This　paper　introduces　a　new　class　of　generalized　invex　function　called　d-ρηθ-univex　function,　and　discusses　the　relationship　among　d-invex,　d-univex,　d-ρηθ-invex,　and　d-ρηθ-univex　functions.　Under　d-ρηθ-univexity　assumption,　one　type　of　multiobjective　programming　problem　(P)　is　considered.　The　sufficient　optimality　conditions　for　the　existence　of　the　weak　Pareto　efficient　solution　of　the　problem　(P)　are　first　established.　The　results　on　the　weak,　strong　and　converse　duality　of　Mond-Weir　type　duality,　and　the　weak　and　strong　duality　assertions　of　the　generalized　Mond-Weir　type　duality　of　the　problem　(P)　are　then　obtained.