The present disclosure describes various systems and methods for creating and presenting optimization visualizations that use normalized achievement variables. At least one illustrative method includes defining achievement functions that each operates on at least one of several achievement variables (each of the achievement variables representing a characteristic of a physical object or process), and transforming value ranges for at least two achievement variables into corresponding achievement level ranges by applying at least one of the achievement functions to the value ranges of the achievement variables (the achievement variables being a function of at least one common control variable). The method further includes combining the corresponding achievement level ranges to produce a combined achievement level range, and presenting a visual representation of the combined achievement level range to a user, enabling the user to select value ranges for the common control variable.