{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T19:45:47Z","timestamp":1774381547831,"version":"3.50.1"},"reference-count":45,"publisher":"Association for Computing Machinery (ACM)","issue":"4","license":[{"start":{"date-parts":[[2024,11,28]],"date-time":"2024-11-28T00:00:00Z","timestamp":1732752000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-sa\/4.0\/"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["ACM Trans. Evol. Learn. Optim."],"published-print":{"date-parts":[[2024,12,31]]},"abstract":"<jats:p>Topology optimization is a powerful design tool in structural engineering and other engineering problems. The design domain is discretized into elements, and a finite element method model is iteratively solved to find the element that maximizes the structure's performance. Although gradient-based solvers have been used to solve topology optimization problems, they may be susceptible to suboptimal solutions or difficulty obtaining feasible solutions, particularly in non-convex optimization problems. The presence of non-convexities can hinder convergence, leading to challenges in achieving the global optimum. With this in mind, we discuss in this article the application of the quality diversity approach to topological optimization problems. Quality diversity (QD) algorithms have shown promise in the research field of optimization and have many applications in engineering design, robotics, and games. MAP-Elites is a popular QD algorithm used in robotics. In soft robotics, the MAP-Elites algorithm has been used to optimize the shape and control of soft robots, leading to the discovery of new and efficient motion strategies. This article introduces an approach based on MAP-Elites to provide diverse designs for structural optimization problems. Three fundamental topology optimization problems are used for experimental testing, and the results demonstrate the ability of the proposed algorithm to generate diverse, high-performance designs for those problems. Furthermore, the proposed algorithm can be a valuable engineering design tool capable of creating novel and efficient designs.<\/jats:p>","DOI":"10.1145\/3670693","type":"journal-article","created":{"date-parts":[[2024,6,5]],"date-time":"2024-06-05T07:54:01Z","timestamp":1717574041000},"page":"1-23","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":2,"title":["Evolutionary Seeding of Diverse Structural Design Solutions via Topology Optimization"],"prefix":"10.1145","volume":"4","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7959-4563","authenticated-orcid":false,"given":"Yue","family":"Xie","sequence":"first","affiliation":[{"name":"University of Cambridge, Cambridge, UK and CSIRO, Pullenvale, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8878-9012","authenticated-orcid":false,"given":"Josh","family":"Pinskier","sequence":"additional","affiliation":[{"name":"CSIRO, Pullenvale, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8676-7821","authenticated-orcid":false,"given":"Xing","family":"Wang","sequence":"additional","affiliation":[{"name":"CSIRO, Pullenvale, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-5012-7224","authenticated-orcid":false,"given":"David","family":"Howard","sequence":"additional","affiliation":[{"name":"CSIRO, Pullenvale, Australia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"320","published-online":{"date-parts":[[2024,11,28]]},"reference":[{"key":"e_1_3_1_2_1","doi-asserted-by":"crossref","first-page":"1642","DOI":"10.1109\/CEC.2016.7743985","volume-title":"Proceedings of the IEEE Congress on Evolutionary Computation (CEC \u201916)","author":"Aulig Nikola","year":"2016","unstructured":"Nikola Aulig and Markus Olhofer. 2016. State-based representation for structural topology optimization and application to crashworthiness. In Proceedings of the IEEE Congress on Evolutionary Computation (CEC \u201916). IEEE, 1642\u20131649."},{"key":"e_1_3_1_3_1","volume-title":"Topology Optimization: Theory, Methods, and Applications","author":"Bendsoe Martin P.","year":"2003","unstructured":"Martin P. Bendsoe and Ole Sigmund. 2003. Topology Optimization: Theory, Methods, and Applications. Springer Science & Business Media."},{"key":"e_1_3_1_4_1","doi-asserted-by":"publisher","DOI":"10.1002\/admt.202100361"},{"key":"e_1_3_1_5_1","doi-asserted-by":"publisher","DOI":"10.1109\/TEVC.2022.3152384"},{"key":"e_1_3_1_6_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.robot.2017.11.010"},{"key":"e_1_3_1_7_1","doi-asserted-by":"publisher","DOI":"10.1109\/TEVC.2010.2104157"},{"key":"e_1_3_1_8_1","volume-title":"Nonparametric Statistics: A Step-By-Step Approach","author":"Corder Gregory W.","year":"2014","unstructured":"Gregory W. Corder and Dale I. Foreman. 2014. Nonparametric Statistics: A Step-By-Step Approach. John Wiley & Sons."},{"key":"e_1_3_1_9_1","doi-asserted-by":"publisher","DOI":"10.1109\/TEVC.2017.2704781"},{"key":"e_1_3_1_10_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00158-013-0956-z"},{"key":"e_1_3_1_11_1","doi-asserted-by":"publisher","DOI":"10.1109\/TEVC.2017.2722101"},{"key":"e_1_3_1_12_1","first-page":"5922","volume-title":"Proceedings of the AAAI Conference on Artificial Intelligence","author":"Fontaine Matthew C.","year":"2021","unstructured":"Matthew C. Fontaine, Ruilin Liu, Ahmed Khalifa, Jignesh Modi, Julian Togelius, Amy K. Hoover, and Stefanos Nikolaidis. 2021. Illuminating mario scenes in the latent space of a generative adversarial network. In Proceedings of the AAAI Conference on Artificial Intelligence. AAAI Press, 5922\u20135930."},{"key":"e_1_3_1_13_1","article-title":"A quality diversity approach to automatically generating human-robot interaction scenarios in shared autonomy","author":"Fontaine Matthew C.","year":"2021","unstructured":"Matthew C. Fontaine and Stefanos Nikolaidis. 2021. A quality diversity approach to automatically generating human-robot interaction scenarios in shared autonomy. In Robotics: Science and Systems.","journal-title":"Robotics: Science and Systems"},{"key":"e_1_3_1_14_1","doi-asserted-by":"publisher","DOI":"10.1145\/358523.358553"},{"key":"e_1_3_1_15_1","doi-asserted-by":"crossref","unstructured":"Kang Gao Duy M. Doc Sheng Chu Gang Wu H. Alicia Kim and Carol A. Featherston. 2022. Robust topology optimization of structures under uncertain propagation of imprecise stochastic-based uncertain field. arXiv:2201.11513. Retrieved from https:\/\/arxiv.org\/abs\/2201.11513","DOI":"10.1016\/j.tws.2022.109238"},{"key":"e_1_3_1_16_1","doi-asserted-by":"crossref","first-page":"500","DOI":"10.1007\/978-3-319-99253-2_40","volume-title":"Proceedings of the 15th International Conference: Parallel Problem Solving from Nature\u2013PPSN XV","author":"Hagg Alexander","year":"2018","unstructured":"Alexander Hagg, Alexander Asteroth, and Thomas B\u00e4ck. 2018. Prototype discovery using quality-diversity. In Proceedings of the 15th International Conference: Parallel Problem Solving from Nature\u2013PPSN XV, Part I 15. Springer, 500\u2013511."},{"key":"e_1_3_1_17_1","doi-asserted-by":"crossref","first-page":"377","DOI":"10.1145\/3512290.3528870","volume-title":"Proceedings of the Genetic and Evolutionary Computation Conference (GECCO \u201922)","author":"Howard David","year":"2022","unstructured":"David Howard, Humphrey Munn, Davide Dolcetti, Josh Kannemeyer, and Nicole L. Robinson. 2022. Assessing evolutionary terrain generation methods for curriculum reinforcement learning. In Proceedings of the Genetic and Evolutionary Computation Conference (GECCO \u201922). ACM, 377\u2013384."},{"key":"e_1_3_1_18_1","doi-asserted-by":"publisher","DOI":"10.1002\/9780470689486"},{"key":"e_1_3_1_19_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00158-019-02442-0"},{"key":"e_1_3_1_20_1","doi-asserted-by":"publisher","DOI":"10.1162\/EVCO_a_00025"},{"key":"e_1_3_1_21_1","doi-asserted-by":"publisher","DOI":"10.1145\/2001576.2001606"},{"key":"e_1_3_1_22_1","doi-asserted-by":"publisher","DOI":"10.1109\/TEVC.2016.2638437"},{"key":"e_1_3_1_23_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00158-014-1107-x"},{"key":"e_1_3_1_24_1","doi-asserted-by":"crossref","first-page":"172","DOI":"10.3390\/rs15010172","article-title":"Tree reconstruction using topology optimisation","volume":"15","author":"Lowe Thomas","year":"2023","unstructured":"Thomas Lowe and Joshua Pinskier. 2023. Tree reconstruction using topology optimisation. Remote Sensing 15, 172 (2023), 1\u201324.","journal-title":"Remote Sensing"},{"key":"e_1_3_1_25_1","doi-asserted-by":"crossref","unstructured":"Valentin Mac\u00e9 Rapha\u00ebl Boige Felix Chalumeau Thomas Pierrot Guillaume Richard and Nicolas Perrin-Gilbert. 2023. The quality-diversity transformer: Generating behavior-conditioned trajectories with decision transformers. arXiv:2303.16207.","DOI":"10.1145\/3583131.3590433"},{"key":"e_1_3_1_26_1","doi-asserted-by":"publisher","DOI":"10.1145\/3449639.3459315"},{"key":"e_1_3_1_27_1","doi-asserted-by":"crossref","first-page":"129","DOI":"10.1145\/3449639.3459315","volume-title":"Proceedings of the Genetic and Evolutionary Computation Conference (GECCO \u201921)","author":"Medvet Eric","year":"2021","unstructured":"Eric Medvet, Alberto Bartoli, Federico Pigozzi, and Marco Rochelli. 2021b. Biodiversity in evolved voxel-based soft robots. In Proceedings of the Genetic and Evolutionary Computation Conference (GECCO \u201921). ACM, 129\u2013137."},{"key":"e_1_3_1_28_1","unstructured":"Jean-Baptiste Mouret and Jeff Clune. 2015. Illuminating search spaces by mapping elites. arXiv:1504.04909."},{"key":"e_1_3_1_29_1","doi-asserted-by":"publisher","DOI":"10.1145\/3377930.3390203"},{"key":"e_1_3_1_30_1","doi-asserted-by":"publisher","DOI":"10.1145\/1569901.1569988"},{"key":"e_1_3_1_31_1","doi-asserted-by":"publisher","DOI":"10.1162\/EVCO_a_00048"},{"key":"e_1_3_1_32_1","doi-asserted-by":"publisher","DOI":"10.1109\/TG.2021.3113313"},{"key":"e_1_3_1_33_1","doi-asserted-by":"publisher","DOI":"10.1145\/325165.325247"},{"key":"e_1_3_1_34_1","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1145\/3512290.3528823","volume-title":"Proceedings of the Genetic and Evolutionary Computation Conference (GECCO \u201922)","author":"Pierrot Thomas","year":"2022","unstructured":"Thomas Pierrot, Guillaume Richard, Karim Beguir, and Antoine Cully. 2022. Multi-objective quality diversity optimization. In Proceedings of the Genetic and Evolutionary Computation Conference (GECCO \u201922). ACM, 139\u2013147."},{"issue":"1","key":"e_1_3_1_35_1","doi-asserted-by":"crossref","first-page":"2100086","DOI":"10.1002\/aisy.202100086","article-title":"From bioinspiration to computer generation: Developments in autonomous soft robot design","volume":"4","author":"Pinskier Joshua","year":"2022","unstructured":"Joshua Pinskier and David Howard. 2022. From bioinspiration to computer generation: Developments in autonomous soft robot design. Advanced Intelligent Systems 4, 1 (2022), 2100086.","journal-title":"Advanced Intelligent Systems"},{"key":"e_1_3_1_36_1","first-page":"1","volume-title":"Proceedings of the IEEE International Conference on Soft Robotics (RoboSoft \u201923)","author":"Pinskier Josh","year":"2023","unstructured":"Josh Pinskier, Prabhat Kumar, Matthijs Langelaar, and David Howard. 2023. Automated design of pneumatic soft grippers through design-dependent multi-material topology optimization. In Proceedings of the IEEE International Conference on Soft Robotics (RoboSoft \u201923). Singapore, 1\u20137."},{"key":"e_1_3_1_37_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.mechmachtheory.2020.103874"},{"key":"e_1_3_1_38_1","doi-asserted-by":"publisher","DOI":"10.1007\/s001580050176"},{"key":"e_1_3_1_39_1","doi-asserted-by":"publisher","DOI":"10.1016\/S0045-7825(01)00251-1"},{"key":"e_1_3_1_40_1","doi-asserted-by":"publisher","DOI":"10.1007\/s10710-007-9028-8"},{"key":"e_1_3_1_41_1","doi-asserted-by":"publisher","DOI":"10.1007\/s00158-013-0999-1"},{"key":"e_1_3_1_42_1","first-page":"417","volume-title":"Proceedings of the IEEE 17th International Conference on Computer Supported Cooperative Work in Design (CSCWD \u201913)","author":"Wang Xiaohui","year":"2013","unstructured":"Xiaohui Wang, Zhiwei Lin, and Renwei Xia. 2013. SIMP based topology optimization of a folding wing with mixed design variables. In Proceedings of the IEEE 17th International Conference on Computer Supported Cooperative Work in Design (CSCWD \u201913). IEEE, 417\u2013421."},{"key":"e_1_3_1_43_1","doi-asserted-by":"publisher","DOI":"10.1145\/237170.237267"},{"key":"e_1_3_1_44_1","doi-asserted-by":"publisher","DOI":"10.1016\/j.addma.2023.103545"},{"key":"e_1_3_1_45_1","first-page":"191","article-title":"Multi-functional topology optimization of Victoria cruziana veins","volume":"19","author":"Zhang Hui-Kai","year":"2022","unstructured":"Hui-Kai Zhang, Jingyi Zhou, Wei Fang, Huichan Zhao, Zi-Long Zhao, Xindong Chen, Hong-Ping Zhao, and Xi-Qiao Feng. 2022. Multi-functional topology optimization of Victoria cruziana veins. Journal of the Royal Society Interface 19, 191 (2022), 20220298.","journal-title":"Journal of the Royal Society Interface"},{"key":"e_1_3_1_46_1","doi-asserted-by":"publisher","DOI":"10.1016\/0045-7825(91)90046-9"}],"container-title":["ACM Transactions on Evolutionary Learning and Optimization"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3670693","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/3670693","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,19]],"date-time":"2025-06-19T00:58:21Z","timestamp":1750294701000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/3670693"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,11,28]]},"references-count":45,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2024,12,31]]}},"alternative-id":["10.1145\/3670693"],"URL":"https:\/\/doi.org\/10.1145\/3670693","relation":{},"ISSN":["2688-3007"],"issn-type":[{"value":"2688-3007","type":"electronic"}],"subject":[],"published":{"date-parts":[[2024,11,28]]},"assertion":[{"value":"2023-05-01","order":0,"name":"received","label":"Received","group":{"name":"publication_history","label":"Publication History"}},{"value":"2024-05-28","order":2,"name":"accepted","label":"Accepted","group":{"name":"publication_history","label":"Publication History"}},{"value":"2024-11-28","order":3,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}