A variety of optimization algorithms have been developed to solve engineering design problems in which the solution space is too large to manually determine the optimal solution. The Modular Optimization Framework (MOF) was developed to facilitate the development and application of these optimization algorithms. MOF is written in Python 3, and it used object-oriented programming to create a modular design that allows users to easily incorporate new optimization algorithms, methods, or engineering design problems into the framework. Additionally, a common input file allows users to easily specify design problems, update the optimization parameters, and perform comparisons between various optimization methods and algorithms. In the current MOF version, genetic algorithm (GA) and simulated annealing (SA) approaches are implemented. Applications in different nuclear engineering optimization problems are included as examples. The effectiveness of the GA and SA optimization algorithms within MOF are demonstrated through an unconstrained nuclear fuel assembly pin lattice optimization, a first cycle fuel loading constrained optimization of a three-loop pressurized water reactor (PWR), and a third cycle constrained optimization of a four-loop PWR. In all cases, the algorithms efficiently searched the solution spaces and found optimized solutions to the given problems that satisfied the imposed constraints. These results demonstrate the capabilities of the existing optimization tools within MOF, and they also provide a set of benchmark cases that can be used to evaluate the progress of future optimization methodologies with MOF.