The　Meet-in-the-Middle　(MITM)　preimage　attack　is　highly　effective　in　breaking　the　preimage　resistance　of　many　hash　functions,　including　but　not　limited　to　the　full　MD5,　HAVAL,　and　Tiger,　and　reduced　SHA-0/1/2.　It　was　also　shown　to　be　a　threat　to　hash　functions　built　on　block　ciphers　like　AES　by　Sasaki　in　2011.　Recently,　such　attacks　on　AES　hashing　modes　evolved　from　merely　using　the　freedom　of　choosing　the　internal　state　to　also　exploiting　the　freedom　of　choosing　the　message　state.　However,　detecting　such　attacks　especially　those　evolved　variants　is　difficult.　In　previous　works,　the　search　space　of　the　configurations　of　such　attacks　is　limited,　such　that　manual　analysis　is　practical,　which　results　in　sub-optimal　solutions.　In　this　paper,　we　remove　artificial　limitations　in　previous　works,　formulate　the　essential　ideas　of　the　construction　of　the　attack　in　well-defined　ways,　and　translate　the　problem　of　searching　for　the　best　attacks　into　optimization　problems　under　constraints　in　Mixed-Integer-Linear-Programming　(MILP)　models.　The　MILP　models　capture　a　large　solution　space　of　valid　attacks;　and　the　objectives　of　the　MILP　models　are　attack　configurations　with　the　minimized　computational　complexity.　With　such　MILP　models　and　using　the　off-the-shelf　solver,　it　is　efficient　to　search　for　the　best　attacks　exhaustively.　As　a　result,　we　obtain　the　first　attacks　against　the　full　(5-round)　and　an　extended　(5.5-round)　version　of　Haraka-512　v2,　and　8-round　AES-128　hashing　modes,　as　well　as　improved　attacks　covering　more　rounds　of　Haraka-256　v2　and　other　members　of　AES　and　Rijndael　hashing　modes.