During a conceptual design effort we find we are making the most far-reaching decisions on product and process form and robustness, while under great pressure to quickly definitize the product. Success is a function of how well we optimize to market needs and producibility, among other constraints. In this paper we focus on implementation of optimization early in the design process, within the structured environment of the House of Quality. Using a normalized weighting format for parameter correlations and relationships, several formulations are presented and discussed, each with its own appropriate use. Using mathematical programming techniques, opportunities exist to greatly reduce the rank of the matrix, facilitating early design iteration and optimization. We present several new roles for the correlation matrix, or roof of the house of quality, which to date has been underutilized in product optimization. Formulations are proposed to employ design information contained in the roof to facilitate concurrent design optimization and management of complexity at the early stages of design.