A　challenge　in　designing　a　bistable　structure　is　the　need　to　have　low　energy　input　for　state　change　while　maximizing　the　load-carrying　capability.　Here,　we　present　an　optimization　framework　for　a　bistable　structure　such　that　the　maximum　load-bearing　ability　can　be　achieved　based　on　the　investigation　on　mechanical　performance　and　surrogate　models.　Firstly,　an　analytical　expression　of　radius　for　the　second　state　of　the　bistable　structure　is　derived　and　verified　by　numerical　simulation　using　a　two-point　loading　method.　Then,　the　transforming　process　of　a　bistable　structure　is　analyzed　by　the　force-displacement　curve,　and　the　transformed　load　is　identified　as　an　indicator　measuring　the　load-bearing　capacity.　Secondly,　the　influence　of　changing　parameters,　including　length,　ply　angle,　thickness,　and　radius　of　the　bistable　shell　structure　on　the　transformed　load　is　carried　out　systematically　to　choose　optimal　design　variables.　Thirdly,　the　optimal　model　is　established,　targeting　the　transformed　load　with　the　constraint　of　coupling　stress　in　the　second　stable　state.　Model　selection　is　conducted　to　determine　the　surrogate　model　that　maps　design　variables　into　objective　and　constraint　functions.　And　then,　the　improved　genetic　algorithm　is　developed　to　solve　the　optimal　model,　and　optimal　results　are　analyzed　and　discussed.　Ultimately,　we　achieve　an　optimal　bistable　structure　with　the　maximum　load-bearing　capacity　while　satisfying　constraint,　which　is　validated　by　numerical　simulation.　These　computational　and　optimal　strategies　can　provide　design　ideas　for　new　structural　optimization　design.