In　this　paper,　grey　and　entropy　parallel　analysis　(GEPA)　is　presented　as　a　new　fitness-assignment　strategy　for　solving　multi-objective　optimization　problems.　An　evolutionary　algorithm　based　on　GEPA　is　proposed,　and　the　grey　and　entropy　parallel　relational　grade　(GEPRG)　is　used　as　the　fitness　value　to　guide　the　development　of　the　evolutionary　algorithm.　Under　the　analysis　of　the　existing　research　work,　the　multi　objective　flow　shop　scheduling　problem　is　chosen　as　the　application　object　and　a　flow　shop　scheduling　model　with　five　objectives　is　established.　GEPA_GA,　the　GA　based　on　GEPA,　is　described.　To　verify　the　performance　of　the　proposed　algorithm,　GEPA_GA,　together　with　the　GA　based　on　the　random　weighting　method　(RW_GA),　NSGA-11　and　the　GA　based　on　g-dominance　(g_GA),　are　used　to　optimize　the　multi-objective　flow　shop　scheduling　problem.　The　experimental　data　are　analyzed　by　the　statistical　analysis　method,　the　Kruskal-Wallis　test,　and　three　evaluation　metrics.　The　influences　of　the　five　grey　relational　operators　and　the　distinguishing　coefficient　on　the　algorithm　performance　are　also　studied.　Experiments　shows　that　the　results　obtained　by　GEPA_GA　are　better　than　those　of　RW_GA,　NSGA-II　and　g_GA　even　under　the　situation　that　the　combination　of　operator　and　distinguishing　coefficient　is　not　the　best.　It　is　proven　that　GEPA_GA　works　well　in　solving　the　multi-objective　flow　shop　scheduling　optimization　problem,　and　GEPA　is　a　promising　strategy　for　solving　multi-objective　optimization　problems.　(C)　2017　Elsevier　B.V.　All　rights　reserved.