The nutritional consequences of progressively replacing meat products with plant-based foods need to be systematically evaluated. Modeling analyses provide insights into the predicted food consumption and nutritional adequacy of plant-based diets. We developed a novel methodology to simulate food patterns and evaluate diet quality. Meal data from the National Health and Nutrition Examination Survey (NHANES) 2017–2018 was used to create 100 7-day meal plans subject to various nutrient and food group optimization criteria. Omnivore (reference diet), flexitarian, pescatarian, and vegetarian food patterns were modeled using mixed integer linear programming. The modeled food patterns used the 25th and 75th percentiles of the US Usual Dietary Intakes to set the optimization constraints. The diet quality was determined using the Healthy Eating Index 2015 (HEI-2015). The modeled vegetarian, pescatarian, and flexitarian food patterns outperformed the omnivore diet on the HEI-2015, with the vegetarian pattern achieving the highest score (82 for females, 78 for males). Modeled flexitarian patterns, with a 25 to 75% reduction in animal protein, offer viable options for those seeking to reduce but not eliminate their animal protein intake while supporting the transition from omnivore to fully plant-based diets. This methodology could be applied to evaluate the nutrient and diet quality of different dietary patterns with various constraints.