https://github.com/shah314/gamultiknapsack
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README.md
<H1>GKNAP: A Java and C++ package for solving the multidimensional knapsack problem</H1>
<i><h3>Shalin Shah</h3></i>
<a style="border-width:0" href="https://doi.org/10.21105/joss.01756">
<img src="https://joss.theoj.org/papers/10.21105/joss.01756/status.svg" alt="DOI badge" >
</a>
<a href="https://zenodo.org/badge/latestdoi/134312370"><img src="https://zenodo.org/badge/134312370.svg" alt="DOI"></a>
<br>
<P>A genetic algorithm implementation for the multidimensional knapsack problem. The multi-constraint (or multidimensional) knapsack problem is a generalization of the 0/1 knapsack problem. The multi-constraint knapsack problem has m constraints and one objective function to be maximized while all the m constraints are satisfied.<P>The implementation is similar to the one described in [Chu98], but its <i>significantly different</i>. It uses Lagrangian multipliers as constraint weights and compared to the paper, it finds close to optimum solutions much faster. (Convergence can be controlled using the parameters).</p>
<p>Please see <a href="https://arxiv.org/abs/1908.08022">this paper</a> for a detailed description of the algorithm.</p>
<h2>Cite this work</h2>
<pre>
@article{shah2019gknap,
title={GKNAP: A Java and C++ package for solving the multidimensional knapsack problem},
author={Shah, Shalin},
journal={Journal of Open Source Software},
volume={4},
number={42},
pages={1756},
year={2019}
}
</pre>
<pre>
<b>Usage</b>
The usage of this code base is to just compile the code and run it on the command line.
The code will output the solution found, the value of the objective function and
the chosen items for the knapsack. The code requires a <b>weing</b> formatted file or an <b>orlib</b> formatted file.
The <b>weing</b> formatted files are available <a href="http://people.brunel.ac.uk/~mastjjb/jeb/orlib/files/mknap2.txt">here</a>.
The <b>orlib</b> formatted files are available <a href="http://people.brunel.ac.uk/~mastjjb/jeb/orlib/mknapinfo.html">here</a> (used by P.C.Chu and J.E.Beasley).
The orlib formatted files are available <a href="http://people.brunel.ac.uk/~mastjjb/jeb/orlib/files/">here</a> which are named mknapcb1.txt, mknapcb2.txt and so on.
Please note that these files contain multiple instances, so to run the algorithm,
please use any <b>one</b> of the instances.
The distributions of the files are quite different between orlib and weing.
If the algorithm is stuck, please increase Constants.DIFF_TOLERANCE on line 31 of GeneticAlgorithm.java.
<b>The format of all files is described <a href="http://people.brunel.ac.uk/~mastjjb/jeb/orlib/mknapinfo.html">here</a>.</b>
<b>Java implementation</b>
I tested the code using JDK 1.8, but any JDK should work fine.
If the code does not compile, please open an issue.
Compile the Java code and then run GeneticAlgorithm.
javac *.java
java GeneticAlgorithm filename format
(The file name contains the instance in weing or orlib format)
(The format is either weing or orlib)
Example:
java GeneticAlgorithm data.DAT weing
<b>C++ implementation</b>
The code was tested on a Mac with gcc version 8, downloaded using homebrew.
If the code does not compile, please open an issue.
Compile the C++ code and then run the executable.
g++ cmultiknapsack.cpp
./a.out filename format
(The file name contains the instance in weing or orlib format)
(The format is either weing or orlib)
Example:
./a.out data.DAT weing
(Please remove all comments and other extraneous text from data.DAT)
(See the tests directory for <b>testcpp.sh and testjava.sh</b> for an example run)
<b>Dependencies</b>
The code has no other dependencies. A JDK or a gcc compiler is all that is required.
<b>Using the code as an API</b>
If you want to use the code as an API call from your own code:
<b>Java:</b> In GeneticAlgorithm.java, please see the main method.
<b>C++:</b> In the C++ code, please see the main method.
</pre>
The benchmark instances are available <a href="http://people.brunel.ac.uk/~mastjjb/jeb/orlib/files/mknap2.txt">here</a>. They have the following format:
<pre>
//This is the WEING1.DAT data file plus some comments, that are NOT part of the problem instance.
2 28 // 2 knapsacks, 28 objects
1898 440 22507 270 14148 3100 4650 30800 615 4975
1160 4225 510 11880 479 440 490 330 110 560
24355 2885 11748 4550 750 3720 1950 10500 // 28 weights
600 600 // 2 knapsack capacities
45 0 85 150 65 95 30 0 170 0
40 25 20 0 0 25 0 0 25 0
165 0 85 0 0 0 0 100 // #1 constr.
30 20 125 5 80 25 35 73 12 15
15 40 5 10 10 12 10 9 0 20
60 40 50 36 49 40 19 150 // #2 constr.
141278 // optimum value
</pre>
The comments beginning with "//" are only for the purpose of explaining the format. <b>Please remove all comments before running the algorithm</b>.
<p>The algorithm was run on a few <a href="http://people.brunel.ac.uk/~mastjjb/jeb/orlib/files/mknap2.txt">benchmark
instances</a>:</p>
<div align="left">
<table>
<tr>
<td ><b>Instance</b></td>
<td ><b>Optimum</b></td>
<td ><b>Found - Best</b></td>
<td ><b>Found - Worst</b></td>
<td ><b>Time (s)</b></td>
</tr>
<tr>
<td >Weing1</td>
<td >141278</td>
<td >141278</td>
<td >141278</td>
<td >0</td>
</tr>
<tr>
<td >Weing2</td>
<td >130883</td>
<td >130883</td>
<td >130883</td>
<td >1</td>
</tr>
<tr>
<td >Weing3</td>
<td >95677</td>
<td >95677</td>
<td >95677</td>
<td >1</td>
</tr>
<tr>
<td >Weing4</td>
<td >119337</td>
<td >119337</td>
<td >119337</td>
<td >0</td>
</tr>
<tr>
<td >Weing5</td>
<td >98796</td>
<td >98796</td>
<td >98796</td>
<td >0</td>
</tr>
<tr>
<td >Weing6</td>
<td >130623</td>
<td >130623</td>
<td >130623</td>
<td >0</td>
</tr>
<tr>
<td >Weing7</td>
<td >1095445</td>
<td >1095445</td>
<td >1095445</td>
<td >2</td>
</tr>
<tr>
<td >Weing8</td>
<td >624319</td>
<td >624319</td>
<td >624319</td>
<td >4</td>
</tr>
<tr>
<td >Sento1</td>
<td >7772</td>
<td >7772</td>
<td >7772</td>
<td >1</td>
</tr>
<tr>
<td >Sento2</td>
<td >8722</td>
<td >8722</td>
<td >8722</td>
<td >0</td>
</tr>
<tr>
<td >Weish01</td>
<td >4554</td>
<td >4554</td>
<td >4554</td>
<td >0</td>
</tr>
<tr>
<td >Weish02</td>
<td >4536</td>
<td >4536</td>
<td >4536</td>
<td >0</td>
</tr>
<tr>
<td height="25">Weish03</td>
<td height="25">4115</td>
<td height="25">4115</td>
<td height="25">4115</td>
<td height="25">0</td>
</tr>
<tr>
<td >Weish04</td>
<td >4561</td>
<td >4561</td>
<td >4561</td>
<td >0</td>
</tr>
<tr>
<td >Weish05</td>
<td >4514</td>
<td >4514</td>
<td >4514</td>
<td >0</td>
</tr>
<tr>
<td >Weish06</td>
<td >5557</td>
<td >5557</td>
<td >5557</td>
<td >0</td>
</tr>
<tr>
<td >Weish07</td>
<td >5567</td>
<td >5567</td>
<td >5567</td>
<td >0</td>
</tr>
<tr>
<td >Weish08</td>
<td >5605</td>
<td >5605</td>
<td >5605</td>
<td >0</td>
</tr>
<tr>
<td >Weish09</td>
<td >5246</td>
<td >5246</td>
<td >5246</td>
<td >0</td>
</tr>
<tr>
<td >Weish10</td>
<td >6339</td>
<td >6339</td>
<td >6339</td>
<td >0</td>
</tr>
<tr>
<td >Weish11</td>
<td >5643</td>
<td >5643</td>
<td >5643</td>
<td >0</td>
</tr>
<tr>
<td >Weish12</td>
<td >6339</td>
<td >6339</td>
<td >6339</td>
<td >0</td>
</tr>
<tr>
<td >Weish13</td>
<td >6159</td>
<td >6159</td>
<td >6159</td>
<td >0</td>
</tr>
<tr>
<td >Weish14</td>
<td >6954</td>
<td >6954</td>
<td >6954</td>
<td >0</td>
</tr>
<tr>
<td >Weish15</td>
<td >7486</td>
<td >7486</td>
<td >7486</td>
<td >1</td>
</tr>
<tr>
<td >Weish16</td>
<td >7289</td>
<td >7289</td>
<td >7289</td>
<td >0</td>
</tr>
<tr>
<td >Weish17</td>
<td >8633</td>
<td >8633</td>
<td >8633</td>
<td >0</td>
</tr>
<tr>
<td >Weish18</td>
<td >9580</td>
<td >9580</td>
<td >9580</td>
<td >0</td>
</tr>
<tr>
<td >Weish19</td>
<td >7698</td>
<td >7698</td>
<td >7698</td>
<td >0</td>
</tr>
<tr>
<td >Weish20</td>
<td >9450</td>
<td >9450</td>
<td >9450</td>
<td >0</td>
</tr>
<tr>
<td >Weish21</td>
<td >9074</td>
<td >9074</td>
<td >9074</td>
<td >1</td>
</tr>
<tr>
<td >Weish22</td>
<td >8947</td>
<td >8947</td>
<td >8947</td>
<td >1</td>
</tr>
<tr>
<td >Weish23</td>
<td >8344</td>
<td >8344</td>
<td >8344</td>
<td >0</td>
</tr>
<tr>
<td >Weish24</td>
<td >10220</td>
<td >10220</td>
<td >10220</td>
<td >2</td>
</tr>
<tr>
<td >Weish25</td>
<td >9939</td>
<td >9939</td>
<td >9939</td>
<td >1</td>
</tr>
<tr>
<td >Weish26</td>
<td >9584</td>
<td >9584</td>
<td >9584</td>
<td >0</td>
</tr>
<tr>
<td >Weish27</td>
<td >9819</td>
<td >9819</td>
<td >9819</td>
<td >0</td>
</tr>
<tr>
<td >Weish28</td>
<td >9492</td>
<td >9492</td>
<td >9492</td>
<td >0</td>
</tr>
<tr>
<td >Weish29</td>
<td >9410</td>
<td >9410</td>
<td >9410</td>
<td >0</td>
</tr>
<tr>
<td >Weish30</td>
<td >11191</td>
<td >11191</td>
<td >11191</td>
<td >0</td>
</tr>
<tr>
<td >PB1</td>
<td >3090</td>
<td >3090</td>
<td >3076</td>
<td >9</td>
</tr>
<tr>
<td >PB2</td>
<td >3186</td>
<td >3186</td>
<td >3186</td>
<td >2</td>
</tr>
<tr>
<td >PB4</td>
<td >95168</td>
<td >95168</td>
<td >95168</td>
<td >1</td>
</tr>
<tr>
<td >PB5</td>
<td >2139</td>
<td >2139</td>
<td >2139</td>
<td >2</td>
</tr>
<tr>
<td >PB6</td>
<td >776</td>
<td >776</td>
<td >776</td>
<td >0</td>
</tr>
<tr>
<td >PB7</td>
<td >1035</td>
<td >1035</td>
<td >1035</td>
<td >0</td>
</tr>
<tr>
<td >HP1</td>
<td >3418</td>
<td >3404</td>
<td >3404</td>
<td >0</td>
</tr>
<tr>
<td >HP2</td>
<td >3186</td>
<td >3186</td>
<td >3186</td>
<td >4</td>
</tr>
</table>
</div>
<h2>References</h2>
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