The　combinatorial　optimization　problem　(COP),　which　aims　to　find　the　optimal　solution　in　discrete　space,　is　fundamental　in　various　fields.　Unfortunately,　many　COPs　are　NP-complete,　and　require　much　more　time　to　solve　as　the　problem　scale　increases.　Troubled　by　this,　researchers　may　prefer　fast　methods　even　if　they　are　not　exact,　so　approximation　algorithms,　heuristic　algorithms,　and　machine　learning　have　been　proposed.　Some　works　proposed　chaotic　simulated　annealing　(CSA)　based　on　the　Hopfield　neural　network　and　did　a　good　job.　However,　CSA　is　not　something　that　current　general-purpose　processors　can　handle　easily,　and　there　is　no　special　hardware　for　it.　To　efficiently　perform　CSA,　we　propose　a　software　and　hardware　co-design.　In　software,　we　quantize　the　weight　and　output　using　appropriate　bit　widths,　and　then　modify　the　calculations　that　are　not　suitable　for　hardware　implementation.　In　hardware,　we　design　a　specialized　processing-in-memory　hardware　architecture　named　COPPER　based　on　the　memristor.　COPPER　is　capable　of　efficiently　running　the　modified　quantized　CSA　algorithm　and　supporting　the　pipeline　further　acceleration.　The　results　show　that　COPPER　can　perform　CSA　remarkably　well　in　both　speed　and　energy.