Copyright 2014 NTT DATA SEKISUI SYSTEMS Corporation 8
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色分け問題 • Copyright © 2014 NTT DATA SEKISUI SYSTEMS Corporation 8
色分け問題 (充足問題) • Copyright © 2014 NTT DATA SEKISUI SYSTEMS Corporation 9
アーク整合性 • Copyright © 2014 NTT DATA SEKISUI SYSTEMS Corporation 11
一般的な構造 制約伝播 例えば… • Copyright © 2014 NTT DATA SEKISUI SYSTEMS Corporation 13
Mini. Zinc とは • 中間レベルのモデリング言語 – – ほとんどの制約問題を表現できる程度に高レベル 既存のソルバ用に容易に矛盾なくマップできる程度には低レベル より高レベルの Zinc のサブセットとなっている 制約プログラミングのコミュニティで標準となることを狙っている Mini. Zinc is a medium-level constraint modelling language. It is highlevel enough to express most constraint problems easily, but low-level enough that it can be mapped onto existing solvers easily and consistently. It is a subset of the higher-level language Zinc. We hope it will be adopted as a standard by the Constraint Programming community. 参考 http: //www. minizinc. org/ Copyright © 2014 NTT DATA SEKISUI SYSTEMS Corporation 15
Mini. Zinc による問題記述例 include "alldifferent. mzn"; var var 1. . 9: 0. . 9: S; E; N; D; M; O; R; Y; constraint 1000 * S + 100 * E + 10 * N + D + 1000 * M + 100 * O + 10 * R + E = 10000 * M + 1000 * O + 100 * N + 10 * E + Y; constraint alldifferent([S, E, N, D, M, O, R, Y]); solve satisfy; output [" ", show(S), show(E), show(N), show(D), "n", "+ ", show(M), show(O), show(R), show(E), "n", "= ", show(M), show(O), show(N), show(E), show(Y), "n"]; Mini. Zinc Tutorial より Copyright © 2014 NTT DATA SEKISUI SYSTEMS Corporation 17
パズル: SEND + MORE = MONEY i. Z-Cによる実際のコード #include <stdio. h> #include "iz. h" CSint **Digit; CSint *L 1, *L 2, *L 3; enum {s = 0, e, n, d, m, o, r, y, NB_DIGITS }; void constraints() { Digit = cs_create. CSint. Array(NB_DIGITS, 0, 9); L 1 = cs_VScal. Prod(4, Digit[s], Digit[e], Digit[n], Digit[d], 1000, 10, 1); L 2 = cs_VScal. Prod(4, Digit[m], Digit[o], Digit[r], Digit[e], 1000, 10, 1); void print. Solution() { cs_printf(" %Dn", L 1); cs_printf("+%Dn", L 2); cs_printf("-----n"); cs_printf("%Dn", L 3); cs_print. Stats(); } int main(int argc, char **argv) { cs_init(); L 3 = cs_VScal. Prod(5, Digit[m], Digit[o], Digit[n], Digit[e], Digit[y], 10000, 100, 1); constraints(); if (cs_search(Digit, NB_DIGITS, cs_find. Free. Var. Nb. Elements)) print. Solution(); else printf("fail!n"); cs_Eq(L 3, cs_Add(L 1, L 2)); cs_NEQ(Digit[s], 0); cs_NEQ(Digit[m], 0); cs_All. Neq(Digit, NB_DIGITS); cs_end(); return 0; } } Copyright © 2014 NTT DATA SEKISUI SYSTEMS Corporation 24
結果 (2014年度) • カンファレンス CP 2014 で結果発表 (9/8~ 9/12) 結果は… Copyright © 2014 NTT DATA SEKISUI SYSTEMS Corporation 31
結果 (2014年度) • Free search: – Gold medal: i. Zplus – Silver medal: Opturion CPX – Bronze medal: Choco (12参加者中) その他に Open class 3位 分析はまだ行っていないが、改善点の有効性が確認できた。 参考 http: //www. minizinc. org/challenge 2014/results 2014. html Copyright © 2014 NTT DATA SEKISUI SYSTEMS Corporation 32
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