Mobile　edge　computing　(MEC),　as　a　promising　paradigm,　delivers　computation　and　storage　capacities　at　the　edge　of　the　network.　It　supports　delay-sensitive　services　for　mobile　users　(MUs).　However,　dynamic　and　stochastic　characteristics　of　MEC　networks　necessitate　constant　migration　of　installed　services　across　edge　servers　to　keep　up　with　the　mobility　of　MUs.　As　a　result,　the　cost　of　maintaining　the　network　increases　significantly.　Existing　studies　of　MEC　rarely　consider　the　cost　of　service　migration　due　to　MU　mobility.　To　minimize　the　long-term　cost　for　microservices　in　a　hybrid　cloudedge　system　comprising　of　MUs,　small　base　stations　(SBSs),　and　a　cloud　data　center　(CDC),　the　total　cost　minimization　is　formulated　as　a　constrained　mixed-integer　nonlinear　program.　To　solve　it,　this　work　designs　a　novel　meta-heuristic　optimization　algorithm　called　Multi-swarm　Grey-wolf-optimizer　based　on　Genetic-learning　(MGG),　which　effectively　combines　strong　local　search　capabilities　of　grey　wolf　optimizer　with　superior　global　search　capabilities　of　genetic　algorithm.　MGG　simultaneously　optimizes　service　request　routing　among　MUs,　SBSs,　and　CDC,　CPU　speeds　of　SBSs,　service　deployment　of　SBSs,　service　migration　cost　of　SBSs,　as　well　as　MUs＇　transmission　power　and　channel　bandwidth　allocation.　Simulation　results　with　Google　cluster　trace　demonstrate　that　MGG　outperforms　several　state-of-the-art　peers　with　respect　to　the　overall　cost　of　the　hybrid　system.　©　2023　IEEE.