This article introduces an innovative design automation method aimed at systematically exploring and categorizing various 3D spatial layouts within interconnected engineering systems, encompassing diverse applications such as automotive cooling systems and building HVAC designs. Employing spatial graphs to depict component connectivity, the authors seek to unveil a spectrum of unique design alternatives capable of meeting the complex requirements of these systems. This methodology empowers engineers to efficiently explore a broad array of spatial configurations, potentially yielding creative solutions to enhance system performance and functionality. Demonstrating the inadequacies of manual approaches, the study underscores the significance of automated methods in design exploration, facilitating a more exhaustive examination of design possibilities. Through practical illustrations like automotive fuel cell cooling system design, the framework’s efficacy is showcased, leveraging mathematical tools such as Yamada polynomials to swiftly identify and distill unique designs, thus furnishing invaluable insights for engineers. This groundbreaking approach not only streamlines the design process but also fosters exploration of novel design avenues.