This paper evaluates the cost competitiveness of microreactors in today's electricity markets, with a focus on uncertainties in reactor costs. A Genetic Algorithm (GA) is used to optimize key technical parameters, such as reactor capacity, fuel enrichment, tail enrichment, refueling interval, and discharge burnup, to minimize the Levelized Cost of Energy (LCOE). Base case results are validated using Simulated Annealing (SA). By incorporating Probability Distribution Functions (PDFs) for fuel cycle costs, the study identifies optimal configurations under uncertainty. Methodologically, it introduces a novel framework combining probabilistic cost modeling with evolutionary optimization. Results show that microreactors can remain cost-competitive, with LCOEs ranging from \$48.21/MWh to \$78.32/MWh when supported by the Production Tax Credit (PTC). High reactor capacity, low fuel enrichment, moderate tail enrichment and refueling intervals, and high discharge burnup enhance cost efficiency. Among all factors, overnight capital cost (OCC) has the most significant impact on LCOE, while O&M and fuel cost uncertainties have lesser effects. The analysis highlights how energy policies like the PTC can reduce LCOE by 22-24%, improving viability despite cost variability. Compared to conventional nuclear, coal, and renewable sources like offshore wind, hydro, and biomass, optimized microreactors show strong economic potential. This research defines a realistic design space and key trade-offs, offering actionable insights for policymakers, reactor designers, and energy planners aiming to accelerate the deployment of affordable, sustainable microreactors.