Many　real-world　engineering　optimization　problems　usually　need　a　lot　of　time　for　function　evaluations　or　have　massive　decision　variables.　It　is　still　a　big　challenge　to　address　these　problems　effectively.　Recently,　surrogate-assisted　meta-heuristic　algorithms　have　drawn　increasing　attention,　and　have　shown　their　potential　to　deal　with　such　expensive　complex　optimization　problems.　In　this　study,　a　surrogate-assisted　quasi-affine　transformation　evolutionary　(SA-QUATRE)　algorithm　is　proposed　to　further　enhance　the　optimization　efficiency　and　effectiveness.　In　SA-QUATRE,　the　global　and　the　local　surrogate　models　are　effectively　combined　for　fitness　estimation.　The　global　surrogate　model　is　built　based　on　all　data　in　the　database　for　global　exploration.　While,　the　local　surrogate　model　is　constructed　with　a　predefined　number　of　top　best　samples　for　local　exploitation.　Meanwhile,　both　the　generation-　and　individual-based　evolution　controls　as　well　as　a　top　best　restart　strategy　are　incorporated　in　the　global　and　the　local　searches.　To　enhance　the　exploration　and　the　exploitation　capabilities,　the　global　search　uses　the　mean　of　the　population　to　be　evaluated　with　the　expensive　real　fitness　function,　while　the　local　search　chooses　the　individual　with　the　best　fitness　according　to　the　surrogate　for　real　evaluation.　The　proposed　SA-QUATRE　is　compared　with　five　state-of-the-art　optimization　approaches　over　seven　commonly　used　benchmark　functions　with　dimensions　varying　from　10　to　100.　Moreover,　the　proposed　SA-QUATRE　is　also　applied　to　solve　the　tension/compression　spring　design　problem.　The　experimental　results　show　that　SA-QUATRE　is　promising　for　optimizing　computationally　expensive　problems.　©　2020　Elsevier　B.V.