Currently,　deep　neural　networks　(DNNs)　have　achieved　a　great　success　in　various　applications.　Traditional　deployment　for　DNNs　in　the　cloud　may　incur　a　prohibitively　serious　delay　in　transferring　input　data　from　the　end　devices　to　the　cloud.　To　address　this　problem,　the　hybrid　computing　environments,　consisting　of　the　cloud,　edge,　and　end　devices,　are　adopted　to　offload　DNN　layers　by　combining　the　larger　layers　(more　amount　of　data)　in　the　cloud　and　the　smaller　layers　(less　amount　of　data)　at　the　edge　and　end　devices.　A　key　issue　in　hybrid　computing　environments　is　how　to　minimize　the　system　cost　while　accomplishing　the　offloaded　layers　with　their　deadline　constraints.　In　this　article,　a　self-adaptive　discrete　particle　swarm　optimization　(PSO)　algorithm　using　the　genetic　algorithm　(GA)　operators　is　proposed　to　reduce　the　system　cost　caused　by　data　transmission　and　layer　execution.　This　approach　considers　the　characteristics　of　DNNs　partitioning　and　layers　off-loading　over　the　cloud,　edge,　and　end　devices.　The　mutation　operator　and　crossover　operator　of　GA　are　adopted　to　avert　the　premature　convergence　of　PSO,　which　distinctly　reduces　the　system　cost　through　enhanced　population　diversity　of　PSO.　The　proposed　off-loading　strategy　is　compared　with　benchmark　solutions,　and　the　results　show　that　our　strategy　can　effectively　reduce　the　system　cost　of　off-loading　for　DNN-based　applications　over　the　cloud,　edge　and　end　devices　relative　to　the　benchmarks.