In this study, a multiobjective, multiperiod, global optimization for design, sizing and dispatch of an islanded, hybrid microgrid was performed using a model built in MATLAB. The system was simulated over one year for sizing and over one day for dispatch, both using hourly time steps. The model minimized lifecycle levelized costs, emissions, lost load and dumped power while maximizing penetration of clean, renewable sources in the microgrid. This found optimal capacities of the renewable, energy storage and backup generation components which provide the best combination of affordability, sustainability, reliability and efficiency. After experimenting with several global solvers, it was determined that particle swarm optimization is most well-suited to solving the sizing optimization problem. The PV-wind microgrid using Li-ion batteries along with diesel engines was found to perform best among all the combinations considered. It was found that in spite of including additional objectives, monetary costs are the primary driver while allocating generation capacity between different renewable sources like wind versus solar PV. Furthermore, the sizing of PV, wind and battery storage depends strongly on the rating of the standby distributed generator, mainly due to reliability consideration. Generating Pareto-optimal sets revealed interesting relationships between different input variables (i.e. PV, wind and battery capacities) as well as trade-offs that arise while pursuing different objectives. Pursuing cost-minimization alone may lead to sub-optimal outcomes in terms of environmental impact, reliability and excess energy production. A sensitivity analysis was also conducted to understand the effects of various parameters like fuel price and energy storage costs on the optimal system's design and operation. Such accurate sizing programs help reduce the extent of oversizing of sub-systems during the design and planning stage, which is usually needed to achieve high reliability with distributed and decentralized energy systems like off-grid microgrids. This reduces the upfront capital investment needed to build the system, making clean electricity access affordable in the short term. The economic-environmental dispatch produced day-ahead scheduling strategies to meet the above mentioned objectives. The system was found to be relatively robust to short-term uncertainties and disturbances in renewable generation and load, although this does cause sub-optimal performance due to increased reliance on fossil fuels. It was found that dispatching of the batteries and backup generators is most critical in minimizing impacts of such events. However, the response to longer-term disturbances still remains to be assessed. The study also includes a comprehensive literature review of tools available for microgrid design as well as different optimization algorithms that have been used to solve microgrid sizing, dispatch and scheduling problems. Additionally, an overview is provided of various control strategies that can be used to improve robustness and resiliency of microgrids.