other Optimal design Optimal design پژوهشي Research <span style="font-size:11.5pt"><span style="text-justify:inter-ideograph"><span style="text-autospace:none"><span new="" roman="" style="font-family:" times="">This paper introduces a novel two-phase metamodel-driven methodology for the simultaneous topology and size optimization of truss structures. The approach addresses critical limitations in computational efficiency and solution quality. The framework integrates the Flexible Stochastic Gradient Optimizer (FSGO) with adaptive sampling and machine learning to minimize the number of structural analyses (NSAs), while achieving lighter, high-performance designs. In Phase One, FSGO employs a dual global-local search strategy governed by Extensive Constraints (EC), a dynamic constraint relaxation mechanism to balance exploration of unconventional topologies and exploitation of optimal member sizes. By creating adaptive margins around design constraints, EC enables broader exploration of the design space while ensuring feasibility. Phase Two focuses on precision size optimization, leveraging pruned metamodels trained on critical regions of the design space to refine cross-sectional areas for the finalized topology. Comparative evaluations on benchmark planar and spatial trusses demonstrate the method&rsquo;s superiority: it reduces NSAs by 22&ndash;79% compared to state-of-the-art approaches and achieves 0.04&ndash;0.7% lighter designs while eliminating up to 31% of redundant members. Results validate the framework as a paradigm shift in truss optimization, merging computational efficiency with structural innovation.</span></span></span></span> Machine learning, Metamodel, Adaptive sampling, Topology optimization, Size optimization 181 201 http://ijoce.iust.ac.ir/browse.php?a_code=A-10-6463-23&slc_lang=other&sid=1 M. Ilchi Ghazaan ilchi@iust.ac.ir 180031947532846002828 180031947532846002828 Yes School of Civil Engineering, Iran University of Science and Technology, P.O. Box 16846-13114, Iran M. Sharifi 180031947532846002829 180031947532846002829 No School of Civil Engineering, Iran University of Science and Technology, P.O. Box 16846-13114, Iran