Page 46 - 《软件学报》2020年第11期

3362 Journal of Software 软件学报 Vol.31, No.11, November 2020

• 问题 5 [22] :
10
max ( )fx = ∑ x i
5
i= 1
⎧ (x + x + 1) (x + 2x + 2x + 3x + 3x + 3x + 4x + 10x )≤ 170
2
⎪ 1 2 3 2 4 2 5 6 7 8 9 10
⎪ x − 1 x + 4 x − 5 x + 6 x − 7 x + 8 x ≥ 0
9
⎪
s.t. x + ⎨ 1 2 x − 3 3x + 6 4x = 10 0 .
⎪ xx + 3x − 2x − 3x =
⎪ 23 4 8 9 0
⎪− ⎩ 100≤ x ≤ i 100,x ∈ i , Z i = 1,...,10
最优解为[(0,−1,0,57,100,0,100,0,57,0),312].
• 问题 6 [23] :
min ( )f x = 6 x + 1 2 x + 2 2 3x + 3 2 4x + 4 2 2x − 2 5 8x − 1 2x − 2 3x − 3 x − 4 2x 5
x + ⎧ 1 x + 2 x + 3 x + 4 x ≤ 400
5
⎪ x + 2x + 2x + x +
⎪ 1 2 3 4 6x ≤ 800
5
⎪ 2x + x + 6x ≤ 200
⎪ 1 2 3
x + ⎪ x + 5x ≤ 200
s.t. ⎨ 3 4 5 .
⎪ x + 1 x + 2 x + 3 x ≥ 48
4
⎪ x + x + x ≥ 34
⎪ 2 4 5
⎪ 6x + 7x ≥ 104
1
5
⎪
⎩ 0≤ x ≤ i 99;x ∈ i , Z i = 1,...,5
最优解为[(16,22,5,5,7),819].
• 问题 7 [23] :
max fx = ( ) 215x + 116x + 670x + 924x + 510x + 600x + 424x + 942x + 43x + 369x + 408x + 52x +
7 1 2 3 4 5 6 7 8 9 10 11 12
319x + 13 214x + 14 851x + 15 394x + 16 88x + 17 124x + 18 17x + 19 779x + 20 278x + 21 258x + 22 271x + 23
281x + 24 326x + 25 819x + 26 485x + 27 454x + 28 297x + 29 53x + 30 136x + 31 7962x + 32 114x + 33 43x + 34
80x + 35 268x + 36 179x + 37 78x + 38 105x + 39 281x + 40 454x + 28 297x + 29 53x + 30 136x + 31 7962x + 32
114x + 43x + 80x + 268x + 179x + 78x + 105x + 281x + 454x + 297x + 53x +
33 34 35 36 37 38 39 40 28 29 30
136x + 31 7962x + 32 114x + 33 43x + 34 80x + 35 268x + 36 179x + 37 78x + 38 105x + 39 281x 40
8x + ⎧ 1 11x + 2 6x + 3 x + 4 7x + 5 9x + 6 10x + 7 18x + 14 2x + 15 x + 16 x + 17 2x + 18 3x + 19 4x + 20 7x + 21 6x + 22 2x + 23 2x + 24
⎪
⎪ x + 25 2x + 26 x + 27 8x + 28 10x + 29 2x + 30 x + 31 9x + 32 x + 33 9x + 34 2x + 35 4x + 36 10x + 37 8x + 38 6x + 39 x ≤ 25000
40
5x + ⎪ 3x + 2x + 7x + 7x + 3x + 6x + 2x + 15x + 8x + 16x + x + 2x + 2x + 7x +
⎪ 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
7x + ⎪ 16 2x + 17 2x + 18 4x + 19 3x + 20 2x + 21 13x + 22 8x + 23 2x + 24 3x + 25 4x + 26 3x + 27 2x + 28 x + 29
⎪ 10x + ⎪ 6x + 3x + 4x + x + 8x + 6x + 3x + 4x + 6x + 2x ≤ 25000
s.t. ⎨ 30 31 32 33 34 35 36 37 38 39 40 .
⎪ 3x + 1 4x + 2 6x + 3 2x + 4 2x + 5 3x + 6 7x + 7 10x + 8 3x + 9 7x + 10 2x + 11 16x + 12 3x + 13 3x + 14 9x + 15
⎪ 8x + 9x + 7x + 6x + 16x + 12x + x + 3x + 14x + 7x + 13x + 6x + 16x +
⎪ 16 17 18 19 20 21 22 23 24 25 26 27 28
3x + ⎪ 29 2x + 30 x + 31 2x + 32 8x + 33 3x + 34 2x + 35 7x + 36 x + 37 2x + 38 6x + 39 5x ≤ 25000
40
⎪ 99;integer =
⎪ 10≤ x ≤ i ,i 1,2,...,20
⎪ 20≤ x ≤ 99;integer = 21,...,40
,i
⎩
i
最优解为[(99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,99,
99,99,99,99,99,99,99,99,99,99),1352439].

• 问题 8 [23] :