Coursework: Memetic Algorithm for Multi-Knapsack Problem

Introduction

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 mknapinstances.zip, 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

or

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

moodle.

(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%)

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