An　algorithm　whose　performance　depends　on　the　objective　function　being　aligned　with　a　privileged　coordinate　system　is　a　poor　choice　in　general　because　it　is　unlikely　that　the　optimal　orientation　will　be　known　in　advance.　In　this　paper,　a　property　of　meta-heuristic　algorithms,　named　affine　invariance,　is　introduced　to　verify　whether　the　algorithm　is　depended　on　the　privileged　coordinate　system　or　not.　The　concept　of　affine　invariance　is　described　in　detail,　and　some　classical　algorithms,　efficient　in　most　test　and　actual　problems,　are　proved　to　be　affine　invariant.　While　some　recent　algorithms　in　the　literature　are　proved　to　be　not　affine　invariant.　As　a　conclusion,　particle　swarm　optimization　(PSO),　differential　evolution　(DE)　and　optimal　foraging　algorithm　(OFA)　are　affine　invariant,　while　grey　wolf　optimizer　(GWO),　sine　cosine　algorithm　(SCA)　and　butterfly　optimization　algorithm　(BOA)　are　not　affine　invariant.　Furthermore,　comparison　tests　are　designed　to　support　the　theoretical　analysis　results.　In　these　tests,　same　random　numbers　and　initial　population　are　used　to　avoid　the　influence　of　randomness,　thus,　the　conclusion　is　reliable.　©　2021　Elsevier　Inc.