Many real world problems in science and engineering can be treated as optimization problems with multiple objectives or criteria. The demand for fast and robust stochastic algorithms to cater to the optimization needs is very high. When the cost function for the problem is nonlinear and non-differentiable, direct search approaches are the methods of choice. Many such approaches use the greedy criterion, which is based on accepting the new parameter vector only if it reduces the value of the cost function. This could result in fast convergence, but also in misconvergence where it could lead the vectors to get trapped in local minima. Inherently, parallel search techniques have more exploratory power. These techniques discourage premature convergence and consequently, there are some candidate solution vectors which do not converge to the global minimum solution at any point of time. Rather, they constantly explore the whole search space for other possible solutions.;In this thesis, we concentrate on benchmarking three popular algorithms: Real-valued Genetic Algorithm (RGA), Particle Swarm Optimization (PSO), and Differential Evolution (DE). The DE algorithm is found to out-perform the other algorithms in fast convergence and in attaining low-cost function values. The DE algorithm is selected and used to build a model for forecasting auroral oval boundaries during a solar storm event. This is compared against an established model by Feldstein and Starkov. As an extended study, the ability of the DE is further put into test in another example of a nonlinear system study, by using it to study and design phase-locked loop circuits. In particular, the algorithm is used to obtain circuit parameters when frequency steps are applied at the input at particular instances.
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