The　architecture,　engineering,　and　construction　sector　has　stressed　the　concepts　of　efficiency　and　sustainability　because　of　the　industry’s　high　resource　consumption.　Efficiency　is　a　major　criterion　for　building　large-scale　structures　in　order　to　meet　performance　requirements　while　using　the　least　amount　of　structural　material.　With　the　emergence　and　development　of　computer　tools,　mathematical　computation-based　structural　optimization　has　become　a　popular　way　of　designing　sustainable　and　efficient　buildings.　Classical　and　traditional　procedures　might　not　always　produce　an　optimal　solution　effectively　because　optimization　problems　are　often　non-linear,　discontinuous　and　complex.　As　a　result　of　their　versatility,　metaheuristic　algorithms　have　grown　in　popularity,　notably　in　the　engineering　profession.　The　effectiveness　of　different　meta-heuristic　algorithms,　including　the　Genetic　Algorithm　(GA),　Simulated　Annealing　(SA,　and　Estimation　of　Distribution　Algorithm　(EDA),　is　investigated　in　this　work.　As　a　case　study,　a　parametric　arch　structure　is　utilized.　Numerical　results　are　achieved　by　minimizing　structural　weight　while　checking　that　the　Von　Mises　stress　is　lower　than　the　yielding　limit　all　along　the　arch.　Three　single-objective　algorithms　are　used　in　the　study,　and　their　performance　is　objectively　evaluated.　The　parametric　modeling,　structural　analysis,　and　optimization　phases　are　conducted　entirely　in　the　virtual　environment　offered　by　the　software　packages　Rhino,　Grasshopper,　Karamba,　and　Galapagos.　These　interoperable　software　programs　were　chosen　because　of　their　flexibility,　customizability,　and　widespread　usage　in　engineering　and　architectural　offices,　making　the　techniques　and　findings　of　this　study　valuable　to　design　practitioners.　©　The　Author(s),　under　exclusive　license　to　Springer　Nature　Switzerland　AG　2025.