Hybrid　cloud-edge　systems　combine　the　advantages　of　cloud　computing　and　mobile　edge　computing　(MEC)　to　achieve　flexible　integration　and　fluidity　of　data　between　the　cloud　and　the　edge.　To　address　dynamic　and　stochastic　loads　caused　by　mobile　users　(MUs)　and　time-varying　tasks,　MEC　network　operators　need　to　continuously　migrate　installed　services　among　edge　servers,　significantly　increasing　network　maintenance　costs.　Existing　studies　often　overlook　the　service　migration　cost　resulting　from　MU　mobility.　Therefore,　we　present　a　joint　optimization　scheme　focusing　on　minimizing　the　operational　cost　of　hybrid　cloud-edge　systems　while　considering　the　dynamic　service　migration　cost　induced　by　MUs.　With　the　rapid　development　of　5G/6G　technologies,　many　MUs　require　connectivity　to　edge　nodes　(ENs)　or　cloud　data　centers　(CDCs)　for　processing.　Minimizing　the　operational　cost　of　hybrid　cloud-edge　systems　while　considering　many　heterogeneous　decision　variables　is　a　challenge.　To　solve　this　complex　high-dimensional　mixed-integer　nonlinear　problem,　we　develop　a　novel　deep　learning-based　evolutionary　algorithm　called　autoencoder-based　multiswarm　gray　wolf　optimizer　based　on　genetic　learning　(AMGG).　Experimental　results　with　real　data　demonstrate　that　AMGG　achieves　lower　system　cost　by　49.69%　while　strictly　meeting　task　latency　requirements　of　MUs　compared　with　state-of-the-art　algorithms.