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dekker.one
1/***
2!Test
3expected:
4- !Result
5 solution: !Solution
6 objective: 17
7 x: [0, 1, 0, 1, 1]
8***/
9
10%------------------------------------------------------------------------------%
11% The classical 0/1 multidimensional knapsack problem.
12%
13% There is a knapsack with m different capacity constraints and n items with
14% profits and weights. The goal is to maximise the total profit of the items
15% in the knapsack while not violating any of the capacity constraints.
16%------------------------------------------------------------------------------%
17
18int: n;
19int: m;
20
21array[1..n] of int: Profits;
22array[1..n,1..m] of int: Weights;
23array[1..m] of int: Capacities;
24
25array[1..n] of var 0..1: x;
26
27constraint
28 forall(i in 1..m) (
29 sum([Weights[j,i] * x[j] | j in 1..n]) <= Capacities[i]
30 );
31
32solve maximize
33 sum([x[j] * Profits[j] | j in 1..n]);
34
35output [ "multidimknapsack_simple " ] ++
36 [ show(x[i]) ++ if i = n then "\n" else " " endif | i in 1..n ];
37
38%------------------------------------------------------------------------------%
39% data
40
41n = 5;
42m = 3;
43
44Profits = [5,6,3,7,4];
45
46Capacities = [5,10,15];
47
48Weights = [| 2, 3, 2
49 | 1, 4, 4
50 | 1, 2, 5
51 | 3, 2, 3
52 | 1, 3, 5 |];
53