Dynamic　group　optimization　has　recently　appeared　as　a　novel　algorithm　developed　to　mimic　animal　and　human　socialising　behaviours.　Although　the　algorithm　strongly　lends　itself　to　exploration　and　exploitation,　it　has　two　main　drawbacks.　The　first　is　that　the　greedy　strategy,　used　in　the　dynamic　group　optimization　algorithm,　guarantees　to　evolve　a　generation　of　solutions　without　deteriorating　than　the　previous　generation　but　decreases　population　diversity　and　limit　searching　ability.　The　second　is　that　most　information　for　updating　populations　is　obtained　from　companions　within　each　group,　which　leads　to　premature　convergence　and　deteriorated　mutation　operators.　The　dynamic　group　optimization　with　a　mean–variance　search　framework　is　proposed　to　overcome　these　two　drawbacks,　an　improved　algorithm　with　a　proportioned　mean　solution　generator　and　a　mean–variance　Gaussian　mutation.　The　new　proportioned　mean　solution　generator　solutions　do　not　only　consider　their　group　but　also　are　affected　by　the　current　solution　and　global　situation.　The　mean–variance　Gaussian　mutation　takes　advantage　of　information　from　all　group　heads,　not　solely　concentrating　on　information　from　the　best　solution　or　one　group.　The　experimental　results　on　public　benchmark　test　suites　show　that　the　proposed　algorithm　is　effective　and　efficient.　In　addition,　comparative　results　of　engineering　problems　in　welded　beam　design　show　the　promise　of　our　algorithms　for　real-world　applications.　©　2021　Elsevier　Ltd