Measuring the Performance of Ant Colony Optimization Algorithms for the Dynamic Traveling Salesman Problem
Abstract
:1. Introduction
2. The Dynamic Traveling Salesman Problem
2.1. Problem Definition
2.2. Generating Dynamic Environments
3. Addressing the Dynamic Traveling Salesman Problem
3.1. Ant Colony Optimization Metaheuristic
3.1.1. Constructing Solutions
3.1.2. Updating Pheromone Trails
Algorithm 1 Construct Solutions (t) 

3.2. Adapting in Dynamic Environments
Algorithm 2 Pheromone Update ($t,{s}^{ib},{s}^{bs}$) 

Algorithm 3 ACO for DTSP 

4. Experimental Results
4.1. Experimental Setup
4.2. Statistical Comparisons Using Mean and Standard Deviation
4.3. Quantile Comparisons Using Peak, Average, and BadCase Performances
5. Conclusions
Author Contributions
Funding
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Algorithm $\mathit{m}\Rightarrow $  0.1  0.25  0.5  0.75 

kroA100  
$\mathcal{MM}$AS  22,223.86 ± 102.9  22,492.60 ± 108.1  22,537.36 ± 95.2  22,472.96 ± 70.7 
PACO  22,118.66 ± 49.0  22,350.54 ± 67.1  22,419.70 ± 54.7  22,320.62 ± 48.8 
rat575  
$\mathcal{MM}$AS  6573.22 ± 25.1  6577.54 ± 66.1  6399.26 ± 22.5  6401.76 ± 15.3 
PACO  6581.46 ± 25.9  6443.86 ± 20.4  6566.00 ± 43.8  6392.60 ± 19.8 
pr1002  
$\mathcal{MM}$AS  305,793.32 ± 1719.4  315,315.60 ± 1633.72  314,533.80 ± 1364.8  315,447.28 ± 1419.8 
PACO  308,342.64 ± 733.1  315,763.52 ± 456.0  313,705.60 ± 445.2  315,500.44 ± 490.4 
Algorithm $\mathit{m}\Rightarrow $  0.1  0.25  0.5  0.75 

kroA100  
$\mathcal{MM}$AS  20,543.36 ± 164.7  20,600.40 ± 62.0  20,222.00 ± 60.6  19,869.66 ± 58.2 
PACO  20,462.34 ± 36.4  20,663.38 ± 64.7  20,196.60 ± 44.7  19,900.18 ± 37.9 
rat575  
$\mathcal{MM}$AS  6621.04 ± 23.4  6465.78 ± 23.1  6404.72 ± 22.1  6399.72 ± 12.7 
PACO  6758.06 ± 70.5  6675.62 ± 25.3  6643.98 ± 15.0  6618.88 ± 13.2 
pr1002  
$\mathcal{MM}$AS  266,132.52 ± 1625.4  264,653.36 ± 1902.2  268,062.60 ± 1104.2  268,531.12 ± 1255.6 
PACO  282,904.76 ± 592.3  276.911.88 ± 394.2  275,933.72 ± 382.7  275,841.04 ± 494.7 
Algorithm  kroA100  rat575  pr1002  

$\mathit{m}\Rightarrow $  0.1  0.25  0.5  0.75  0.1  0.25  0.5  0.75  0.1  0.25  0.5  0.75 
${Q}_{0.10}$  
$\mathcal{MM}$AS  22,127  22,390  22,440  22,385  6573  6459  6375  6381  302,494  311,643  311,175  312,291 
PACO  22,084  22,266  22,356  22,268  6546  6418  6397  6367  307,513  315,147  313,007  314,951 
${Q}_{0.50}$  
$\mathcal{MM}$AS  22,186  22,467  22,520  22,486  6570  6483  6395  6402  306,249  315,903  314,514  316,560 
PACO  22,102  22,341  22,416  22,319  6583  6445  6432  6390  308,586  315,880  313,964  315,455 
${Q}_{0.90}$  
$\mathcal{MM}$AS  22,400  22,670  22,676  22,556  6613  6518  6431  6420  309,279  318,927  317,478  318,266 
PACO  27,212  22,432  22,506  22,386  6610  6467  6481  6419  309,059  316,302  314,222  316,100 
Algorithm  kroA100  rat575  pr1002  

$\mathit{m}\Rightarrow $  0.1  0.25  0.5  0.75  0.1  0.25  0.5  0.75  0.1  0.25  0.5  0.75 
${Q}_{0.10}$  
$\mathcal{MM}$AS  20,415  20,531  20,147  19,804  6594  6493  6380  6383  260,009  258,675  266,618  267,049 
PACO  20,424  20,590  20,147  19,854  6658  6643  6624  6603  28,2195  276,460  275,443  275,157 
${Q}_{0.50}$  
$\mathcal{MM}$AS  20,483  20,590  20,223  19,873  6618  6465  6402  6399  267,186  265,953  268,035  268,321 
PACO  20,453  20,654  20,196  19,895  6767  6680  6644  6620  282,958  276,900  275,998  275,900 
${Q}_{0.90}$  
$\mathcal{MM}$AS  20,881  20,689  20,308  19,944  6658  6499  6439  6417  270,615  269,053  269,799  270,295 
PACO  20,519  20,753  20,245  19,956  6833  6706  6662  6634  283,574  277,404  276,372  276,496 
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Mavrovouniotis, M.; Anastasiadou, M.N.; Hadjimitsis, D. Measuring the Performance of Ant Colony Optimization Algorithms for the Dynamic Traveling Salesman Problem. Algorithms 2023, 16, 545. https://doi.org/10.3390/a16120545
Mavrovouniotis M, Anastasiadou MN, Hadjimitsis D. Measuring the Performance of Ant Colony Optimization Algorithms for the Dynamic Traveling Salesman Problem. Algorithms. 2023; 16(12):545. https://doi.org/10.3390/a16120545
Chicago/Turabian StyleMavrovouniotis, Michalis, Maria N. Anastasiadou, and Diofantos Hadjimitsis. 2023. "Measuring the Performance of Ant Colony Optimization Algorithms for the Dynamic Traveling Salesman Problem" Algorithms 16, no. 12: 545. https://doi.org/10.3390/a16120545