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Full-Text Articles in Applied Mathematics
Basins Of Attraction And Metaoptimization For Particle Swarm Optimization Methods, David Ma
Basins Of Attraction And Metaoptimization For Particle Swarm Optimization Methods, David Ma
Honors Projects
Particle swarm optimization (PSO) is a metaheuristic optimization method that finds near- optima by spawning particles which explore within a given search space while exploiting the best candidate solutions of the swarm. PSO algorithms emulate the behavior of, say, a flock of birds or a school of fish, and encapsulate the randomness that is present in natural processes. In this paper, we discuss different initialization schemes and meta-optimizations for PSO, its performances on various multi-minima functions, and the unique intricacies and obstacles that the method faces when attempting to produce images for basins of attraction, which are the sets of …
Sensitivity Analysis Of Basins Of Attraction For Nelder-Mead, Sonia K. Shah
Sensitivity Analysis Of Basins Of Attraction For Nelder-Mead, Sonia K. Shah
Honors Projects
The Nelder-Mead optimization method is a numerical method used to find the minimum of an objective function in a multidimensional space. In this paper, we use this method to study functions - specifically functions with three-dimensional graphs - and create images of the basin of attraction of the function. Three different methods are used to create these images named the systematic point method, randomized centroid method, and systemized centroid method. This paper applies these methods to different functions. The first function has two minima with an equivalent function value. The second function has one global minimum and one local minimum. …
Sensitivity Analysis Of Basins Of Attraction For Gradient-Based Optimization Methods, Gillian King
Sensitivity Analysis Of Basins Of Attraction For Gradient-Based Optimization Methods, Gillian King
Honors Projects
This project is an analysis of the effectiveness of five distinct optimization methods in their ability in producing clear images of the basins of attraction, which is the set of initial points that approach the same minimum for a given function. Basin images are similar to contour plots, except that they depict the distinct regions of points--in unique colors--that approach the same minimum. Though distinct in goal, contour plots are useful to basin research in that idealized basin images can be inferred from the steepness levels and location of extrema they depict. Effectiveness of the method changes slightly depending on …