Arithmetic　Optimization　Algorithm　(AOA)　is　a　physically　inspired　optimization　algorithm　that　mimics　arithmetic　operators　in　mathematical　calculation.　Although　the　AOA　has　an　acceptable　exploration　and　exploitation　ability,　it　also　has　some　shortcomings　such　as　low　population　diversity,　premature　convergence,　and　easy　stagnation　into　local　optimal　solutions.　The　Golden　Sine　Algorithm　(Gold-SA)　has　strong　local　searchability　and　fewer　coefficients.　To　alleviate　the　above　issues　and　improve　the　performance　of　AOA,　in　this　paper,　we　present　a　hybrid　AOA　with　Gold-SA　called　HAGSA　for　solving　industrial　engineering　design　problems.　We　divide　the　whole　population　into　two　subgroups　and　optimize　them　using　AOA　and　Gold-SA　during　the　searching　process.　By　dividing　these　two　subgroups,　we　can　exchange　and　share　profitable　information　and　utilize　their　advantages　to　find　a　satisfactory　global　optimal　solution.　Furthermore,　we　used　the　Levy　flight　and　proposed　a　new　strategy　called　Brownian　mutation　to　enhance　the　searchability　of　the　hybrid　algorithm.　To　evaluate　the　efficiency　of　the　proposed　work,　HAGSA,　we　selected　the　CEC　2014　competition　test　suite　as　a　benchmark　function　and　compared　HAGSA　against　other　well-known　algorithms.　Moreover,　five　industrial　engineering　design　problems　were　introduced　to　verify　the　ability　of　algorithms　to　solve　real-world　problems.　The　experimental　results　demonstrate　that　the　proposed　work　HAGSA　is　significantly　better　than　original　AOA,　Gold-SA,　and　other　compared　algorithms　in　terms　of　optimization　accuracy　and　convergence　speed.