The　main　goal　of　multitask　optimization　(MTO)　is　the　parallel　optimization　of　multiple　different　tasks.　However,　since　different　tasks　in　the　MTO　problem　usually　have　heterogeneous　characteristics,　it　is　difficult　to　realize　the　positive　knowledge　transfer　among　tasks,　resulting　in　poor　convergence.　To　cope　with　this　problem,　a　multi-task　particle　swarm　optimization　with　a　heterogeneous　domain　adaptation　strategy　(MTPSO-HDA)　is　proposed　to　transfer　positive　knowledge　among　heterogeneous　tasks.　First,　a　nonlinear　mapping　between　the　source　task　and　the　target　task　is　constructed　based　on　the　adaptive　kernel　function.　Then,　source　tasks　are　mapped　to　the　target　task　space　to　reduce　the　differences　among　heterogeneous　tasks.　Second,　a　multi-source　domain　adaptive　strategy　based　on　fitness　landscape　similarity　is　designed　to　implement　domain　adaptation.　Then,　the　importance　of　each　source　domain　is　quantitatively　described　to　reduce　the　differences　between　multiple　source　domains　and　a　target　domain　and　achieve　domain　adaptation　among　heterogeneous　tasks.　Third,　a　heterogeneous　multitask　particle　swarm　optimization　mechanism　is　introduced　to　facilitate　positive　knowledge　transfer　among　heterogeneous　tasks.　Then,　an　appropriate　evolutionary　mechanism　is　designed　according　to　the　fitness　landscape　similarity　to　achieve　positive　knowledge　transfer.　Finally,　to　assess　the　effectiveness　of　the　MTPSO-HDA　algorithm,　some　experiments　are　designed　based　on　some　benchmark　problems　and　real-world　application　of　wastewater　treatment　process.　The　results　demonstrate　that　the　proposed　MTPSO-HDA　algorithm　can　promote　positive　knowledge　transfer　among　heterogeneous　tasks　to　improve　convergence.　IEEE