As　integrated　circuit　processes　become　more　advanced,　feature　sizes　become　smaller　and　smaller,　and　more　and　more　processing　cores　and　memory　components　are　integrated　on　a　single　chip.　However,　the　traditional　bus-based　System-on-Chip　(SoC)　communication　is　inefficient,　has　poor　scalability,　and　cannot　handle　the　communication　tasks　between　the　processing　cores　well.　Network-on-chip　(NoC)　has　become　an　important　development　direction　in　this　field　by　virtue　of　its　efficient　transmission　and　scalability　of　data　between　multiple　cores.　The　mapping　problem　is　a　hot　spot　in　NoC＇s　research　field,　and　its　mapping　results　will　directly　affect　the　power　consumption,　latency,　and　other　properties　of　the　chip.　The　mapping　problem　is　a　NP-hard　problem,　so　how　to　effectively　obtain　low-power　and　low-latency　mapping　schemes　becomes　a　research　difficulty.　Aiming　at　this　problem,　this　paper　proposes　a　two-populations-with-enhanced-initial-population　based　on　genetic　algorithm　(TI_GA)　task　mapping　algorithm　based　on　an　improved　genetic　algorithm　from　the　two　indexes　of　power　consumption　and　delay.　The　quality　of　the　initial　individual　is　optimized　in　the　process　of　constructing　the　population,　so　the　quality　of　initial　population　is　improved.　In　addition,　a　two-population　genetic　mechanism　is　added　during　the　iterative　process　of　the　algorithm.　The　experimental　results　show　that　TI_GA　is　very　effective　for　optimizing　network　power　consumption　and　delay　of　heterogeneous　multi-core.