This study analyzed the effect of genetic algorithm parameter tuning on route optimization for the travelling salesman problem. It used a full factorial design to analyze the effects of population size, crossover probability, mutation probability, and number of iterations on distribution mileage. Testing showed the factors and some interactions significantly affected mileage. The combination of population=90, crossover probability=1.00, mutation probability=0.010, and iterations=800 generated the shortest mean route. This combination was concluded to be the best for optimizing distribution routes in this context.

1. The Effect of Genetic Algorithm Parameters Tuning for
Route Optimization in Travelling Salesman Problem
through General Full Factorial Design Analysis
The 17th International Conference on Quality in Research (QiR)
Nora Nisrina1
, Muhammad Irfan Kemal1
, Ilham Ali Akbar1,
, and Tri Widianti1, 2
1
Industrial Engineering Department, Faculty of Engineering, Universitas Indonesia
2
National Research and Innovation Agency of the Republic of Indonesia

2. ABSTRACT
Background: For a logistic service provider company, determining a distribution route is critical since it correlates
to costs and delivery time. Therefore, optimization is needed to determine the shortest route and operate
efficiently. Finding the shortest route can be approached by traveling salesman problem (TSP) and solved by the
genetic algorithm (GA) method. The population size, crossover probability, mutation probability, and the number of
iterations influenced the GA method in finding the optimal route.
Purpose: This study aims to analyze the effect of the population size, crossover probability, mutation probability,
and the number of iterations on the distribution mileage of Indonesian largest logistics service provider in the
Central Jakarta area with 43 distribution locations.
Method: By using general factorial design and analysis of variance (ANOVA) test. Furthermore, the least
significant difference (LSD) test is carried out to compare the mean differences of the distance by different
treatments and to determine the best treatment combination.
Result: This study revealed that all the four factors, also other three types of interactions were statistically
significant in influencing the distribution mileage. Moreover, the research showed that the combination of
population = 90, crossover probability = 1.00, mutation probability = 0.010, and the number of iteration = 800
generated the lowest mean value and was significantly different from other combinations. It indicated that this
combination was the best combination of factors and levels in the context of this study.
Originality: This study provides a different approach to analyze those four factors' influence and the interactions in
finding the shortest route using GA. It also provides empirical evidence in the Indonesian context.
2

3. Introduction
Research Design
3
Results and Discussion
Research Methodology
Outline

4. Introduction
Let’s start with the first set of slides
4
1

5. Introduction (1)
5
Routing problem is the most critical problem in logistics especially for logistic service provider
Routing Problem
Travelling
Salesman Problem
Genetic Algorithm
The wrong choice of
distribution route might
lead to cost increased,
late delivery and
customer
dissatisfaction
(Bosona, 2020)
An approach to solve
routing problem. TSP is
NP-hard problem and
required metaheuristic
algorithm to solve the
problem
One of algorithms that
empirically proven to be
able to solve TSP
(Muniandy et al., 2014)
better than other
algorithms (Bryant,
2000)

6. Introduction (2)
6
In solving routing problem to find the shortest route, GA is affected by several factors
Population Size
Crossover
Probability
Mutation
Probability
Number of
Iterations
The right choice of population size, crossover probability, mutation probability, and number of iterations in GA is really
important

7. Research Purposes
7
To analyze the effect of the population size, crossover probability, mutation probability and number
of iterations on the distribution mileage of Indonesian largest logistics service provider in Central
Jakarta area with 43 distribution locations by using general factorial design and analysis of variance
(ANOVA) test.
To find the best combination of those 4 factors value which resulting the shortest route.
1.
2.

8. Limitations
8
1.
2.
Only considered the branch office of the logistics service provider in Central Jakarta area.
3.
Routing was limited to 43 branch offices of the logistics service provider in Central Jakarta area.
4.
Distance was euclidean distance (symmetric TSP).
Simulation process was conducted using Matlab.

9. Theoretical Background
Let’s start with the second set of slides
9
2

10. GA is one of the methods that can be used to solve TSP
(Akter et al., 2019) and already implemented previously
(Deng et al., 2015; Liu & Zeng, 2009; F. Yu et al., 2016;
Y. Yu et al., 2011).
In general, solution search in GA begin with population (or chromosome)
coding and determination of fitness function (Arkeman et al., 2012).
then following by 6 steps of GA’s cycle, such as generate initial population,
fitness evaluation, reproduce mechanism (crossover and mutation), parents
selection, elitism and generate new population (Arkeman et al., 2012;
Michalewicz, 1992).
The crossover probability is in the range of 0.1-1, while the mutation
probability is in the range of 0.001-0.2 (Arkeman et al., 2012).
The advantages of GA include: has both exploration and exploitation
mechanism (Holland, 1992), flexibility — can be combined with other
methods (Vikhar, 2016; Zukhri, 2014), has a mechanism to escape from local
optimal solution (Kumar & Banka, 2013).
Genetic algorithm is a random search method that imitates the evolution
process of living organisms (Fu et al., 2018).
TSP is a classical non-polynomial problem that is applicable
to approach routing and scheduling problems
(Larranaga & Kuijpers, 2000).
Travelling salesman problem (TSP) is illustrated as a problem
of a salesperson travelling to many destinations with one stop
at each destination and returning to the starting point with
expectation of minimum total costs (Larranaga & Kuijpers, 2000).
Theoretical Background
10
Travelling Salesman Problem
Genetic Algorithm

11. The parameters used in the ANOVA test are the sum of square, degree of
freedom, mean-square, and F-ratio or p-level which represents the
probability of error.
A common practice in statistical testing is to assume 95% confidence in
the results for an effect to be categorized as statistically significant,
which means that the p-level value must be less than 0.05 (Jong, 2005)
Meanwhile, if the test is rejected, further tests can be carried out to find
out which treatment average has the most role with the least significant
difference (LSD) test (Hayter, 1986)
Then the statistical test ANOVA (Analysis of Variance) was carried out to
check whether there was a difference from the mean between two or more
sample groups for further accuracy.
Groebner et al. (2008) stated there are 4 (four) assumptions used in
testing the hypothesis on ANOVA, namely
● all populations are normally distributed
● the population variance is the same (homogeneity)
● observations are independent
● the data are in the form of interval or rate ratio
Factorial design is a well-known technique based on statistical
considerations that can produce meaningful information about the
influence of a factor in the problem, including the effect of
interactions between variables (Chan et al., 2004; Costa et al., 2005).
The analytical steps to obtain the optimal combination of
interactions are the main effect analysis and the interaction plot
(Costa et al., 2007)
Theoretical Background
11
Factorial Design
On the other hand, we should test the data adequacy with a
power data test. The power test is a method to assess the
sufficiency of the observed sample size.

12. Research Design
Let’s start with the third set of slides
12
3

13. Research Design
13
Study Focus
This study focused on finding the shortest route in package distribution of Indonesia’s largest
logistics service provider using GA simulation program
Research
Hypothesis
H0a-d
: The treatment of (a) population size, (b) crossover probability, (c) mutation probability,
and (d) number of iterations has no effect on the shortest route.
H1a-d
: The treatment of (a) population size, (b) crossover probability, (c) mutation probability,
and (d) number of iterations affect the shortest route.
Design Type
This study was designed using a general full factorial design and analyzed using the ANOVA
method

14. Research Design
14
Response
Variable
Mileage or shortest route (meter)
Factor Population size, crossover probability, mutation probability, number of iterations
Level
Population size → 20, 30, 40, 50, 60, 70, 80,
90 and 100
Replications
9 replications → the assumption number of power data > 0.8 is fulfilled
Crossover probability → 0.75 and 1
mutation probability → 0.001 and 0.01 number of iterations → 800 and 1000

15. Research Methodology
Let’s start with the fourth set of slides
16
4

16. Research Methodology
16
1. Literature Study
Conduct literature review to identify the research subject and unit analysis
2. Research Design & Pre Observation
a. Determine the factors, level of each factor, number of replication and other relevant parameters.
b. Measure the distances between branch offices in Central Jakarta (euclidean coordinate
distances)
3. Running Order Design
Running order was determined by random sequences which were generated from general factorial
design in Minitab software
4. Data Collection
Collect 648 data as a combination result of 9 levels of population size, 2 levels of crossover
probability, 2 levels of mutation probability and 2 levels of iteration number with 9 replications
5. Power and Sample Test
The power data test was conducted to determine the research data sufficiency
6. Assumption Testing
To fulfill ANOVA assumptions, normality, homogeneity and independence tests were conducted using
Minitab software
7. ANOVA Analysis
Hypothesis testing → Null (H0a-d
) and alternative hypothesis (H1a-d
)
8. Least Significant Differences Analysis
if H0
rejected, the significance between treatment will be tested
Figure 1 Research Methodology

17. Results and Discussion
Let’s start with the fifth set of slides
18
5

18. Power and Sample Size Analysis
18
▰ The power test is a method to find out
whether the size of an observed
sample is sufficient or not.
▰ Based on the power test that has been
done by the authors with the
parameters of maximum difference =
9784.8, replication = 9 total runs =
648, standard deviation = 4054.2.
Generate power value = 0.999.
▰ The power value > 0.8, meaning that
the amount of data taken was
sufficient to meet the expected
power value (Casler, 2015).

19. Testing Assumption: Residual Normality
19
▰ The residual normality test was
carried out to determine whether the
data were normally distributed or not
as one of the ANOVA assumptions
that must be met.
▰ The result was that the residual
distribution on the normality
probability plot tends to form a
straight line so that it can be
concluded that the residual data was
normal and meets the normality
assumption in ANOVA.

20. Testing Assumption: Homogeneity
20
▰ The next step is to perform a
homogeneity test to test the
uniformity of variance of each
treatment group.
▰ The homogeneity test was carried out
using the multiple comparison method
and Levene's test on the Minitab
software.
▰ Minitab software output showed that
the P-Value in the multiple comparison
test and Levene's test was greater
than 0.05. This means the data used
are homogeneous.

21. Testing Assumption: Independence of
Samples
21
▰ The residuals versus order plot is
used to verify the assumption that
the residuals are independent from
one another.
▰ Independent residuals showed no
patterns or trends when displayed in
time order.
▰ The residuals were scattered
randomly around the center line and
do not form any pattern. it means the
data from the observations were
independent of each other.

22. ANOVA Analysis
22
▰ From the results of the ANOVA test, it was found
that there is significance for all main effects and
3 types of interactions.
▰ P-value < 0.05 for all main effects. P-value < 0.05
on the interaction between crossover and
mutation; interaction between population,
crossover, and mutation; on the interaction of all
factors.
▰ This shows that there was an influence of the
four factors used and also some interactions
between them on the response variable.

23. ANOVA Analysis: Main Effect &
Interaction Plot
The main effects plot showed that the four variables had a significant
effect on the value of the resulting response variable, where the higher
the population size, crossover probability, mutation probability, and
number of iterations used tend to reduce the means shortest distance
generated.
The interaction plot graph only showed interactions
between 2 variables. In accordance with the
significance of the ANOVA test, in the graph there
were striking line angle differences in the interaction
between crossover and mutation at different
combination levels. 23

24. Least Significant Difference (LSD)
Analysis
24
LSD test helps to identify the populations whose
means are statistically different.
From these results, it can be identified that the
combination of population of 20, crossover of 0.75,
mutation of 0.001, and iteration of 800 generated the
highest mean value and significantly different from
other combinations.
Population*Crossover
*Mutation*Iteration
N Mean Grouping
20 0.75 0.001 800 9 62888.1 A
30 0.75 0.001 1000 9 62295.1 A B
20 0.75 0.001 1000 9 62148.9 A B C
30 0.75 0.001 800 9 61926.9 A B C D
90 0.75 0.010 1000 9 54908.8 D E F G
100 0.75 0.001 800 9 53933.8 E F G
90 1.00 0.001 1000 9 53583.8 F G
90 1.00 0.010 800 9 53103.3 G
The combination of population of 90, crossover of
1.00, mutation of 0.010, and iteration of 800 generates
the lowest mean value and significantly different from
other combinations. So, it can be concluded that this
combination was the best combination of factors and
levels in the context of this study.

25. “
▰ There was an effect of parameter tuning toward the route optimization
▰ This study also proved that the larger the population size, crossover, mutation,
and iteration tend to produce a better shortest distance means.
▰ The results of this study are in line with other studies which state that population
size, crossover probability, and mutation probability, and number of iterations
affect the performance of genetic algorithm.
25
25
Conclusion

26. “
▰ Theoretical Implication:
▻ Provides a good combination of parameter setting used in GA
to solve the TSP problem.
▻ Provides a new understanding of the design of experiments
usage in determining the influence of factors in the genetic
algorithm model.
▰ Managerial implication:
▻ Provides a new strategy that can be applied by logistic
companies to find the shortest route needed to determine the
distribution route.
▻ The companies can use GA simulation and consider the best
combination of factors in the research findings.
26
26
Implications

27. “ ▰ Do more treatment levels of those factors with this research
design.
▰ analyze the ability of those four factors and their
interactions to explain the model that has been made both
linearly and nonlinearly.
▰ use actual distance data that considers the highway route
in determining the 43 distribution points
▰ Use the random method for level selection so that the
inference is about the entire population level.
Limitations Future Research
▰ This study lies in the small range of treatment
levels for crossover probability, mutation
probability and number of iterations factors (only
2 levels each).
▰ In this study, the fixed method was chosen to
determine the levels of each factor. The
disadvantages of this method is that inference
only applies to those levels.
Limitations & Future Research
27

28. 28
THANK YOU
For Your Attention

29. References (1)
29
1. T. Bosona, “Urban Freight Last Mile Logistics—Challenges and Opportunities to Improve Sustainability: A Literature Review,” Sustainability, vol. 12,
pp. 1-20, 2020.
2. L. Pečený, P. Meško, R. Kampf, and J. Gašparík, “Optimisation in Transport and Logistic Processes,” Transportation Research Procedia, vol. 44, pp.
15–22, 2020.
3. M. R. Bonyadi, M. R. Azghadi and H. Shah-Hosseini, "Population-Based Optimization Algorithms for Solving the Travelling Salesman Problem," in
Traveling Salesman Problem, Croatia, Intech, 2008, pp. 1-34.
4. M.A. Muniandy, L. K. Mee and L. K. Ooi, "Efficient route planning for travelling salesman problem," in 2014 IEEE Conference on Open Systems
(ICOS), Subang, Malaysia, 2014.
5. K. Bryant, "Genetic Algorithms and the Traveling Salesman Problem," Departmen of Mathematics Harvey Mudd College, Claremont, 2000.
6. J. H. Holland, Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence,
Cambridge: MIT Press, 1992.
7. Y. Arkeman, K. B. Seminar and H. Gunawan, Algoritma Genetika: Teori dan Aplikasinya untuk Bisnis dan Industri [Genetic Algorithm: Theory and Its
Application to Business and Industry], Bogor: IPB Press, 2012.
8. Y. Zhang, Q. Ma, M. Sakamoto, and H. Furutani, “Effects of Population Size on the Performance of Genetic Algorithms and the Role of Crossover,”
Artificial Life and Robotics, vol. 15, pp. 239-243, 2010.
9. Y.-a. Zhang, M. Sakamoto and H. Furutani, "Effects of Population Size and Mutation Rate on Results of Genetic Algorithm," in Fourth International
Conference on Natural Computation, Jinan, 2008
10. I. Younas, F. Kamrani, C. Schulte and R. Ayani, "Optimization of task assignment to collaborating agents," in IEEE Symposium on Computational
Intelligence in Scheduling (SCIS), Paris, 2011..

30. References (2)
30
11. O. Roeva, S. Fidanova and M. Paprzycki, "Influence of the Population Size on the Genetic Algorithm Performance in Case of Cultivation Process
Modelling," in Proceedings of the 2013 Federated Conference on Computer Science and Information Systems, Krakow, Poland, 2013.
12. BPS, "Jumlah Kantor Pos Pembantu Menurut Kabupaten/Kota (km), 2015 - 2018 2016-2018 [Number of Sub-post Offices by Regency/City
2015-2018 2016-2018]]," Badan Pusat Statistik Provinsi DKI Jakarta, 2018. [Online]. Available:
https://jakarta.bps.go.id/indicator/17/320/1/jumlah-kantor-pos-pembantu-menurut-kabupaten-kota-km-2015---2018.html. [Accessed June 5,
2021].
13. P. Larrañaga, C. Kuijpers, R. Murga, I. Inza and S. Dizdarevic, "Genetic Algorithms for the Travelling Salesman Problem: A Review of
Representations and Operators," Artificial Intelligence Review: An International Survey and Tutorial Journal, vol. 13, no. 2, pp. 129-170, 1999.
14. S. Akter, N. Nahar, M. ShahadatHossain and K. Andersson, "A New Crossover Technique to Improve Genetic Algorithm and Its Application to TSP,"
in International Conference on Electrical, Computer and Communication Engineering (ECCE), Cox'sBazar, 2019.
15. F. Yu, X. Fu, H. Li and G. Dong, "Improved Roulette Wheel Selection-Based Genetic Algorithm for TSP," in International Conference on Network and
Information Systems for Computers, Wuhan, China, 2016.
16. Y. Deng, Y. Liu and D. Zhou, "An Improved Genetic Algorithm with Initial Population Strategy for Symmetric TSP," Mathematical Problems in
Engineering, pp. 1-6, 2015.
17. Y. Yu, Y. Chen and T. Li, "A New Design of Genetic Algorithm for Solving TSP," in Fourth International Joint Conference on Computational Sciences
and Optimization, Kunming and Lijiang City, China, 2011.
18. F. Liu and G. Zeng, “Study of Genetic Algorithm with Reinforcement Learning to Solve the TSP,” Expert Systems with Applications, vol. 36 no. 3, pp.
6995-7001, 2009.
19. C. Fu, L. Zhang, X. Wang and L. Qiao, " Solving TSP Problem with Improved Genetic Algorithm," in 6th International Conference on Computer-Aided
Design, Manufacturing, Modeling and Simulation (CDMMS 2018), 2018.
20. J. Holland, Adaptation in Natural and Artificial Systems, The University of Michigan, 1975.

31. References (3)
31
21. Z. Zukhri, Algoritma Genetika: Metode Komputasi Evolusioner untuk Menyelesaikan Masalah Optimasi, Yogyakarta: Penerbit Andi , 2013.
22. P. A. Vikhar, "Evolutionary algorithms: A critical review and its future prospects," in the International Conference on Global Trends in Signal
Processing, Information Computing and Communication (ICGTSPICC), Jaglaon, India, 2016.
23. M. Kumar and H. Banka, “Changing Mutation Operator of Genetic Algorithms for Optimizing Multiple Sequence Alignment,” International Journal of
Information and Computation Technology, vol. 3, no. 5, pp. 465-470, 2013.
24. T. A. El-Mihoub, A. A. Hopgood, L. Nolle, and A. Battersby, “Hybrid Genetic Algorithms: A Review,” Engineering Letters, vol. 13, no. 2, 2006.
25. K. D. Jong, "Genetic algorithms: a 30 year perspective," in Perspectives on Adaptation in Natural and Artificial Systems, Oxford University Press,
2005
26. P. Preux and E. G. Talbi, “Towards Hybrid Evolutionary Algorithms,” International Transactions in Operational Research, vol. 6, pp. 557-570, 1999.
27. H. Asoh and H. Mühlenbein, "On the mean convergence time of evolutionary algorithms without selection and mutation," in Parallel Problem
Solving from Nature, Berlin, Germany, Springer-Verlag, 1994, pp. 88-97.
28. Z. Michalewicz, Genetic Algorithms + Data Structures = Evolution Programs, 3 ed., Springer-Verlag, 1996..
29. K. Chan, M. Aydin and T. Fogarty, "An empirical study on the performance of factorial design based crossover on parametrical problems," in
Proceedings of the 2004 Congress on Evolutionary Computation, Portland, 2004
30. C. B. B. Costa, M. R. W. Maciel, and R. M. I. Filho, “Factorial Design Technique Applied to Genetic Algorithm Parameters in a Batch Cooling
Crystallization Optimisation,” Computers and Chemical Engineering, vol. 29, no. 10, pp. 2229–2241, 2005.

32. References (4)
32
31. C. B. B. Costa, E. A. C. Rivera, M. C. A. F. Rezende, M. R. W. Maciel, and R. M. Filho, “Prior Detection of Genetic Algorithm Significant Parameters:
Coupling Factorial Design Technique to Genetic Algorithm,” Chemical Engineering Science, vol. 62, no. 17, pp. 4780–4801, 2007.
32. D. C. Montgomery, Design and Analysis of Experiments, 9th
ed. Hoboken, NJ: John Wiley & Sons, Inc, 2017.
33. D. Groebner, Business Statistics: A Decision-Making Approach, 7th
ed.. Upper Saddle River, NJ: Pearson Prentice Hall, 2008.
34. A. J. Hayter, “The Maximum Familywise Error Rate of Fisher’s Least Significant Difference Test,” Journal of the American Statistical Association,
vol. 81, no. 396, pp. 1000–1004, 1986.
35. M. D. Casler, “Fundamentals of Experimental Design: Guidelines for Designing Successful Experiments,” Agronomy Journal, vol. 107, no. 2, pp.
692-705, 2015.
36. Support Minitab, "Residual plots for Fitted Line Plot," Minitab, 2019. [Online]. Available:
https://support.minitab.com/en-us/minitab/18/help-and-how-to/modeling-statistics/regression/how-to/fitted-line-plot/interpret-the-results/all-st
atistics-and-graphs/residual-plots/#residuals-versus-order. [Accessed June 23, 2021].
37. Y. Dodge, The Concise Encyclopedia of Statistics, New York: Springer, New York, NY, 2008.
38. Minitab Support, "What is power?," Minitab, 2020. [Online]. Available:
https://support.minitab.com/en-us/minitab/19/help-and-how-to/statistics/power-and-sample-size/supporting-topics/what-is-power/. [Accessed
June 23, 2021].