Three-dimensional (3D) printing, also known as additive manufacturing (AM), has emerged in the last decades as an innovative technology to build complex structures. It enables increasing design complexity and low-cost customization with a vast range of materials. AM capabilities contributed to a widespread acceptance of 3D printing in different industries such as the aerospace and the automotive. However, important issues and limitations still need to be addressed, namely in printing complex objects where supports and material roughness surface are to be minimized. In this work we consider a 5–axis printer with the three traditional xyz movements and two additional degrees of freedom on the printer table bed. These extra degrees of freedom (table bed rotation and tilt) allow printing of more complex objects, and we propose an approach which consists on the decomposition of complex objects into simpler parts, allowing each part to be printed in an optimal way. We aim to reduce the number of supports needed and attain high final object quality due to lower material surface roughness. The optimal printing direction (or, equivalently, rotation) and sequencing of the object parts is determined by solving a combinatorial sequencing optimization problem. All the local or global optimal parts rotations are obtained by solving a global optimization sub-problem for each part, and are taken as input parameters for the sequencing optimization problem. We provide a heuristic approach for the combinatorial sequencing optimization problem, and a multistart multisplit search methodology for computing all the local or global optimal parts rotations for the sub-problems.

三维（3D）打印，也称为增材制造（AM），在过去的几十年中作为一种用于构建复杂结构的创新技术而出现。它可以使用多种材料来提高设计的复杂性和低成本的定制。AM功能推动了3D打印在航空航天和汽车等不同行业中的广泛接受。但是，仍然需要解决重要的问题和局限性，即在要打印复杂物体的过程中，要最小化支撑和材料粗糙表面。在这项工作中，我们考虑使用带有三个传统xyz的5轴打印机在打印机工作台上的运动和两个额外的自由度。这些额外的自由度（工作台旋转和倾斜）允许打印更复杂的对象，我们提出了一种方法，该方法包括将复杂的对象分解为更简单的部分，从而以最佳方式打印每个部分。我们的目标是减少所需的支撑件数量，并由于较低的材料表面粗糙度而获得较高的最终物体质量。通过解决组合排序优化问题来确定对象部分的最佳打印方向（或等效地，旋转）和排序。通过求解每个零件的全局优化子问题，可以获得所有局部或全局最优零件旋转，并将其用作排序优化问题的输入参数。