Stock design in hybrid manufacturing using a constrained clustering approach

Hybrid Manufacturing (HM) is a key pillar of smart manufacturing, enabling the production of complex parts with high precision and superior surface quality while minimizing costs and enhancing sustainability. A key challenge in HM systems is selecting the appropriate stock geometry to initiate processing both additive and subtractive features while achieving these benefits. Poor stock design can lead to increased waste and energy consumption, whereas an optimized configuration improves operational efficiency and maximizes sustainability. This paper addresses finding stock designs in HM, a problem that has not been tackled before using hybridized machine learning optimization techniques. A constrained clustering machine learning approach to determine stock dimensions for prismatic end parts is proposed. Given the geometry of the features included in these end parts, a novel combinatorial optimization model is developed to assign these features to pre-defined clusters such that the Hausdorff distance between features within clusters is minimized. Multiple scenarios are explored by evaluating different numbers of clusters. The proposed optimization model is validated, and its computational efficiency is evaluated through a case study that includes two test parts extending an existing test part from the literature. The first test part includes 22 additive and subtractive features while the other one includes 27 features. Due to the intractability of this combinatorial optimization clustering problem, problem instances representing small and medium-sized scenarios can be solved to optimality within a short time, whereas for large instances, only feasible solutions are obtained within a limited computational time of two hours.