Coursework: Memetic Algorithm for Multi-Knapsack Problem

Multi-dimensional knapsack problem is a classic NP-Hard combinatorial optimisition
problem used to test the performance metaheuristics. In this coursework, you are asked to
write a C/C++ program to solve this problem using a memetic algorithm (a variant of
genetic algorithm). In addition to submitting source code, a report (no more than 2000 words
and 6 pages) is required to describe the algorithm, the experimental results, discussions and
reflections on results and performance of the algorithm. This coursework carries 50% of
the module marks. The rest of module marks comes from the final written exam.

Multi-dimensional Knapsack Problem
Multi-dimensional knapsack problem is an extension of the 1D knapsack problem by adding
capacity constraints in multiple dimensions. The problem can be formally defined as follows.
Given a set of n items numbered from 1 up to n, each with a size vector v=(v1j, v2j, v3j, …, vmj)
where vij is the i-th dimensional size of item j. bi is the i-th dimensional size of knapsack. pj
is the profit of item j if it is included in the knapsack. Denote xj be the binary variables to
indicate whether item j is included in the knapsack (=1) or not (=0). The problem to be solved
is then formulated as follows

Problem instances
In this lab, you are asked to attempt some more challenging instances from paper: P.C. Chu
and J.E.Beasley “A genetic algorithm for the multidimensional knapsack problem”, Journal
of Heuristics, vol. 4, 1998, pp63-86. All the data files are compressed in mknap￾, downloadable from Moodle. The zip file includes 9 problem instance
files (each containing 30 instances), 1 data format file file-format.txt and 1best
known solution file best-feasible-slns.txt.

Experiments conditions and requirements
The following requirements should be satisfied by your program:
(1) You are required to submit two files only. The first file should contain all your
program source codes. The second file is your report.
(2) Your source code should be properly commented.
(3) Your report should include the details of your algorithm (pseudo-code), a description
of the parameter tuning process, the results that your algorithm obtains in comparison
with the best results in the literature (i.e. gap% to the best results), a short
reflection/discussion on the strengths and weaknesses of GA/MA methods.
(4) Name your program file after your student id. For example, if your student number is
2019560, name your program as 2019560.c (or 2019560.cpp).
(5) Your program should compile without errors using one of the following commands
(assuming your student id is 2019560 and your program is named after your id):
gcc -std=c99 2019560.c -o 2019560
g++ 2019560.cpp -o 2019560
(6) After compilation, your program should be executable using the following command:
./2019560 -s data_file -o solution_file -t max_time
where 2019560 is the executable file of your program, data_file is one of
problem instance files specified in Section 3. max_time is the maximum time
permitted for a single run of your MA algorithm. soluton_file is the file for
output the best solutions by your MA algorithm. The format should be as follows:

of problems

objective value of instance 1
x1 x2 x3 … x_n
objective value of instance 2
x1 x2 x3 … x_n
… …
objective value of last instance
x1 x2 x3 … x_n
An example solution file for problem data file “mknapcb1.txt” is available on
(7) The solution file that your algorithm (solution_file) is expected to pass a
solution checking test successfully using the following command:
./mk_checker -s problem_file -c solution_file
where problem_file is one of problem data files in Section 3. If your solution file
format is correct, you should get the following command line message “All solutions
are feasible with correct objective values.”
The solution checker can be downloaded from moodle page. The checker is runnable
on CS linux server only.
(8) Your program should take no more than 10 min (i.e. 10 min max_time is set as your
stopping criteria of your MA algorithm).
5. Marking criteria • The quality of the experimental results (30%).
• The quality of codes (30%)
• Report (40%)