Multi-objective　optimization　for　the　municipal　solid　waste　incineration　process　is　considered　as　a　valuable　technique　to　improve　energy　recovery　and　reduce　pollutant　emission.　However,　the　complex　mechanism　analysis　and　multimodal　problem　of　the　municipal　solid　waste　incineration　process　set　challenges　for　both　the　modeling　and　optimization　studies.　To　overcome　this　problem,　an　adaptive　multi-objective　optimization　for　the　municipal　solid　waste　incineration　process　is　proposed　in　this　paper.　First,　a　bi-objective　model　of　the　municipal　solid　waste　incineration,　the　basis　for　optimization,　is　established　based　on　mass　balance　and　energy　balance,　which　takes　furnace　temperature　and　flue　gas　oxygen　content　as　decision　variables　to　mathematically　deduce　the　generated　heat　and　exhaust　gases.　Second,　an　adaptive　multi-objective　competitive　swarm　optimization　algorithm　is　proposed　for　the　optimization　of　the　municipal　solid　waste　incineration　process.　Two-step　competition　and　multi-strategy　learning　are　designed　to　provide　a　clear　division　of　labor　for　particles　and　a　novel　idea　for　detecting　evolutionary　environment　is　proposed　based　on　kinematic　analysis　of　particles.　Finally,　relevant　experiments　are　conducted　on　benchmark　instances　and　the　municipal　solid　waste　incineration　optimization　model.　The　proposed　algorithm　shows　promising　convergence,　diversity,　fastness　by　comparing　with　several　representative　and　state-of-the-art　algorithms.　The　proposed　algorithm　achieves　the　optimization　effects　with　4.36%　improvement　of　the　available　heat　for　power　generation　and　4.13%　reduction　of　the　exhaust　gas　assessment　in　the　optimization　of　the　municipal　solid　waste　incineration　process.　©　2023　Elsevier　B.V.