Many　new　IoT　applications　have　emerged　with　the　fast　evolution　of　5G　and　the　Internet　of　Things　(IoT).　These　applications　place　higher　demands　on　network　energy　consumption　and　processing　capabilities.　Mobile　edge　computing　(MEC)　significantly　enhances　execution　efficiency,　while　energy　harvesting　(EH)　modules　further　augment　the　operational　features　of　IoT　devices.　However,　existing　studies　mainly　concentrate　on　energy　consumption　and　latency　problems,　often　neglecting　issues　about　user　mobility　and　potential　privacy　leakage　within　the　MEC　environment.　Therefore,　optimizing　computation　offloading　and　resource　allocation　for　MEC-enabled　IoT　networks　is　essential.　This　work　proposes　an　innovative　architecture　with　EH　for　collaborative　computing　between　multiple　mobile　devices　(MDs)　and　MEC　servers.　To　tackle　the　problem,　this　work　also　proposes　an　advanced　hybrid　algorithm　named　Self-adaptive　Bat　Optimizer　with　Genetic　operations　and　individual　update　of　Grey　wolf　optimizer　(SBG2).　With　SBG2,　this　work　aims　to　minimize　the　energy　consumption　of　MDs　while　providing　user　mobility　and　privacy　protection.　Simulation　experiments　show　that　SBG2　reduces　energy　consumption　by　79.15%,　93.20%,　and　89.58%,　respectively,　compared　to　the　other　three　typical　algorithms.　©　2024　IEEE.