Smart　mobile　devices　(SMDs)　are　integral　for　running　advanced　applications　that　demand　significant　computing　resources　and　quick　response　time,　e.g.,　immersive　gaming　and　advanced　image　editing.　However,　SMDs　often　face　constraints　in　computational　capacity　and　battery　duration,　restricting　their　ability　to　process　these　tasks　instantaneously.　Cloud　computing　can　circumvent　these　limitations　by　computation　offloading,　but　cloud　data　centers　(CDCs)　are　often　deployed　at　long　distances　from　users,　which　results　in　longer　computational　latency.　To　address　the　latency　issue,　the　incorporation　of　small　base　stations　(SBSs)　in　the　vicinity　of　the　user　provides　services　with　high　bandwidth　and　low　latency.　The　primary　challenge　lies　in　balancing　the　economics　of　the　system　consisting　of　different　SMDs,　SBSs,　and　a　CDC,　i.e.,　minimizing　cost　while　still　meeting　the　latency　requirements　of　applications.　In　this　work,　a　cost-minimized　computation　offloading　framework　is　formulated　and　solved　by　a　two-stage　optimization　algorithm　named　Lévy　flight　and　Simulated　Annealing-based　Grey　wolf　optimizer　(LSAG).　The　optimal　edge　selection　strategy　is　defined　in　the　first　stage　for　dealing　with　the　case　of　several　available　SBSs.　The　second　stage　coordinates　task　scheduling　and　optimizes　the　allocation　of　resources　among　SMDs,　SBSs,　and　CDC.　LSAG　integrates　the　extended　search　property　of　Lévy　flight　and　the　individual　selection　strategy　of　simulated　annealing　in　the　grey　wolf　optimizer,　which　reduces　the　risk　of　falling　into　local　optima　and　finds　the　global　optimum.　Experimental　results　of　executing　real-life　tasks　show　that　LSAG　outperforms　its　state-of-the-art　peers　in　terms　of　cost　and　speed　of　convergence.　IEEE