Gas turbine combustor design is a complex multi-objective problem. In the present study, parametric design space study and optimization of a gas turbine combustor using computational fluid dynamics (CFD) simulations is presented. Baseline case validation, automated workflow setup for geometry modification, meshing, boundary condition specification, CFD solution and output parameter calculations are discussed. Response surface methodology is used to study combustor performance based on combustion efficiency, pattern factor, total pressure drop, Carbon monoxide (CO) and Nitrogen oxides (NOx) with variations in three design variables: swirl number, secondary hole diameter and dilution hole diameter. We use central composite design for design of experiments (DOE) and genetic aggregation for response surface generation. Design space refinement is carried out to identify the blow-off region and limit the search space for optimal designs to swirl number greater than 0.9. Exclusion of blow-off design points while generating the response surface resulted not only in 57.2% average reduction of root mean square error in the response surface predictions but also smoother trends away from the blow-off region. A candidate optimal design point with swirl number = 1.0, secondary hole diameter = 12.24 mm and dilution hole diameter = 15.26 mm is chosen using multi objective genetic algorithm on the response surface. Finally, uncertainty quantification with six sigma DOE analysis quantifies the confidence intervals for performance parameters based on the variations in geometric design variables. This preliminary design methodology can be used to improve existing combustors and guide the design of novel combustor concepts.