions, particularly unwanted particle roaming, can not be fully mitigated by any of the techniques examined. The thesis provides deeper insight into the reasons for PSO's poor performance by means of extensive empirical tests and theoretical reasoning. / Dissertation (MSc)--University of Pretoria, 2017. / Computer Science / MSc / Unrestricted

Indiana University-Purdue University Indianapolis (IUPUI) / Efficient topic modeling is needed to support applications that aim at identifying main themes from a collection of documents. In this thesis, a reduced vector embedding representation and particle swarm optimization (PSO) are combined to develop a topic modeling strategy that is able to identify representative themes from a large collection of documents. Documents are encoded using a reduced, contextual vector embedding from a general-purpose pre-trained language model (sBERT). A modified PSO algorithm (pPSO) that tracks particle fitness on a dimension-by-dimension basis is then applied to these embeddings to create clusters of related documents. The proposed methodology is demonstrated on three datasets across different domains. The first dataset consists of posts from the online health forum r/Cancer. The second dataset is a collection of NY Times abstracts and is used to compare

Gradient-based optimisers are a natural way to solve optimisation problems, and have long been used for their efficacy in exploiting the search space. Particle swarm optimisers (PSOs), when using reasonable algorithm parameters, are considered to have good exploration characteristics. This thesis proposes a specific way of constructing hybrid gradient PSOs. Heterogeneous, hybrid gradient PSOs are constructed by allowing the gradient algorithm to optimise local best particles, while the PSO algorithm governs the behaviour of the rest of the swarm. This approach allows the distinct algorithms to concentrate on performing the separate tasks of exploration and exploitation. Two new PSOs, the Gradient Descent PSO, which combines the Gradient Descent and PSO algorithms, and the LeapFrog PSO, which combines the LeapFrog and PSO algorithms, are introduced. The GDPSO represents arguably the simplest hybrid gradient PSO possible, while the LeapFrog PSO incorporates the more sophisticated LFOP1(b) algorithm, exhibiting a heuristic algorithm design and dynamic time step adjustment mechanism. The strong tendency of these hybrids to prematurely converge is examined, and it is shown that by modifying algorithm parameters and delaying the introduction of gradient information, it is possible to retain strong exploration capabilities of the original PSO algorithm while also benefiting from the exploitation of the gradient algorithms. / Dissertation (MSc)--University of Pretoria, 2010. / Computer Science / unrestricted

Indiana University-Purdue University Indianapolis (IUPUI) / This research improves the realism of an electronic warfare (EW) environment involving dynamic motion of assets and transmitters. Particle Swarm Optimization (PSO) continues to be used to place assets in such a manner where they can communicate with the largest number of highest priority transmitters. This new research accomplishes improvement in three areas. First, the previously stationary assets and transmitters are given a velocity component, allowing them to change positions over time. Because the assets now have a starting position and velocity, they require time to reach the PSO solution. In order to optimally assign each asset to move in the direction of a PSO solution location, a graph-based method is implemented. This encompasses the second area of research. The graph algorithm runs in O(n^3) time and consumes less than 0.2% of the total measured computation time to find a solution. Transmitter location updates prompt a recalculation of the PSO, causing the assets to change their assignments and trajectories every second. The computation required to ensure accuracy with this behavior is less than 0.5% of the total computation time. The final area of research is the completion of algorithmic performance analysis. A scenario with 3 assets and 30 transmitters only requires an average of 147ms to update all relevant information in a single time interval of one second. Analysis conducted on the data collected in this process indicates that more than 95% of the time providing automatic updates is spent with PSO calculations. Recommendations on minimizing the impact of the PSO are also provided in this research.