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dekker.one
1/***
2--- !Test
3solvers: [gecode, chuffed]
4expected: !Result
5 status: OPTIMAL_SOLUTION
6 solution: !Solution
7 Beamtime: 21
8 K: 7
9 N: [2, 1, 1, 1, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0]
10 Q:
11 - - [0, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
12 - [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
13 - [0, 1, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
14 - [0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
15 - [1, 0, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
16 - - [1, 0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
17 - [1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
18 - [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
19 - [2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
20 - [2, 1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
21 - - [0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0]
22 - [0, 1, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0]
23 - [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
24 - [2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
25 - [0, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
26 - - [0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0]
27 - [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
28 - [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
29 - [2, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
30 - [0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
31 - - [0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0]
32 - [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
33 - [2, 1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
34 - [2, 1, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
35 - [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
36 objective: 175
37--- !Test
38solvers: [cbc]
39check_against: [gecode]
40expected: !Result
41 status: OPTIMAL_SOLUTION
42 solution: !Solution {}
43***/
44
45%-----------------------------------------------------------------------------%
46% Radiation problem, Minizinc version
47%
48% Sebastian Brand
49% 05/2007
50%-----------------------------------------------------------------------------%
51
52%-----------------------------------------------------------------------------%
53% Instances
54%-----------------------------------------------------------------------------%
55
56m = 5; % Rows
57n = 5; % Columns
58
59Intensity = [| % g5c
60 7, 2, 14, 8, 9 |
61 13, 4, 1, 2, 9 |
62 5, 12, 2, 11, 9 |
63 10, 2, 4, 9, 7 |
64 10, 2, 8, 11, 1 |];
65
66%-----------------------------------------------------------------------------%
67% Parameters
68%-----------------------------------------------------------------------------%
69
70int: m; % Rows
71int: n; % Columns
72
73set of int: Rows = 1..m;
74set of int: Columns = 1..n;
75
76 % Intensity matrix
77array[Rows, Columns] of int: Intensity;
78
79
80set of int: BTimes = 1..Bt_max;
81
82int: Bt_max = max(i in Rows, j in Columns) (Intensity[i,j]);
83int: Ints_sum = sum(i in Rows, j in Columns) (Intensity[i,j]);
84
85%-----------------------------------------------------------------------------%
86% Variables
87%-----------------------------------------------------------------------------%
88
89 % Total beam-on time
90var 0..Ints_sum: Beamtime;
91
92 % Number of shape matrices
93var 0..m*n: K;
94
95 % N[b] is the number of shape matrices with associated beam-on time b
96array[BTimes] of var 0..m*n: N;
97
98 % Q[i,j,b] is the number of shape matrices with associated beam-on time
99 % b that expose cell (i,j)
100array[Rows, Columns, BTimes] of var 0..m*n: Q;
101%-----------------------------------------------------------------------------%
102% Constraints
103%-----------------------------------------------------------------------------%
104
105 % For FD/LP hybrid solving, all these should go the LP solver
106 % (with a suitable linearisation of the 'max' expressions).
107constraint
108 Beamtime = sum(b in BTimes) (b * N[b])
109 /\
110 K = sum(b in BTimes) (N[b])
111 /\
112 forall(i in Rows, j in Columns)
113 ( Intensity[i,j] = sum([b * Q[i,j,b] | b in BTimes]) )
114 /\
115 forall(i in Rows, b in BTimes)
116 ( upper_bound_on_increments(N[b], [Q[i,j,b] | j in Columns]) );
117
118
119predicate upper_bound_on_increments(var int: N_b, array[int] of var int: L) =
120 N_b >= L[1] + sum([ max(L[j] - L[j-1], 0) | j in 2..n ]);
121
122%-----------------------------------------------------------------------------%
123% Objective
124%-----------------------------------------------------------------------------%
125
126solve :: int_search(
127 [Beamtime] ++ N ++
128 [ Q[i,j,b] | i in Rows, j in Columns, b in BTimes ],
129 input_order, indomain_split, complete)
130 minimize (ub(K) + 1) * Beamtime + K;
131 % really: (Beamtime, K), i.e. in lexicographic order
132
133%-----------------------------------------------------------------------------%
134
135output ["radiation:\n",
136 "B / K = ", show(Beamtime), " / ", show(K), "\n",
137 % "N = ", show(N), "\n"
138];
139
140%-----------------------------------------------------------------------------%
141%-----------------------------------------------------------------------------%