lemon-project-template-glpk
view deps/glpk/examples/sat.mod @ 9:33de93886c88
Import GLPK 4.47
| author | Alpar Juttner <alpar@cs.elte.hu> |
|---|---|
| date | Sun, 06 Nov 2011 20:59:10 +0100 |
| parents | |
| children |
line source
1 /* SAT, Satisfiability Problem */
3 /* Written in GNU MathProg by Andrew Makhorin <mao@gnu.org> */
5 param m, integer, > 0;
6 /* number of clauses */
8 param n, integer, > 0;
9 /* number of variables */
11 set C{1..m};
12 /* clauses; each clause C[i], i = 1, ..., m, is disjunction of some
13 variables or their negations; in the data section each clause is
14 coded as a set of indices of corresponding variables, where negative
15 indices mean negation; for example, the clause (x3 or not x7 or x11)
16 is coded as the set { 3, -7, 11 } */
18 var x{1..n}, binary;
19 /* main variables */
21 /* To solve the satisfiability problem means to determine all variables
22 x[j] such that conjunction of all clauses C[1] and ... and C[m] takes
23 on the value true, i.e. all clauses are satisfied.
25 Let the clause C[i] be (t or t' or ... or t''), where t, t', ..., t''
26 are either variables or their negations. The condition of satisfying
27 C[i] can be most naturally written as:
29 t + t' + ... + t'' >= 1, (1)
31 where t, t', t'' have to be replaced by either x[j] or (1 - x[j]).
32 The formulation (1) leads to the mip problem with no objective, i.e.
33 to a feasibility problem.
35 Another, more practical way is to write the condition for C[i] as:
37 t + t' + ... + t'' + y[i] >= 1, (2)
39 where y[i] is an auxiliary binary variable, and minimize the sum of
40 y[i]. If the sum is zero, all y[i] are also zero, and therefore all
41 clauses are satisfied. If the sum is minimal but non-zero, its value
42 shows the number of clauses which cannot be satisfied. */
44 var y{1..m}, binary, >= 0;
45 /* auxiliary variables */
47 s.t. c{i in 1..m}:
48 sum{j in C[i]} (if j > 0 then x[j] else (1 - x[-j])) + y[i] >= 1;
49 /* the condition (2) */
51 minimize unsat: sum{i in 1..m} y[i];
52 /* number of unsatisfied clauses */
54 data;
56 /* These data correspond to the instance hole6 (pigeon hole problem for
57 6 holes) from SATLIB, the Satisfiability Library, which is part of
58 the collection at the Forschungsinstitut fuer anwendungsorientierte
59 Wissensverarbeitung in Ulm Germany */
61 /* The optimal solution is 1 (one clause cannot be satisfied) */
63 param m := 133;
65 param n := 42;
67 set C[1] := -1 -7;
68 set C[2] := -1 -13;
69 set C[3] := -1 -19;
70 set C[4] := -1 -25;
71 set C[5] := -1 -31;
72 set C[6] := -1 -37;
73 set C[7] := -7 -13;
74 set C[8] := -7 -19;
75 set C[9] := -7 -25;
76 set C[10] := -7 -31;
77 set C[11] := -7 -37;
78 set C[12] := -13 -19;
79 set C[13] := -13 -25;
80 set C[14] := -13 -31;
81 set C[15] := -13 -37;
82 set C[16] := -19 -25;
83 set C[17] := -19 -31;
84 set C[18] := -19 -37;
85 set C[19] := -25 -31;
86 set C[20] := -25 -37;
87 set C[21] := -31 -37;
88 set C[22] := -2 -8;
89 set C[23] := -2 -14;
90 set C[24] := -2 -20;
91 set C[25] := -2 -26;
92 set C[26] := -2 -32;
93 set C[27] := -2 -38;
94 set C[28] := -8 -14;
95 set C[29] := -8 -20;
96 set C[30] := -8 -26;
97 set C[31] := -8 -32;
98 set C[32] := -8 -38;
99 set C[33] := -14 -20;
100 set C[34] := -14 -26;
101 set C[35] := -14 -32;
102 set C[36] := -14 -38;
103 set C[37] := -20 -26;
104 set C[38] := -20 -32;
105 set C[39] := -20 -38;
106 set C[40] := -26 -32;
107 set C[41] := -26 -38;
108 set C[42] := -32 -38;
109 set C[43] := -3 -9;
110 set C[44] := -3 -15;
111 set C[45] := -3 -21;
112 set C[46] := -3 -27;
113 set C[47] := -3 -33;
114 set C[48] := -3 -39;
115 set C[49] := -9 -15;
116 set C[50] := -9 -21;
117 set C[51] := -9 -27;
118 set C[52] := -9 -33;
119 set C[53] := -9 -39;
120 set C[54] := -15 -21;
121 set C[55] := -15 -27;
122 set C[56] := -15 -33;
123 set C[57] := -15 -39;
124 set C[58] := -21 -27;
125 set C[59] := -21 -33;
126 set C[60] := -21 -39;
127 set C[61] := -27 -33;
128 set C[62] := -27 -39;
129 set C[63] := -33 -39;
130 set C[64] := -4 -10;
131 set C[65] := -4 -16;
132 set C[66] := -4 -22;
133 set C[67] := -4 -28;
134 set C[68] := -4 -34;
135 set C[69] := -4 -40;
136 set C[70] := -10 -16;
137 set C[71] := -10 -22;
138 set C[72] := -10 -28;
139 set C[73] := -10 -34;
140 set C[74] := -10 -40;
141 set C[75] := -16 -22;
142 set C[76] := -16 -28;
143 set C[77] := -16 -34;
144 set C[78] := -16 -40;
145 set C[79] := -22 -28;
146 set C[80] := -22 -34;
147 set C[81] := -22 -40;
148 set C[82] := -28 -34;
149 set C[83] := -28 -40;
150 set C[84] := -34 -40;
151 set C[85] := -5 -11;
152 set C[86] := -5 -17;
153 set C[87] := -5 -23;
154 set C[88] := -5 -29;
155 set C[89] := -5 -35;
156 set C[90] := -5 -41;
157 set C[91] := -11 -17;
158 set C[92] := -11 -23;
159 set C[93] := -11 -29;
160 set C[94] := -11 -35;
161 set C[95] := -11 -41;
162 set C[96] := -17 -23;
163 set C[97] := -17 -29;
164 set C[98] := -17 -35;
165 set C[99] := -17 -41;
166 set C[100] := -23 -29;
167 set C[101] := -23 -35;
168 set C[102] := -23 -41;
169 set C[103] := -29 -35;
170 set C[104] := -29 -41;
171 set C[105] := -35 -41;
172 set C[106] := -6 -12;
173 set C[107] := -6 -18;
174 set C[108] := -6 -24;
175 set C[109] := -6 -30;
176 set C[110] := -6 -36;
177 set C[111] := -6 -42;
178 set C[112] := -12 -18;
179 set C[113] := -12 -24;
180 set C[114] := -12 -30;
181 set C[115] := -12 -36;
182 set C[116] := -12 -42;
183 set C[117] := -18 -24;
184 set C[118] := -18 -30;
185 set C[119] := -18 -36;
186 set C[120] := -18 -42;
187 set C[121] := -24 -30;
188 set C[122] := -24 -36;
189 set C[123] := -24 -42;
190 set C[124] := -30 -36;
191 set C[125] := -30 -42;
192 set C[126] := -36 -42;
193 set C[127] := 6 5 4 3 2 1;
194 set C[128] := 12 11 10 9 8 7;
195 set C[129] := 18 17 16 15 14 13;
196 set C[130] := 24 23 22 21 20 19;
197 set C[131] := 30 29 28 27 26 25;
198 set C[132] := 36 35 34 33 32 31;
199 set C[133] := 42 41 40 39 38 37;
201 end;