Swarm Intelligence and Metaphorless Algorithms for Solving Nonlinear Equation Systems - Ribeiro, Sérgio Gonçalves Sumares Betencourt (2023)
The simplicity, flexibility, and ease of implementation have motivated the use of population-based metaheuristic optimization algorithms. By focusing on two classes of such algorithms, particle swarm optimization (PSO) and the metaphorless Jaya algorithm, this thesis proposes to explore the capacity of these algorithms and their respective variants to solve difficult optimization problems, in particular systems of nonlinear equations converted into nonlinear optimization problems. For a numerical comparison to be made, the algorithms and their respective variants were implemented and tested several times in order to achieve a large sample that could be used to compare these approaches as well as find common methods that increase the effectiveness and efficiency of the algorithms. One of the approaches that was explored was dividing the solution search space into several subspaces, iteratively running an optimization algorithm on each subspace, and comparing those results to a greatly increased initial population. The insights from these previous experiments were then used to create a new hybrid approach to enhance the capabilities of the previous algorithms, which was then compared to preexisting alternatives.