The　capacitated　modular　hub　location　problem　is　a　realistic　variant　of　the　popular　hub　location　problem　arising　from　the　design　of　telecommunications　networks.　Given　a　set　of　demand　nodes,　the　problem　consists　in　selecting　a　subset　of　nodes　to　represent　hubs　and　assigning　the　rest　of　the　nodes　to　the　hub　nodes,　such　that　the　transportation　cost　is　minimized　while　satisfying　the　capacity　constraints.　The　adaptive　memory　algorithm　is　a　hybrid　evolutionary　heuristic　that　uses　a　central　memory　to　store　blocks　of　solutions.　At　each　iteration,　the　recombination　operator　uses　these　solution　blocks　to　create　an　offspring　solution.　In　this　paper,　we　present　a　parallel　adaptive　memory　algorithm　for　the　capacitated　modular　hub　location　problem　that　stores　both　solution　blocks　and　complete　solutions　in　a　shared　memory　for　the　creation　of　an　offspring.　Other　distinguishing　features　of　our　proposed　algorithm　include　specially　designed　recombination　and　mutation　operators　for　search　diversification,　an　effective　tabu　search　procedure　for　search　intensification,　and　parallel　computing　for　global　optimization.　Extensive　computational　results　on　three　well-known　data　sets　of　170　benchmark　instances　show　that　the　proposed　algorithm　competes　very　favorably　with　the　state-of-the-art　heuristics　from　the　literature.　In　particular,　it　finds　115　improved　best-known　solutions　(for　more　than　67%　of　the　cases).　Furthermore,　we　analyze　the　key　algorithmic　components　and　shed　lights　on　their　impact　on　the　proposed　algorithm.　©　2023　Elsevier　Ltd