Radial　basis　function　network-based　autoregressive　with　exogenous　input　(RBF-ARX)　models　are　useful　in　nonlinear　system　modelling　and　prediction.　The　identification　of　RBF-ARX　models　includes　optimization　of　the　(model　lags,　number　of　hidden　nodes　and　state　vector)　and　the　parameters　of　the　model.　Previous　works　have　usually　ignored　optimizations　of　the　model＇s　architecture.　In　this　paper,　the　RBF-ARX　architecture,　which　includes　the　selection　of　lags,　number　of　nodes　of　the　RBF　network,　lag　orders　and　state　vector,　is　encoded　into　a　chromosome　and　is　evolved　simultaneously　by　a　genetic　algorithm　(GA).　This　combines　the　advantages　of　the　GA　and　the　variable　projection　(VP)　method　to　automatically　generate　a　parsimonious　RBF-ARX　model　with　a　high　generalization　performance.　The　highly　efficient　VP　algorithm　is　used　as　a　local　search　strategy　to　accelerate　the　convergence　of　the　optimization.　The　experimental　results　demonstrate　the　effectiveness　of　the　proposed　method.　(C)　2022　Elsevier　B.V.　All　rights　reserved.