DASE7111
Coursework 2: Application of a specific data-driven optimization algorithm
This is an individual project, and each student should write a report about 4000 words plus Figures and Tables on an application of a specific intelligent optimization algorithm that is covered by the lectures. You have two options, as listed below. This project accounts for 25% of the total assessment of the course.
Option 1: define a practical problem that cannot be solved by traditional optimization algorithms. Build its mathematical model and design an intelligent optimization algorithm to solve it.
Option 2: build the mathematical model for the multidimensional knapsack problem. Design one intelligent optimization algorithm to solve the model. Give the detailed steps of the algorithm. Use the algorithm to solve three instances below. For each instance, at least 10 runs should be carried out by using different random initial solutions.
Multidimensional Knapsack Problem
In this problem, the weight of item j (j = 1,2, … , n) is given by a m-dimensional vector wj = {w1j, w2j, ..., wmj} and the knapsack has a m-dimensional capacity vector {w1, w2, ..., wm}. Each item j has an associated value pj. The objective is to maximize the total values of the items in the knapsack so that the sum of weights in any dimension i does not exceed wi.
Instance I:
n = 10, m = 10
pj: 600.1 310.5 1800 3850 18.6 198.7 882 4200 402.5 327
wij:
20 5 100 200 2 4 60 150 80 40
20 7 130 280 2 8 110 210 100 40
60 3 50 100 4 2 20 40 6 12
60 8 70 200 4 6 40 70 16 20
60 13 70 250 4 10 60 90 20 24
60 13 70 280 4 10 70 105 22 28
5 2 20 100 2 5 10 60 0 0
45 14 80 180 6 10 40 100 20 0
55 14 80 200 6 10 50 140 30 40
65 14 80 220 6 10 50 180 30 50
wi: 450 540 200 360 440 480 200 360 440 480
Instance II:
n = 15, m = 10
pj: 100 220 90 400 300 400 205 120 160 580 400 140 100 1300 650
wij:
8 24 13 80 70 80 45 15 28 90 130 32 20 120 40
8 44 13 100 100 90 75 25 28 120 130 32 40 160 40
3 6 4 20 20 30 8 3 12 14 40 6 3 20 5
5 9 6 40 30 40 16 5 18 24 60 16 11 30 25
5 11 7 50 40 40 19 7 18 29 70 21 17 30 25
5 11 7 55 40 40 21 9 18 29 70 21 17 35 25
0 0 1 10 4 10 0 6 0 6 32 3 0 70 10
3 4 5 20 14 20 6 12 10 18 42 9 12 100 20
3 6 9 30 29 20 12 12 10 30 42 18 18 110 20
3 8 9 35 29 20 16 15 10 30 42 20 18 120 20
wi: 550 700 130 240 280 310 110 205 260 275
Instance III:
n = 50, m = 5
pj: 560 1125 300 620 2100 431 68 328 47 122 322 196 41 25 425 4260 416 115 82 22 631 132 420 86 42 103 215 81 91 26 49 420 316 72 71 49 108 116 90 738 1811 430 3060 215 58 296 620 418 47 81
wij:
40 91 10 30 160 20 3 12 3 18 9 25 1 1 10 280 10 8 1 1 49 8 21 6 1 5 10 8 2 1 0 10 42 6 4 8 0 10 1 40 86 11 120 8 3 32 28 13 2 4
16 92 41 16 150 23 4 18 6 0 12 8 2 1 0 200 20 6 2 1 70 9 22 4 1 5 10 6 4 0 4 12 8 4 3 0 10 0 6 28 93 9 30 22 0 36 45 13 2 2
38 39 32 71 80 26 5 40 8 12 30 15 0 1 23 100 0 20 3 0 40 6 8 0 6 4 22 4 6 1 5 14 8 2 8 0 20 0 0 6 12 6 80 13 6 22 14 0 1 2
8 71 30 60 200 18 6 30 4 8 31 6 3 0 18 60 21 4 0 2 32 15 31 2 2 7 8 2 8 0 2 8 6 7 1 0 0 20 8 14 20 2 40 6 1 14 20 12 0 1
38 52 30 42 170 9 7 20 0 3 21 4 1 2 14 310 8 4 6 1 18 15 38 10 4 8 6 0 0 3 0 10 6 1 3 0 3 5 4 0 30 12 16 18 3 16 22 30 4 0
wi: 800 650 550 550 650
1. Submit the soft copy of the report (pdf document) to Moodle by 5pm November 30, 2025.
2. Ensure that the report file is not corrupted and can be opened.
3. Source code of the algorithm should be given as the Appendix in the report.
4. Give your name and student ID in the reports.
5. Late submission will be discounted by 10% on a daily basis.
6. Never give it up!!!