{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T21:57:52Z","timestamp":1773784672253,"version":"3.50.1"},"reference-count":63,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2024,12,6]],"date-time":"2024-12-06T00:00:00Z","timestamp":1733443200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper investigates the possibility of the application of different optimization techniques in the design and production planning phase in the metal additive manufacturing process, specifically laser powder bed fusion (L-PBF) additive technology. This technology has a significant market share and belongs to the group of mature additive technology for the production of end-use metal parts. In the application of this technology, there is a space for additional cost\/time reduction by simultaneously optimizing topology structure and part orientations. Simultaneous optimization reduces the production time and, indirectly, the cost of parts production, which is the goal of effective process planning. The novelty in this paper is the comparison of the part orientation solutions defined by the software algorithm and the experienced operator, where the optimal result was selected from the aspect of time and production costs. A feature recognition method together with symmetry operations in the part orientation process were also examined. A framework for the optimal additive manufacturing planning process has been proposed. This framework consists of design and production planning phases, within which there are several other activities: the redesign of the part, topological optimization, the creation of alternative build orientations (ABOs), and, as a final step, the selection of the optimal build orientation (OBO) using the multi-criteria decision method (MCDM). The results obtained after the MCDM hybrid method application clearly indicated that simultaneous topology optimization and part orientation has significant influence on the cost and time of the additive manufacturing process. The paper also proposed a further research direction that should take into consideration the mechanical as well as geometric, dimensioning and tolerances (GDT) characteristics of the part during the process of ABOs and OBO, as well as the uses of symmetry in these fields.<\/jats:p>","DOI":"10.3390\/sym16121616","type":"journal-article","created":{"date-parts":[[2024,12,6]],"date-time":"2024-12-06T06:25:16Z","timestamp":1733466316000},"page":"1616","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":3,"title":["Topology Optimization, Part Orientation, and Symmetry Operations as Elements of a Framework for Design and Production Planning Process in Additive Manufacturing L-PBF Technology"],"prefix":"10.3390","volume":"16","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-5053-4033","authenticated-orcid":false,"given":"Slobodan","family":"Malba\u0161i\u0107","sequence":"first","affiliation":[{"name":"Department for Defence Technologies, 11000 Belgrade, Serbia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2856-6578","authenticated-orcid":false,"given":"Aleksandar","family":"\u0110or\u0111evi\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Engineering, University of Kragujevac, 34000 Kragujevac, Serbia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2241-7344","authenticated-orcid":false,"given":"Sr\u0111an","family":"\u017divkovi\u0107","sequence":"additional","affiliation":[{"name":"Military Technical Institute, 11000 Belgrade, Serbia"}]},{"given":"Dragan","family":"D\u017euni\u0107","sequence":"additional","affiliation":[{"name":"Faculty of Engineering, University of Kragujevac, 34000 Kragujevac, Serbia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0782-0506","authenticated-orcid":false,"given":"Vlada","family":"Sokolovi\u0107","sequence":"additional","affiliation":[{"name":"Military Academy, University of Defence, 11000 Belgrade, Serbia"}]}],"member":"1968","published-online":{"date-parts":[[2024,12,6]]},"reference":[{"key":"ref_1","unstructured":"Sarah Gaffney (2024, April 24). The Benefits of Simulation-Driven Design. Available online: https:\/\/resources.sw.siemens.com\/en-US\/white-paper-benefits-of-simulation-driven-design."},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Sheng, H., Xu, J., Zhang, S., Tan, J., and Wang, K. (2023). Build Orientation Determination of Multi-Feature Mechanical Parts in Selective Laser Melting via Multi-Objective Decision Making. Front. Mech. Eng., 18.","DOI":"10.1007\/s11465-022-0737-8"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/j.matpr.2022.02.604","article-title":"A Review on Additive Manufacturing and Topology Optimization Process for Weight Reduction Studies in Various Industrial Applications","volume":"62","author":"Prathyusha","year":"2022","journal-title":"Mater. Today Proc."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"710","DOI":"10.1016\/j.promfg.2020.10.100","article-title":"Planning for Metal Additive Manufacturing","volume":"51","author":"Dotcheva","year":"2020","journal-title":"Procedia Manuf."},{"key":"ref_5","unstructured":"Liu, Z. (2017). Economic Comparison of Selective Laser Melting and Conventional Subtractive Manufacturing Processes. [Master\u2019s Thesis, Northeastern University Boston]."},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Luo, Z., Yang, F., Dong, G., Tang, Y., and Zhao, Y.F. (2016, January 21\u201324). Orientation Optimization in Layer-Based Additive Manufacturing Process. Proceedings of the ASME 2016 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference, Charlotte, NC, USA.","DOI":"10.1115\/DETC2016-59969"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"698","DOI":"10.1108\/RPJ-12-2016-0208","article-title":"An Automatic and Optimal Selection of Parts Orientation in Additive Manufacturing","volume":"24","author":"Abdulhameed","year":"2018","journal-title":"Rapid Prototyp. J."},{"key":"ref_8","unstructured":"(2021). Additive Manufacturing\u2014General Principles\u2014Fundamentals and Vocabulary (Standard No. ISO\/ASTM 52900:2021)."},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Dietrich, D.M., Cudney, E.A., and Kenworthy, M. (2019). Additive Manufacturing Change Management\u2014Best Practices, CRC Press, Taylor & Francis Group.","DOI":"10.1201\/9780429465246"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"6484","DOI":"10.1016\/j.jmrt.2023.11.049","article-title":"Laser Powder Bed Fusion of Metallic Components: Latest Progress in Productivity, Quality, and Cost Perspectives","volume":"27","author":"Taghian","year":"2023","journal-title":"J. Mater. Res. Technol."},{"key":"ref_11","doi-asserted-by":"crossref","unstructured":"Wang, H., and Fuh, J.Y.H. (2023). Metal Additive Manufacturing and Its Post-Processing Techniques. J. Manuf. Mater. Process., 7.","DOI":"10.3390\/jmmp7010047"},{"key":"ref_12","first-page":"011008","article-title":"Focus Variation Measurement and Prediction of Surface Texture Parameters Using Machine Learning in Laser Powder Bed Fusion","volume":"142","author":"Altay","year":"2019","journal-title":"J. Manuf. Sci. Eng."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"57","DOI":"10.1007\/s00170-020-05825-6","article-title":"Manufacturability Analysis of Metal Laser-Based Powder Bed Fusion Additive Manufacturing\u2014A Survey","volume":"110","author":"Zhang","year":"2020","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_14","doi-asserted-by":"crossref","unstructured":"Gibson, I., Rosen, D., Stucker, B., and Khorasani, M. (2021). Additive Manufacturing Technologies, Springer Nature. [3rd ed.].","DOI":"10.1007\/978-3-030-56127-7"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2399","DOI":"10.1017\/pds.2021.501","article-title":"Part orientation and separation to reduce process costs in additive manufacturing","volume":"1","author":"Reichwein","year":"2021","journal-title":"Proc. Des. Soc."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"061701","DOI":"10.1115\/1.4042112","article-title":"Concurrent Structure and Process Optimization for Minimum Cost Metal Additive Manufacturing","volume":"141","author":"Ulu","year":"2019","journal-title":"J. Mech. Des."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"114227","DOI":"10.1016\/j.cma.2021.114227","article-title":"Simultaneous Optimization of Build Orientation and Topology for Self-Supported Enclosed Voids in Additive Manufacturing","volume":"388","author":"Wang","year":"2021","journal-title":"Comput. Methods Appl. Mech. Eng."},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"107453","DOI":"10.1016\/j.compstruc.2024.107453","article-title":"A Thermal Model for Topology Optimization in Additive Manufacturing: Design of Support Structures and Geometry Orientation","volume":"301","author":"Haveroth","year":"2024","journal-title":"Comput. Struct."},{"key":"ref_19","unstructured":"Livesu, M., Attene, M., Spagnuolo, M., and Falcidieno, B. (2024, May 28). A Study of the State of the Art of Process Planning for Additive Manufacturing. Available online: https:\/\/irs.imati.cnr.it\/reports\/irs16-04."},{"key":"ref_20","first-page":"8674","article-title":"A Framework for Production Planning in Additive Manufacturing","volume":"61","author":"Poza","year":"2022","journal-title":"Int. J. Prod. Res."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"5425","DOI":"10.1007\/s00170-024-13042-8","article-title":"Powder Bed Fusion Integrated Product and Process Design for Additive Manufacturing: A Systematic Approach Driven by Simulation","volume":"130","author":"Dalpadulo","year":"2024","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Di Angelo, L., Di Stefano, P., and Guardiani, E. (2020). Search for the Optimal Build Direction in Additive Manufacturing Technologies: A Review. J. Manuf. Mater. Process., 4.","DOI":"10.3390\/jmmp4030071"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"1544","DOI":"10.1108\/RPJ-01-2018-0002","article-title":"A Decision Support System for Additive Manufacturing Process Selection Using a Hybrid Multiple Criteria Decision-Making Method","volume":"24","author":"Wang","year":"2018","journal-title":"Rapid Prototyp. J."},{"key":"ref_24","first-page":"100014","article-title":"Roadmap for Additive Manufacturing: Toward Intellectualization and Industrialization","volume":"1","author":"Tian","year":"2022","journal-title":"Chin. J. Mech. Eng. Addit. Manuf. Front."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Balasubramanian, K.R., and Senthilkumar, V. (2020). Optimization and simulation of additive manufacturing processes: Challenges and opportunities\u2014A review. Advances in Civil and Industrial Engineering, IGI Global.","DOI":"10.4018\/978-1-7998-4054-1"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/j.cja.2020.09.020","article-title":"A Review of Topology Optimization for Additive Manufacturing: Status and Challenges","volume":"34","author":"Zhu","year":"2020","journal-title":"Chin. J. Aeronaut."},{"key":"ref_27","doi-asserted-by":"crossref","unstructured":"Mat\u00fa\u0161, M., Kri\u017ean, P., Kijovsk\u00fd, J., Strig\u00e1\u010d, S., Beniak, J., and \u0160oo\u0161, L. (2023). Implementation of Finite Element Method Simulation in Control of Additive Manufacturing to Increase Component Strength and Productivity. Symmetry, 15.","DOI":"10.3390\/sym15112036"},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"408","DOI":"10.1016\/j.procir.2016.05.016","article-title":"Considering Part Orientation in Design for Additive Manufacturing","volume":"50","author":"Klahn","year":"2016","journal-title":"Procedia CIRP"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"1295","DOI":"10.1007\/s00170-021-06996-6","article-title":"Status, Issues, and Future of Computer-Aided Part Orientation for Additive Manufacturing","volume":"115","author":"Qin","year":"2021","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"674","DOI":"10.1007\/s001700050118","article-title":"Part Orientation in Stereolithography","volume":"15","author":"Pham","year":"1999","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"69","DOI":"10.1016\/j.rcim.2005.03.001","article-title":"Determination of the Optimal Build Direction for Different Rapid Prototyping Processes Using Multi-criterion Decision Making","volume":"22","author":"Byun","year":"2005","journal-title":"Robot. Comput. Manuf."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"1647","DOI":"10.1108\/RPJ-12-2018-0309","article-title":"Personalized Design of Part Orientation in Additive Manufacturing","volume":"25","author":"Yu","year":"2019","journal-title":"Rapid Prototyp. J."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"187","DOI":"10.1108\/RPJ-04-2018-0102","article-title":"A Statistical Method for Build Orientation Determination in Additive Manufacturing","volume":"25","author":"Zhang","year":"2019","journal-title":"Rapid Prototyp. J."},{"key":"ref_34","unstructured":"Gade, P.K., and Osuri, M. (2014). Evaluation of Multi Criteria Decision Making Methods for Potential Use in Application Security. [Master\u2019s Thesis, School of Computing, Blekinge Institute of Technology]."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"358","DOI":"10.1108\/RPJ-03-2014-0037","article-title":"Feature Based Building Orientation Optimization for Additive Manufacturing","volume":"22","author":"Zhang","year":"2016","journal-title":"Rapid Prototyp. J."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1007\/BF00124677","article-title":"Expert system-based selection of the preferred direction of build for rapid prototyping processes","volume":"6","author":"Frank","year":"1995","journal-title":"J. Intell. Manuf."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"43","DOI":"10.1007\/s40964-017-0018-y","article-title":"Holistic Approach for Industrializing AM Technology: From Part Selection to Test and Verification","volume":"2","author":"Reiher","year":"2017","journal-title":"Prog. Addit. Manuf."},{"key":"ref_38","unstructured":"Pecharsky, V.K., and Zavalij, P.V. (2009). Finite Symmetry Elements and Crystallographic Point Groups. Fundamentals of Powder Diffraction and Structural Characterization of Materials, Springer."},{"key":"ref_39","doi-asserted-by":"crossref","unstructured":"Uralde, V., Veiga, F., Suarez, A., Aldalur, E., and Ballesteros, T. (2023). Symmetry Analysis in Wire Arc Direct Energy Deposition for Overlapping and Oscillatory Strategies in Mild Steel. Symmetry, 15.","DOI":"10.3390\/sym15061231"},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"2935","DOI":"10.1007\/s00170-023-11205-7","article-title":"Symmetry-Based Decomposition for Optimised Parallelisation in 3D Printing Processes","volume":"127","author":"Hatton","year":"2023","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_41","doi-asserted-by":"crossref","unstructured":"Hedjazi, L., Belhabib, S., D\u2019orlando, A., and Guessasma, S. (2022). Breaking Material Symmetry to Control Mechanical Performance in 3D Printed Objects. Symmetry, 15.","DOI":"10.3390\/sym15010028"},{"key":"ref_42","first-page":"39","article-title":"Recursive Symmetries for Geometrically Complex and Materially Heterogeneous Additive Manufacturing","volume":"81","author":"Bader","year":"2016","journal-title":"Comput. Des."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Uralde, V., Veiga, F., Aldalur, E., Suarez, A., and Ballesteros, T. (2022). Symmetry and its application in metal additive manufacturing (MAM). Symmetry, 14.","DOI":"10.3390\/sym14091810"},{"key":"ref_44","first-page":"1141","article-title":"Multicriteria Decision Analysis Framework for Part Orientation Analysis in Additive Manufacturing","volume":"8","author":"Ransikarbum","year":"2021","journal-title":"J. Comput. Des. Eng."},{"key":"ref_45","doi-asserted-by":"crossref","first-page":"4039253","DOI":"10.1155\/2020\/4039253","article-title":"Assessment and Comparison of Various MCDM Approaches in the Selection of Manufacturing Process","volume":"2020","author":"Ghaleb","year":"2020","journal-title":"Adv. Mater. Sci. Eng."},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"106948","DOI":"10.1016\/j.asoc.2020.106948","article-title":"AHP Integrated TOPSIS and VIKOR Methods with Pythagorean Fuzzy Sets to Prioritize Risks in Self-Driving Vehicles","volume":"99","author":"Bakioglu","year":"2020","journal-title":"Appl. Soft Comput."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"100115","DOI":"10.1016\/j.rinma.2020.100115","article-title":"Application of MCDM Method in Material Selection for Optimal Design: A Review","volume":"7","author":"Emovon","year":"2020","journal-title":"Results Mater."},{"key":"ref_48","doi-asserted-by":"crossref","first-page":"121824","DOI":"10.1016\/j.eswa.2023.121824","article-title":"Comparative Analysis of Three Categories of Multi-Criteria Decision-Making Methods","volume":"238","author":"Li","year":"2023","journal-title":"Expert Syst. Appl."},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Bachchhav, B., Bharne, S., Choudhari, A., and Pattanshetti, S. (2023). Selection of Spot Welding Electrode Material by AHP, TOPSIS, and SAW. Mater. Today Proc., S2214785323007976.","DOI":"10.1016\/j.matpr.2023.02.253"},{"key":"ref_50","first-page":"100232","article-title":"A Comprehensive and Systematic Review of Multi-Criteria Decision-Making Methods and Applications in Healthcare","volume":"4","author":"Chakraborty","year":"2023","journal-title":"Health Anal."},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"106648","DOI":"10.1016\/j.cie.2020.106648","article-title":"Weight Assignment Method for Multiple Attribute Decision Making with Dissimilarity and Conflict of Belief Distributions","volume":"147","author":"Zhou","year":"2020","journal-title":"Comput. Ind. Eng."},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"118644","DOI":"10.1016\/j.foreco.2020.118644","article-title":"Forest Fire Susceptibility Mapping via Multi-Criteria Decision Analysis Techniques for Mugla, Turkey: A Comparative Analysis of VIKOR and TOPSIS","volume":"480","author":"Sari","year":"2020","journal-title":"For. Ecol. Manag."},{"key":"ref_53","unstructured":"Safian, E.E.M., and Nawawi, A.H. (2024, May 10). The Evolution of Analytical Hierarchy Process (AHP) as a Decision Making Tool in Property Sectors. Available online: https:\/\/www.researchgate.net\/publication\/254445031."},{"key":"ref_54","first-page":"51","article-title":"A Sensitivity Analysis in MCDM Problems: A Statistical Approach","volume":"1","author":"Mukhametzyanov","year":"2018","journal-title":"Decis. Making Appl. Manag. Eng."},{"key":"ref_55","unstructured":"Milo\u0161, M., Bogdan, N., and Miroslav, R. (2015). Business and Engineering Decision-Making Using Multi-Criteria Optimization Methods, Faculty of Engineering Sciences, University of Kragujevac."},{"key":"ref_56","unstructured":"Dragan, P. (2017). Operational Research\u2014Deterministic Methods and Models, RABEK."},{"key":"ref_57","doi-asserted-by":"crossref","first-page":"293","DOI":"10.1017\/pds.2023.30","article-title":"a multi-criteria decision-making approach to optimize the part build orientation in additive manufacturing","volume":"3","author":"Sartini","year":"2023","journal-title":"Proc. Des. Soc."},{"key":"ref_58","first-page":"31","article-title":"Ranking of key performance indicators of the overhaul process of technical systems","volume":"31","author":"Vladimir","year":"2024","journal-title":"Int. J. Ind. Eng. Theory Appl. Pract."},{"key":"ref_59","doi-asserted-by":"crossref","first-page":"382","DOI":"10.1080\/17452759.2021.2018938","article-title":"A Review on Qualification and Certification for Metal Additive Manufacturing","volume":"17","author":"Chen","year":"2021","journal-title":"Virtual Phys. Prototyp."},{"key":"ref_60","unstructured":"Lamei, Z. (2021). A Comprehensive Cost Estimation for Additive Manufacturing. [Master\u2019s Thesis, Faculty of the Graduate School of Wichita State University]."},{"key":"ref_61","doi-asserted-by":"crossref","first-page":"208","DOI":"10.1108\/13552541311312201","article-title":"An Integrated Cost-Model for Selective Laser Melting (SLM)","volume":"19","author":"Rickenbacher","year":"2013","journal-title":"Rapid Prototyp. J."},{"key":"ref_62","doi-asserted-by":"crossref","first-page":"4275","DOI":"10.1007\/s00170-017-0492-x","article-title":"A New Mixed Production Cost Allocation Model for Additive Manufacturing (MiProCAMAM)","volume":"92","author":"Fera","year":"2017","journal-title":"Int. J. Adv. Manuf. Technol."},{"key":"ref_63","doi-asserted-by":"crossref","first-page":"11","DOI":"10.61552\/JEMIT.2023.01.002","article-title":"The role of the cost and quality in additive manufacturing","volume":"1","year":"2023","journal-title":"J. Eng. Manag. Inf. Technol."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/12\/1616\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T16:48:33Z","timestamp":1760114913000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/16\/12\/1616"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,12,6]]},"references-count":63,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2024,12]]}},"alternative-id":["sym16121616"],"URL":"https:\/\/doi.org\/10.3390\/sym16121616","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,12,6]]}}}