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IAES International Journal of Artificial Intelligence (IJ-AI)
Vol. 13, No. 3, September 2024, pp. 2923∼2933
ISSN: 2252-8938, DOI: 10.11591/ijai.v13.i3.pp2923-2933 r 2923
A comparison of meta-heuristic and hyper-heuristic
algorithms in solving an urban transit routing problems
Ahmad Muklason, Shof Rijal Ahlan Robbani, Edwin Riksakomara, I Gusti Agung Premananda
Department of Information Systems, Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia
Article Info
Article history:
Received Jan 24, 2023
Revised Nov 15, 2023
Accepted Dec 3, 2023
Keywords:
Hill climbing
Hyper-heuristics
Particle swarm optimization
Simulated annealing
Urban transit routing problem
ABSTRACT
Public transport is a serious problem that is difficult to solve in many coun-
tries. Public transport routing optimization problem also known as urban tran-
sit routing problem (UTRP) is time-consuming process, therefore effective ap-
proches are urgently needed. UTRP aims to minimize cost passenger and op-
erator from a combination of route set. UTRP can be optimize with heuris-
tics, meta-heuristics, and hyper-heuristics methods. In several previous studies,
UTRP can be optimized with any meta-heuristics and hyper-heuristics meth-
ods. In this study we compare the performance of meta-heuristic methods, i.e.
ill-climbing, simulated annealing, and hyper-heuristics method based on mod-
ified particle swarm optimization algorithm. The experimental results showed
that the proposed methods could solve UTRP effectively. Regarding their per-
formance, the results show that despite the generality of hyper-heuristics, their
performance are competitive. More specifically, hyper-heuristics method is the
best method compared to the other two methods in each dataset. In addition,
compared to prior studies results, he proposed hyper-heuristics could outperform
them in term of cost passenger of small dataset Mandl. The main contribution
of this paper is that to best of our knowledge, it is the first study comparing the
performance of meta-heuristics and hyper-heuristics approaches over UTRP.
This is an open access article under the CC BY-SA license.
Corresponding Author:
Ahmad Muklason
Department of Information Systems, Institut Teknologi Sepuluh Nopember
St. Raya ITS, Kampus ITS Sukolilo Surabaya 60111, East Java, Indonesia
Email: mukhlason@is.its.ac.id
1. INTRODUCTION
Public transport is a solution to overcome traffic jams in an area or regional. However, there are
still many countries that has not implemented public transport properly and optimally, so that cannot be a
solution for any civilian. Traffic congestion is a serious problem in the world and not easy to handle it [1]. An
implementation of public transport can be improved by optimizing routes based on distance and time [2]. But,
it can take a lot of time and energy, so a can be problem classified as combinatorial problems.
A problem of determining public transport routes can also be referred to urban transit routing problem
(UTRP). UTRP is the part of urban transit network design problem (UTNDP) which focuses on solving problem
of finding routes and scheduling public transportation. UTNDP is the part of vehicle routing problem (VRP).
UTRP has a fitness function like cost passenger and operator [3]. A cost passenger point of view is said to be
efficient, if the total travel time and total transfer time can be minimized. Meanwhile, cost operator point of view
the number of routes, and the total number of all bus route lengths can be minimized. To be able to minimize
the UTRP fitness function, a suitable combination is needed to determine a route. Therefore, an UTRP problem
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2924 r ISSN: 2252-8938
can be said to be a combinatorial problem [4]. Combinatorial problems can be solved using heuristics, meta-
heuristics, and hyper-heuristics methods, because they can help find an optimal objective function by providing
several possible combinations of solutions [5], [6].
Hyper-heuristics method has a major difference with metaheuristics, it directly searches for solutions
in the space of heuristics [7]. Hyper-heuristics method aims to find right combination of low-level heuristics
(LLH) is easy to apply and produces an acceptable domain solution [8]. Metaheuristic methods has been used
to solve VRP problems, including: genetic algorithm (GA), simulated annealing (SA) algorithm, tabu search
(TS) algorithm, and particle swarm optimization (PSO) algorithm [9], [10]. Hyper-heuristics have also been
used to solve VRP problems and resulted well-designed hyper-heuristics are useful for building and improving
solutions [2], [7], [11].
In several previous studies, VRP problems have been solved using several metaheuristic methods,
including: GA, PSO, and TS. VRP solution using a hybrid GA method shows that hybrid GA method has better
performance than normal GA method [12]. Completion of VRP using modified PSO shows that, modified PSO
method has better performance than PSO in achieving vehicle routes that focus on problems by considering
complete costs which will reduce total costs and emissions [13]. Completion of VRP using the hybrid TS
method results in better performance, less computation time, and very effective in finding solutions to problems
[14]. VRP solution using GA and PSO methods, shows that can produces a fairly good objective value and
represented that GA is better than PSO [15]. Results of previous research indicate that a modified or hybrid
metaheuristic method can be a solution to obtain a route sequence that is close to optimal solution with fast
processing time.
Several studies on UTRP have been carried out. One of them is to use hill-climbing (HC) and SA
methods to solve an UTRP problem, both of methods can produced competed fitness function with results of
previous studies [16]. Another studies, uses a new heuristic and evolutionary operators methods, and show
a results proposed method can outperform previous research in terms of passenger costs and operator costs
[17]. Another studies, proposed a selection hyper-heuristics methods as a tool to solve an UTRP problem.
Based on this research, it is known that the sequence-based selection methods combined with the great deluge
acceptance has the best performance in terms of passenger and operator costs [18]. Another studies, has
been success implemented a cat swarm optimization for UTRP and produced an objective function can be
compared with previous studies [19]. Another studies, successfully used imported flower pollination algorithms
to solve UTRP and had more effective results in the Mandl dataset [20]. Another studies, applied differential
evolution, show that an objective function is outperformed most of the results from other literatures [21].
Another studies, proposed a sequence-based selection methods combined with the great deluge acceptance (SS-
GD) using dataset development and show that methods is able to improve existing route services for passengers
and operators, and shows great potential to deal with real-world problems in a short time when compared to
GA [22].
Based on several previous studies, an UTRP problem can be solved using meta-heuristics or hyper-
heuristics methods. Therefore, in this study, an UTRP will be solved by using HC and SA as metaheuris-
tics methods and a modified particle swarm optimization algorithm based on gravitational search interactions
(MPSO-GI) with a hyper-heuristics approach as hyper-heuristics methods. These three methods are used for
solving public transport problems to get a more optimal solution of problem. So that result of cost passenger
and operator as objective function can find a better solution. Reason of using a MPSO algorithm is based on
previous research which explains that modified PSO algorithm has better results than standard PSO for solving
VRP problems [13]. MPSO-GI algorithms modifies PSO with the gravitational search algorithm approach and
shows more optimal results than standard PSO [23]. MPSO-GI has a learning coefficient value based on a
position of the gravitational interactions between particles which much more stable than user input value. PSO
algorithm and hyper-heuristics approach has been carried out in research on solving the resource constrained
project scheduling problem (RCPSP) and has a competitive solution result when compared to other methods
[24]. In research on evolving dispatching rules in job shop scheduling, PSO algorithms and hyper-heuristics ap-
proaches can be applied and produce solutions that are more competitive and faster than genetic programming
methods with hyper-heuristics [25].
A dataset used in this study is dataset in previous research, namely Mandl and Mumford [26]. Mandl
data is a representation of bus routes in 15 cities in Switzerland. Meanwhile, Mumford dataset is a represen-
tation of the small transport network and bus routes in the city (Yubei, Brighton, and Cardiff). The results of
this study will be compared with the results of previous studies using the same dataset. So it can find out the
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advantages of proposed methods in solving an UTRP problem.
2. RESEARCH METHOD
In this section, the research methodology employed to tackle the UTRP is elucidated in detail. To
ensure a comprehensive understanding of the approach, the methodology is divided into sub-sections, each
detailing a specific phase of the research. Firstly, the dataset utilized is discussed, which comprises examples
from various global locations, including Yubei in China, Brighton and Cardiff in the UK, and 15 cities in
Switzerland. To analyze this dataset, the design of the algorithm is explored in stages, encompassing data
conversion, initial solution formation, and the incorporation of various algorithmic techniques such as HC, SA,
and hyper-heuristics using MPSO-GI. The implementation phase details the technical setup and computational
resources used, ensuring replicability of the results. Lastly, the results derived from the applied algorithms
will be critically analyzed and compared with the findings of previous studies in the domain. This systematic
approach ensures a holistic and structured examination of the UTRP, facilitating a comprehensive exploration
of potential solutions.
2.1. Dataset
The study utilizes data from a benchmark dataset previously used in research [26]. This dataset in-
cludes five examples, called Mumford0, Mumford1, Mumford2, Mumford3, and Mandl. Mumford1, Mum-
ford2, and Mumford3 represent bus route data in Yubei, China, Brighton, and Cardiff, UK respectively. Mum-
ford0 represents data with a small network, while Mandl represents bus routes in 15 cities in Switzerland.
Table 1 further describes the specifics and features of the dataset used in the study.
Table 1. Description instance
Instances Vertices Edges Routes Vertices per route (min-max)
Mandl4 15 21 4 2 – 8
Mandl6 15 21 6 2 – 8
Mandl7 15 21 7 2 – 8
Mandl8 15 21 8 2 – 8
Mumford0 30 90 12 2 – 15
Mumford1 70 210 15 10 – 30
Mumford2 110 385 56 10 – 22
Mumford3 127 425 60 12 - 25
2.2. Design of algorithm
In this sub-section, a structured, step-by-step algorithmic approach to address the research problem is
outlined. This algorithmic strategy involves several intricate steps, including data conversion, formation of the
initial solution, and application of multiple optimization techniques. Each of these steps, pivotal to the success
of the research, is detailed in subsequent segments to ensure a comprehensive understanding of the approach.
2.2.1. Data conversion and hard constrains
In this step, dataset used is read in .txt format. Then dataset is converted into an array by making
adjustments, so that can be read by program. Adjustments are made by replacing the value ”Inf” to 0 in a
TravelTimes data, so that process of finding hard constraints can be easier. Furthermore, data can be obtained
in the form of an array of TravelTimes and demand data. An array of data can be optimized according to desired
algorithm with program that has been created. Next, search for hard constraints by searching whether points
between an arrays have a value of 0.
2.2.2. Initiate solution
In this step, an initial solution is formed from selected and implemented dataset. The first step in
forming an initial solution is to determine parameters of each dataset. Parameters need to be determined include
number of routes, as well as MIN and MAX lengths on each route. Parameters used are in accordance with
the specifications of each dataset that have been described. Furthermore, the initial solution can be obtained
by determining starting point of a solution on each route by determining point, that has most connections with
A comparison of meta-heuristic and hyper-heuristic algorithms in solving ... (Ahmad Muklason)
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other points. Next point is selected based on the hard constraints of starting point that has been obtained. The
formation of an initial solution can be explained by pseudocode in Algorithm 1.
Algorithm 1: Pseudocode for initiating solution
Function getNewRoute(data, Min, Max, r, datasize):
route ← array;
dataC ← getConnected(data);
startNode ← start node per route;
for i = 0 to r do
initializeRoute(route[i], startNode, dataC);
end
while Unused is not empty do
randRute ← pickRandomRoute();
resetRoute(route[randRute], startNode, dataC);
end
return route;
2.3. Calculate fitness
To proceed to the optimization stage, it is necessary to calculate the fitness value for each iteration that
will be performed. Fitness function of an UTRP is cost passenger and operator. Cost passenger (Cp) obtained
from the total travel time of all passengers which can be calculated as in (1):
Cp(R) =
Pn
i,j=1 dijaij(R)
Pn
i,j=1 dij
(1)
where dij = transit demand from node xi to node xj, αij = shortest time from xi to xj, and R = route set.
Cost operational regarding a number of vehicles to ensure service quality cannot be handled without
considering vehicle scheduling. Other costs operating depend on length of a transportation route. Therefore a
cost operator (Co) defined as total length of a route set as in (2):
Co(R) =
n
X
a=1
X
(i,j)∈r
tij(a) (2)
where: a = typical route R, r = number of routes, and tij(a) = length of transport link.
2.3.1. Hill climbing
In this section, the research is carried out using a results of initial solution that has been formed
including, initial route and cost of passenger and operator. Furthermore, results of the initial solution are
processed using a HC method to get better solution. HC method used is make-small-change as was done in
previous research [9]. Pseudocode of the HC method can be seen in Algorithm 2.
Algorithm 2: Pseudocode for HC
Function getRouteHC():
rand1, rand2 ← pickRouteAndNodeRandomly();
if route[rand1] ¡ max then
while !route[rand1].contains(rand2) do
route[rand1].add(rand2);
end
end
else
swapStartAndEndNodes(rand1);
end
if not isValid then
resetRoute(rand1);
end
return route;
The first step of HC is to determine randomly which route will be modified. After getting the selected
route, then determine the possibilities that can be used. First possibility can be used, if the length of a selected
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route is less than MAX parameter. As well as last possibility can be used, if the route can not run the first
possibility.
After performing the possible procedures of make-small-change method a new route is obtained. Next,
check whether a route meets the requirements as a route in an UTRP problem. If a route is declared valid then,
a route can replace previous route and used for calculating new fitness function.
2.3.2. Simulated annealing
In this SA algorithm, the research is conducted by utilizing the results of the initial solution, which
includes the initial route and the cost for passengers and operators. The results of the initial solution are then
further processed using the SA method to achieve better results. The SA method is applied with the temperature
set to 1000 and the cooling factor as per previous studies [16]. Additionally, the combination of the make-small-
change method, as described in previous research [9], is used. The flowchart for the SA method can be seen in
Figure 1.
Start End
Initiate Solution
Update
Parameter
Modified
Solution
Calculate
Fitness
newFit<CurrFit
Calculate
Probability
rand<probability
Temp<1
Optimized
Solution
Yes
Yes
Yes
No
No
No
Figure 1. Flowchart SA
The first step is to determine the temperature parameter and calculate the cooling factor, which is used
as an iteration for the procedure to be carried out. Next, a random route is selected to be modified. After the
selected route is determined, possible modifications are evaluated. The first possibility is used if the length of
the selected route is less than the MAX parameter. The last possibility is used if the first possibility cannot be
applied.
After performing the possible procedures of the make-small-change method, a new route is obtained.
The procedure is repeated until the temperature drops to zero. Next, the validity of the route as a solution to
the UTRP problem is checked. If the route meets the requirements, it replaces the previous route and is used to
calculate the fitness function.
2.3.3. Hyper-heuristic with modified particle swarm optimization
In this study, a hyper-heuristic approach that combines a modified version of MPSO-GI with sim-
ple random selection and five types of LLH is employed to solve the UTPR. The hyper-heuristic process is
carried out for a pre-determined number of iterations and is constrained by a time limit. Move acceptance is
used in each iteration, and the process of the hyper-heuristics can be observed in the flowchart presented in
Figure 2. The UTRP optimization process using the hyper-heuristics begins with a random selection of an
LLH, followed by the application of MPSO-GI until the desired number of iterations is reached.
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In the move acceptance phase, MPSO-GI is used to select a solution based on the particle, and the
specified number of iterations is run. The initial step of MPSO-GI involves defining the particle parameters and
the number of iterations. A random route is then chosen and transformed using MPSO-GI into a new solution
using the specified number of particles. The new solution is evaluated using the fitness function, and if it has
a better value, it is accepted and replaces the previous solution. The procedure for implementing MPSO-GI
move acceptance can be found in Algorithm 3.
Algorithm 3: Pseudocode MPSO-GI Algorithm
Function MPSO():
particle ← number of solution;
iteration, MaxIter ← number of iteration;
generatePosition();
generateVelocity();
solutionPerParticle();
while iteration¡maxIter do
newVelocity();
newPosition();
solutionPerPartikel();
if bestFit < fitness then
fitness = bestFit;
updateRoute();
end
end
return routeSR;
Start End
Initiate Solution
LLH Selection
Move Acceptance
MPSO
Solution
Accepted
iteration Done
Best Solution
Update Best
Solution
Yes
Yes
Yes
No
No
No
Figure 2. Flowchart hyper-heuristics
In addition, the simple random method is used to randomly select an LLH for each iteration. In this
study, the number of LLH [4] used is:
− LLH0: choose a random route and position of route. Then add random value points to a position and
route that has been selected.
− LLH1: randomly chooses a route and two positions in a route. Then swap two positions that have been
chosen.
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− LLH2: randomly chooses a route and two positions in a route. Then a first point replaces a second point,
and a second point becomes a last point.
− LLH3: choose two routes randomly and a position on each route. Then enter a point on first route into
second route to selected second point.
− LLH4: choose two routes randomly and one position on each route. Then change point that has been
selected on each route.
2.4. Implementation
The algorithm developed in this study was implemented using the Java programming language and the
eclipse integrated development environment (IDE). The computer system used for the implementation had the
following specifications: an Intel i5-8250U processor with a clock speed of 1.60 GHz, 8129 MB of RAM, and
the Windows 10 Home operating system. The program was executed on each dataset for 200 iterations using
the HC algorithm. In the case of the MPSO-GI algorithm, the program was also run for 200 iterations, with a
time constraint of 10 minutes to ensure consistency in running time with the HC algorithm. The SA algorithm
was configured to produce a running time that is comparable to the other algorithms. To ensure the robustness
of the results, all algorithms were run 10 times on each dataset, and the best result was selected for the analysis
phase.
2.5. Analysis of results
The performance of the algorithm will be compared with the methods and outcomes of two prior
studies. The first study, by Mumford [17], developed the new heuristic and evolutionary operators (NH-EO)
algorithm. The second study, by Ahmed et al. [18], developed the sequence selection based great deluge (SS-
GD) algorithm. The analysis and comparison of the results will provide insight into the effectiveness of the
implemented algorithm in comparison to the previously developed ones.
3. RESULTS AND DISCUSSIONS
The results section discusses the outcome of the experiments conducted on the UTRP problem using
three algorithms. The algorithms used were HC and SA, which employ the metaheuristic approach, and MPSO-
GI, which utilizes the hyper-heuristic approach. In the HC method, the parameters used were 200 iterations
and 10 trials, while in the SA method, the temperature was set to 1000 and the cooling factor to 0 < c < 1.
MPSO-GI used 5 particles, 200 iterations, and 10 trials. The best results from the tests will be compared to
analyze the three algorithms.
3.1. Comparison result of MPSO-GI, simulated annealing, and hill climbing
The experiments compared three distinct algorithms: HC, SA, and MPSO-GI. The results, as depicted
in Table 2, show notable differences in their performance across various datasets. The MPSO-GI algorithm,
underpinned by the hyper-heuristic approach, generally displayed superiority. This dominance was evident in
both the ”best” and ”average” results across the majority of datasets. However, there were exceptions. In the
passenger cost (Cp) aspect, the ”best” results from the HC algorithm surpassed MPSO-GI for the Mumford1
and Mumford2 datasets. Additionally, in the operation cost (Co) aspect, the ”best” result of the SA outper-
formed MPSO-GI on the Mumford2 dataset.
When comparing HC and SA, HC typically exhibited better performance. This was particularly evi-
dent in the passenger cost aspect, where HC’s ”best” and ”average” results were superior in most datasets, with
the exception of Mumford0. For operation costs, HC’s ”best” results were better on the Mandl4, Mandl6, and
Mandl8 datasets.
The standout performance of MPSO-GI can be ascribed to two primary factors. Firstly, MPSO-GI is a
population-based algorithm, contrasting with SA and HC, which are local search algorithms. Such population-
based algorithms generally possess a heightened capability for solution exploration and evasion of local optima.
The second factor is MPSO-GI’s hyper-heuristic approach, which incorporates various LLLHs, including the 5
types of LLHs. This not only magnifies the diversity of the search but often leads to enhanced solutions.
In a direct comparison of SA and HC, SA appeared less adept at exploiting solutions. This observa-
tion was substantiated by the ”average” results, where SA often lagged behind HC. However, in more extensive
datasets like Mumford0, Mumford1, and Mumford2, especially in the operation cost aspect, HC, which typ-
A comparison of meta-heuristic and hyper-heuristic algorithms in solving ... (Ahmad Muklason)
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ically accepts superior solutions, seemed more susceptible to local optima. As a result, in these datasets, its
solutions were occasionally outpaced by those of the SA algorithm.
Table 2. Comparison results of proposed method
Fitness function Methods Statistics
Dataset
Mandl4 Mandl6 Mandl7 Mandl8 Mumford0 Mumford1 Mumford2
Cp HC Best 18 15 16 10 15 34 70
Average 29.95 26.3 27.9 24.75 35.9 52.7 81.1
Worst 44 45 43 41 50 63 89
Std Dev 8.20 8.77 7.18 8.09 8.93 10.71 5.79
SA Best 15 27 19 16 19 54 76
Average 23.7 29.3 29.7 18.3 40.3 66 83.2
Worst 35 43 44 38 66 73 89
Std Dev 5.3 5.3 9.1 9.3 10.5 9.5 6.8
MPSO-GI Best 8 9 8 7 17 45 72
Average 15 16.35 17.25 19.65 30 60.35 79.35
Worst 30 24 35 45 39 68 83
Std Dev 4.22 3.5 9.31 9.91 6.85 8.31 3.47
Co HC Best 53 90 107 113 117 1074 3624
Average 73.7 108.55 131.05 151.9 641.95 1106.55 3791.25
Worst 101 157 172 195 1158 1158 3948
Std Dev 12.63 16.13 16.02 24.53 497.45 33.99 153.16
SA Best 69 99 107 135 394 1033 3867
Average 70.3 105 128.44 180.9 410.3 1112.5 3955.66
Worst 100 145 166 195 430 1203 4012
Std Dev 10.3 17.3 17.2 22.32 33.21 60.58 40.05
MPSO-GI Best 41 53 68 61 340 903 3905
Average 47.25 77.55 99.55 125.95 400.5 1013.3 3946.8
Worst 61 101 145 196 440 1106 4002
Std Dev 6.91 12.74 21.21 38.13 31.01 50.84 37.77
3.2. Comparison with previous studies
In this section, the results of the three algorithms are compared to those of two previous studies. The
comparison results are presented in Table 3 and Figures 3 to 4. The results indicate that, on small datasets
such as Mandl4, Mandl6, Mandl7, and Mandl8, the MPSO-GI algorithm performed better overall than the
algorithms in the previous studies. The MPSO-GI algorithm produced worse solutions only on the Mandl7 and
Mandl8 datasets in the operator cost aspect. On the other hand, the NH-EO and SS-GD algorithms performed
significantly better on larger datasets such as Munford0, Munford1, and Munford2.
The significant difference in performance, particularly on larger datasets, can be attributed to a number
of factors. According to Ahmed et al. [18], the algorithm development involved a larger number of LLHs and
a more complex LLH selection strategy, as well as a larger number of iterations run. In contrast, this study had
to limit the number of iterations due to our time constraints. According to Mumford [17], a larger number of
iterations were also employed, which led to better results on larger datasets.
Table 3. Comparison results with several previous studies
Dataset Fitness HC SA MPSO-GI NH-EO SS-GD
Mandl4 Cp 18 15 8 10.57 10.48
Co 53 69 41 63 63
Mandl6 Cp 15 27 9 10.27 10.18
Co 90 99 53 63 63
Mandl7 Cp 16 19 8 10.22 10.1
Co 107 107 68 63 63
Mandl8 Cp 10 16 7 10.17 10.08
Co 113 135 61 63 63
Mumford0 Cp 15 19 17 16.05 14.09
Co 117 394 340 111 94
Mumford1 Cp 34 54 45 24.79 21.69
Co 1074 1033 903 568 403
Mumford2 Cp 70 76 72 28.65 25.19
Co 3624 3867 3905 2244 1330
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Mandl4 Mandl6 Mandl7 Mandl8 Mumford0 Mumford1 Mumford2
Dataset
0
10
20
30
40
50
60
70
Cost
Passenger
HC
SA
MPSO-GI
NH-EO
SS-GD
Figure 3. Comparison results of cost passanger
Mandl4 Mandl6 Mandl7 Mandl8 Mumford0 Mumford1 Mumford2
Dataset
0
500
1000
1500
2000
2500
3000
3500
4000
Cost
Operator
HC
SA
MPSO-GI
NH-EO
SS-GD
Figure 4. Comparison results of cost operator
4. CONCLUSION
In this study, a comprehensive comparison of algorithms tailored for the UTRP was conducted, with
a distinct focus on the novel hyper-heuristic approach via MPSO-GI. Evaluations were benchmarked against
datasets, with a particular emphasis on smaller datasets which posed unique challenges and opportunities.
Empirical findings revealed that the newly introduced MPSO-GI algorithm, with its hyper-heuristic approach,
consistently outperformed traditional metaheuristic techniques such as SA and HC. It’s noteworthy to mention
the significant influence of iteration count on the algorithmic outcomes, an aspect that warrants further explo-
ration. Looking ahead, our research trajectory will encompass a broader analysis involving larger datasets to
test the scalability of the MPSO-GI algorithm. Additionally, delving deeper into performance determinants
across varying algorithms and synergizing with other heuristic methodologies for the UTRP will be pivotal
components of our forthcoming investigations.
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BIOGRAPHIES OF AUTHORS
Ahmad Muklason Assistant Professor at Data Engineering and Business Intelligence
Lab., Department of Information Systems, Faculty of Intelligent Electrical, Electronic Engineering
and Informatics, Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia. Received his doctoral
degree from School of Computer Sciences, The University of Nottingham, UK, in 2017; Master of
Science degree of Computer and Information Sciences Department, Universiti Teknologi Petronas,
Malaysia, in 2009; and Bachelor of Computer Science from Institut Teknologi Sepuluh Nopember,
Surabaya in 2006. He can be contacted at email: mukhlason@is.its.ac.id.
Int J Artif Intell, Vol. 13, No. 3, September 2024: 2923–2933
Int J Artif Intell ISSN: 2252-8938 r 2933
Shof Rijal Ahlan Robbani IT Officer at Application Management & Operation Division,
PT Bank Rakyat Indonesia. He recieved Master of Computer Science in Information Systems Degree
from the Department of Information Systems, Faculty of Intelligent Electrical, Electronic Engineer-
ing and Informatics, Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia. Graduated from
Information Systems Department, University of Airlangga, Surabaya Indonesia. He can be contacted
at email: robbirobbani@gmail.com.
Edwin Riksakomara Assistant Professor at Data Engineering and Business Intelligence
Lab., Department of Information Systems, Faculty of Intelligent Electrical, Electronic Engineering
and Informatics, Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia. Received his Master of
Engineering degree and Bachelor of Computer Science from Institut Teknologi Sepuluh Nopember,
Surabaya Indonesia. He can be contacted at email: erk@is.its.ac.id.
I Gusti Agung Premananda received his master degree from Institut Teknologi Sepuluh
Nopember, Surabaya, Indonesia in 2021 in information systems; and Bachelor of Computer Science
from Institut Teknologi Sepuluh Nopember, Surabaya in 2019. Presently he is taking the doctoral
program in Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia in 2021 in information sys-
tems. He can be contacted at email: igustiagungpremananda@gmail.com.
A comparison of meta-heuristic and hyper-heuristic algorithms in solving ... (Ahmad Muklason)

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46 22971.pdfA comparison of meta-heuristic and hyper-heuristic algorithms in solving an urban transit routing problems

  • 1. IAES International Journal of Artificial Intelligence (IJ-AI) Vol. 13, No. 3, September 2024, pp. 2923∼2933 ISSN: 2252-8938, DOI: 10.11591/ijai.v13.i3.pp2923-2933 r 2923 A comparison of meta-heuristic and hyper-heuristic algorithms in solving an urban transit routing problems Ahmad Muklason, Shof Rijal Ahlan Robbani, Edwin Riksakomara, I Gusti Agung Premananda Department of Information Systems, Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia Article Info Article history: Received Jan 24, 2023 Revised Nov 15, 2023 Accepted Dec 3, 2023 Keywords: Hill climbing Hyper-heuristics Particle swarm optimization Simulated annealing Urban transit routing problem ABSTRACT Public transport is a serious problem that is difficult to solve in many coun- tries. Public transport routing optimization problem also known as urban tran- sit routing problem (UTRP) is time-consuming process, therefore effective ap- proches are urgently needed. UTRP aims to minimize cost passenger and op- erator from a combination of route set. UTRP can be optimize with heuris- tics, meta-heuristics, and hyper-heuristics methods. In several previous studies, UTRP can be optimized with any meta-heuristics and hyper-heuristics meth- ods. In this study we compare the performance of meta-heuristic methods, i.e. ill-climbing, simulated annealing, and hyper-heuristics method based on mod- ified particle swarm optimization algorithm. The experimental results showed that the proposed methods could solve UTRP effectively. Regarding their per- formance, the results show that despite the generality of hyper-heuristics, their performance are competitive. More specifically, hyper-heuristics method is the best method compared to the other two methods in each dataset. In addition, compared to prior studies results, he proposed hyper-heuristics could outperform them in term of cost passenger of small dataset Mandl. The main contribution of this paper is that to best of our knowledge, it is the first study comparing the performance of meta-heuristics and hyper-heuristics approaches over UTRP. This is an open access article under the CC BY-SA license. Corresponding Author: Ahmad Muklason Department of Information Systems, Institut Teknologi Sepuluh Nopember St. Raya ITS, Kampus ITS Sukolilo Surabaya 60111, East Java, Indonesia Email: mukhlason@is.its.ac.id 1. INTRODUCTION Public transport is a solution to overcome traffic jams in an area or regional. However, there are still many countries that has not implemented public transport properly and optimally, so that cannot be a solution for any civilian. Traffic congestion is a serious problem in the world and not easy to handle it [1]. An implementation of public transport can be improved by optimizing routes based on distance and time [2]. But, it can take a lot of time and energy, so a can be problem classified as combinatorial problems. A problem of determining public transport routes can also be referred to urban transit routing problem (UTRP). UTRP is the part of urban transit network design problem (UTNDP) which focuses on solving problem of finding routes and scheduling public transportation. UTNDP is the part of vehicle routing problem (VRP). UTRP has a fitness function like cost passenger and operator [3]. A cost passenger point of view is said to be efficient, if the total travel time and total transfer time can be minimized. Meanwhile, cost operator point of view the number of routes, and the total number of all bus route lengths can be minimized. To be able to minimize the UTRP fitness function, a suitable combination is needed to determine a route. Therefore, an UTRP problem Journal homepage: http://ijai.iaescore.com
  • 2. 2924 r ISSN: 2252-8938 can be said to be a combinatorial problem [4]. Combinatorial problems can be solved using heuristics, meta- heuristics, and hyper-heuristics methods, because they can help find an optimal objective function by providing several possible combinations of solutions [5], [6]. Hyper-heuristics method has a major difference with metaheuristics, it directly searches for solutions in the space of heuristics [7]. Hyper-heuristics method aims to find right combination of low-level heuristics (LLH) is easy to apply and produces an acceptable domain solution [8]. Metaheuristic methods has been used to solve VRP problems, including: genetic algorithm (GA), simulated annealing (SA) algorithm, tabu search (TS) algorithm, and particle swarm optimization (PSO) algorithm [9], [10]. Hyper-heuristics have also been used to solve VRP problems and resulted well-designed hyper-heuristics are useful for building and improving solutions [2], [7], [11]. In several previous studies, VRP problems have been solved using several metaheuristic methods, including: GA, PSO, and TS. VRP solution using a hybrid GA method shows that hybrid GA method has better performance than normal GA method [12]. Completion of VRP using modified PSO shows that, modified PSO method has better performance than PSO in achieving vehicle routes that focus on problems by considering complete costs which will reduce total costs and emissions [13]. Completion of VRP using the hybrid TS method results in better performance, less computation time, and very effective in finding solutions to problems [14]. VRP solution using GA and PSO methods, shows that can produces a fairly good objective value and represented that GA is better than PSO [15]. Results of previous research indicate that a modified or hybrid metaheuristic method can be a solution to obtain a route sequence that is close to optimal solution with fast processing time. Several studies on UTRP have been carried out. One of them is to use hill-climbing (HC) and SA methods to solve an UTRP problem, both of methods can produced competed fitness function with results of previous studies [16]. Another studies, uses a new heuristic and evolutionary operators methods, and show a results proposed method can outperform previous research in terms of passenger costs and operator costs [17]. Another studies, proposed a selection hyper-heuristics methods as a tool to solve an UTRP problem. Based on this research, it is known that the sequence-based selection methods combined with the great deluge acceptance has the best performance in terms of passenger and operator costs [18]. Another studies, has been success implemented a cat swarm optimization for UTRP and produced an objective function can be compared with previous studies [19]. Another studies, successfully used imported flower pollination algorithms to solve UTRP and had more effective results in the Mandl dataset [20]. Another studies, applied differential evolution, show that an objective function is outperformed most of the results from other literatures [21]. Another studies, proposed a sequence-based selection methods combined with the great deluge acceptance (SS- GD) using dataset development and show that methods is able to improve existing route services for passengers and operators, and shows great potential to deal with real-world problems in a short time when compared to GA [22]. Based on several previous studies, an UTRP problem can be solved using meta-heuristics or hyper- heuristics methods. Therefore, in this study, an UTRP will be solved by using HC and SA as metaheuris- tics methods and a modified particle swarm optimization algorithm based on gravitational search interactions (MPSO-GI) with a hyper-heuristics approach as hyper-heuristics methods. These three methods are used for solving public transport problems to get a more optimal solution of problem. So that result of cost passenger and operator as objective function can find a better solution. Reason of using a MPSO algorithm is based on previous research which explains that modified PSO algorithm has better results than standard PSO for solving VRP problems [13]. MPSO-GI algorithms modifies PSO with the gravitational search algorithm approach and shows more optimal results than standard PSO [23]. MPSO-GI has a learning coefficient value based on a position of the gravitational interactions between particles which much more stable than user input value. PSO algorithm and hyper-heuristics approach has been carried out in research on solving the resource constrained project scheduling problem (RCPSP) and has a competitive solution result when compared to other methods [24]. In research on evolving dispatching rules in job shop scheduling, PSO algorithms and hyper-heuristics ap- proaches can be applied and produce solutions that are more competitive and faster than genetic programming methods with hyper-heuristics [25]. A dataset used in this study is dataset in previous research, namely Mandl and Mumford [26]. Mandl data is a representation of bus routes in 15 cities in Switzerland. Meanwhile, Mumford dataset is a represen- tation of the small transport network and bus routes in the city (Yubei, Brighton, and Cardiff). The results of this study will be compared with the results of previous studies using the same dataset. So it can find out the Int J Artif Intell, Vol. 13, No. 3, September 2024: 2923–2933
  • 3. Int J Artif Intell ISSN: 2252-8938 r 2925 advantages of proposed methods in solving an UTRP problem. 2. RESEARCH METHOD In this section, the research methodology employed to tackle the UTRP is elucidated in detail. To ensure a comprehensive understanding of the approach, the methodology is divided into sub-sections, each detailing a specific phase of the research. Firstly, the dataset utilized is discussed, which comprises examples from various global locations, including Yubei in China, Brighton and Cardiff in the UK, and 15 cities in Switzerland. To analyze this dataset, the design of the algorithm is explored in stages, encompassing data conversion, initial solution formation, and the incorporation of various algorithmic techniques such as HC, SA, and hyper-heuristics using MPSO-GI. The implementation phase details the technical setup and computational resources used, ensuring replicability of the results. Lastly, the results derived from the applied algorithms will be critically analyzed and compared with the findings of previous studies in the domain. This systematic approach ensures a holistic and structured examination of the UTRP, facilitating a comprehensive exploration of potential solutions. 2.1. Dataset The study utilizes data from a benchmark dataset previously used in research [26]. This dataset in- cludes five examples, called Mumford0, Mumford1, Mumford2, Mumford3, and Mandl. Mumford1, Mum- ford2, and Mumford3 represent bus route data in Yubei, China, Brighton, and Cardiff, UK respectively. Mum- ford0 represents data with a small network, while Mandl represents bus routes in 15 cities in Switzerland. Table 1 further describes the specifics and features of the dataset used in the study. Table 1. Description instance Instances Vertices Edges Routes Vertices per route (min-max) Mandl4 15 21 4 2 – 8 Mandl6 15 21 6 2 – 8 Mandl7 15 21 7 2 – 8 Mandl8 15 21 8 2 – 8 Mumford0 30 90 12 2 – 15 Mumford1 70 210 15 10 – 30 Mumford2 110 385 56 10 – 22 Mumford3 127 425 60 12 - 25 2.2. Design of algorithm In this sub-section, a structured, step-by-step algorithmic approach to address the research problem is outlined. This algorithmic strategy involves several intricate steps, including data conversion, formation of the initial solution, and application of multiple optimization techniques. Each of these steps, pivotal to the success of the research, is detailed in subsequent segments to ensure a comprehensive understanding of the approach. 2.2.1. Data conversion and hard constrains In this step, dataset used is read in .txt format. Then dataset is converted into an array by making adjustments, so that can be read by program. Adjustments are made by replacing the value ”Inf” to 0 in a TravelTimes data, so that process of finding hard constraints can be easier. Furthermore, data can be obtained in the form of an array of TravelTimes and demand data. An array of data can be optimized according to desired algorithm with program that has been created. Next, search for hard constraints by searching whether points between an arrays have a value of 0. 2.2.2. Initiate solution In this step, an initial solution is formed from selected and implemented dataset. The first step in forming an initial solution is to determine parameters of each dataset. Parameters need to be determined include number of routes, as well as MIN and MAX lengths on each route. Parameters used are in accordance with the specifications of each dataset that have been described. Furthermore, the initial solution can be obtained by determining starting point of a solution on each route by determining point, that has most connections with A comparison of meta-heuristic and hyper-heuristic algorithms in solving ... (Ahmad Muklason)
  • 4. 2926 r ISSN: 2252-8938 other points. Next point is selected based on the hard constraints of starting point that has been obtained. The formation of an initial solution can be explained by pseudocode in Algorithm 1. Algorithm 1: Pseudocode for initiating solution Function getNewRoute(data, Min, Max, r, datasize): route ← array; dataC ← getConnected(data); startNode ← start node per route; for i = 0 to r do initializeRoute(route[i], startNode, dataC); end while Unused is not empty do randRute ← pickRandomRoute(); resetRoute(route[randRute], startNode, dataC); end return route; 2.3. Calculate fitness To proceed to the optimization stage, it is necessary to calculate the fitness value for each iteration that will be performed. Fitness function of an UTRP is cost passenger and operator. Cost passenger (Cp) obtained from the total travel time of all passengers which can be calculated as in (1): Cp(R) = Pn i,j=1 dijaij(R) Pn i,j=1 dij (1) where dij = transit demand from node xi to node xj, αij = shortest time from xi to xj, and R = route set. Cost operational regarding a number of vehicles to ensure service quality cannot be handled without considering vehicle scheduling. Other costs operating depend on length of a transportation route. Therefore a cost operator (Co) defined as total length of a route set as in (2): Co(R) = n X a=1 X (i,j)∈r tij(a) (2) where: a = typical route R, r = number of routes, and tij(a) = length of transport link. 2.3.1. Hill climbing In this section, the research is carried out using a results of initial solution that has been formed including, initial route and cost of passenger and operator. Furthermore, results of the initial solution are processed using a HC method to get better solution. HC method used is make-small-change as was done in previous research [9]. Pseudocode of the HC method can be seen in Algorithm 2. Algorithm 2: Pseudocode for HC Function getRouteHC(): rand1, rand2 ← pickRouteAndNodeRandomly(); if route[rand1] ¡ max then while !route[rand1].contains(rand2) do route[rand1].add(rand2); end end else swapStartAndEndNodes(rand1); end if not isValid then resetRoute(rand1); end return route; The first step of HC is to determine randomly which route will be modified. After getting the selected route, then determine the possibilities that can be used. First possibility can be used, if the length of a selected Int J Artif Intell, Vol. 13, No. 3, September 2024: 2923–2933
  • 5. Int J Artif Intell ISSN: 2252-8938 r 2927 route is less than MAX parameter. As well as last possibility can be used, if the route can not run the first possibility. After performing the possible procedures of make-small-change method a new route is obtained. Next, check whether a route meets the requirements as a route in an UTRP problem. If a route is declared valid then, a route can replace previous route and used for calculating new fitness function. 2.3.2. Simulated annealing In this SA algorithm, the research is conducted by utilizing the results of the initial solution, which includes the initial route and the cost for passengers and operators. The results of the initial solution are then further processed using the SA method to achieve better results. The SA method is applied with the temperature set to 1000 and the cooling factor as per previous studies [16]. Additionally, the combination of the make-small- change method, as described in previous research [9], is used. The flowchart for the SA method can be seen in Figure 1. Start End Initiate Solution Update Parameter Modified Solution Calculate Fitness newFit<CurrFit Calculate Probability rand<probability Temp<1 Optimized Solution Yes Yes Yes No No No Figure 1. Flowchart SA The first step is to determine the temperature parameter and calculate the cooling factor, which is used as an iteration for the procedure to be carried out. Next, a random route is selected to be modified. After the selected route is determined, possible modifications are evaluated. The first possibility is used if the length of the selected route is less than the MAX parameter. The last possibility is used if the first possibility cannot be applied. After performing the possible procedures of the make-small-change method, a new route is obtained. The procedure is repeated until the temperature drops to zero. Next, the validity of the route as a solution to the UTRP problem is checked. If the route meets the requirements, it replaces the previous route and is used to calculate the fitness function. 2.3.3. Hyper-heuristic with modified particle swarm optimization In this study, a hyper-heuristic approach that combines a modified version of MPSO-GI with sim- ple random selection and five types of LLH is employed to solve the UTPR. The hyper-heuristic process is carried out for a pre-determined number of iterations and is constrained by a time limit. Move acceptance is used in each iteration, and the process of the hyper-heuristics can be observed in the flowchart presented in Figure 2. The UTRP optimization process using the hyper-heuristics begins with a random selection of an LLH, followed by the application of MPSO-GI until the desired number of iterations is reached. A comparison of meta-heuristic and hyper-heuristic algorithms in solving ... (Ahmad Muklason)
  • 6. 2928 r ISSN: 2252-8938 In the move acceptance phase, MPSO-GI is used to select a solution based on the particle, and the specified number of iterations is run. The initial step of MPSO-GI involves defining the particle parameters and the number of iterations. A random route is then chosen and transformed using MPSO-GI into a new solution using the specified number of particles. The new solution is evaluated using the fitness function, and if it has a better value, it is accepted and replaces the previous solution. The procedure for implementing MPSO-GI move acceptance can be found in Algorithm 3. Algorithm 3: Pseudocode MPSO-GI Algorithm Function MPSO(): particle ← number of solution; iteration, MaxIter ← number of iteration; generatePosition(); generateVelocity(); solutionPerParticle(); while iteration¡maxIter do newVelocity(); newPosition(); solutionPerPartikel(); if bestFit < fitness then fitness = bestFit; updateRoute(); end end return routeSR; Start End Initiate Solution LLH Selection Move Acceptance MPSO Solution Accepted iteration Done Best Solution Update Best Solution Yes Yes Yes No No No Figure 2. Flowchart hyper-heuristics In addition, the simple random method is used to randomly select an LLH for each iteration. In this study, the number of LLH [4] used is: − LLH0: choose a random route and position of route. Then add random value points to a position and route that has been selected. − LLH1: randomly chooses a route and two positions in a route. Then swap two positions that have been chosen. Int J Artif Intell, Vol. 13, No. 3, September 2024: 2923–2933
  • 7. Int J Artif Intell ISSN: 2252-8938 r 2929 − LLH2: randomly chooses a route and two positions in a route. Then a first point replaces a second point, and a second point becomes a last point. − LLH3: choose two routes randomly and a position on each route. Then enter a point on first route into second route to selected second point. − LLH4: choose two routes randomly and one position on each route. Then change point that has been selected on each route. 2.4. Implementation The algorithm developed in this study was implemented using the Java programming language and the eclipse integrated development environment (IDE). The computer system used for the implementation had the following specifications: an Intel i5-8250U processor with a clock speed of 1.60 GHz, 8129 MB of RAM, and the Windows 10 Home operating system. The program was executed on each dataset for 200 iterations using the HC algorithm. In the case of the MPSO-GI algorithm, the program was also run for 200 iterations, with a time constraint of 10 minutes to ensure consistency in running time with the HC algorithm. The SA algorithm was configured to produce a running time that is comparable to the other algorithms. To ensure the robustness of the results, all algorithms were run 10 times on each dataset, and the best result was selected for the analysis phase. 2.5. Analysis of results The performance of the algorithm will be compared with the methods and outcomes of two prior studies. The first study, by Mumford [17], developed the new heuristic and evolutionary operators (NH-EO) algorithm. The second study, by Ahmed et al. [18], developed the sequence selection based great deluge (SS- GD) algorithm. The analysis and comparison of the results will provide insight into the effectiveness of the implemented algorithm in comparison to the previously developed ones. 3. RESULTS AND DISCUSSIONS The results section discusses the outcome of the experiments conducted on the UTRP problem using three algorithms. The algorithms used were HC and SA, which employ the metaheuristic approach, and MPSO- GI, which utilizes the hyper-heuristic approach. In the HC method, the parameters used were 200 iterations and 10 trials, while in the SA method, the temperature was set to 1000 and the cooling factor to 0 < c < 1. MPSO-GI used 5 particles, 200 iterations, and 10 trials. The best results from the tests will be compared to analyze the three algorithms. 3.1. Comparison result of MPSO-GI, simulated annealing, and hill climbing The experiments compared three distinct algorithms: HC, SA, and MPSO-GI. The results, as depicted in Table 2, show notable differences in their performance across various datasets. The MPSO-GI algorithm, underpinned by the hyper-heuristic approach, generally displayed superiority. This dominance was evident in both the ”best” and ”average” results across the majority of datasets. However, there were exceptions. In the passenger cost (Cp) aspect, the ”best” results from the HC algorithm surpassed MPSO-GI for the Mumford1 and Mumford2 datasets. Additionally, in the operation cost (Co) aspect, the ”best” result of the SA outper- formed MPSO-GI on the Mumford2 dataset. When comparing HC and SA, HC typically exhibited better performance. This was particularly evi- dent in the passenger cost aspect, where HC’s ”best” and ”average” results were superior in most datasets, with the exception of Mumford0. For operation costs, HC’s ”best” results were better on the Mandl4, Mandl6, and Mandl8 datasets. The standout performance of MPSO-GI can be ascribed to two primary factors. Firstly, MPSO-GI is a population-based algorithm, contrasting with SA and HC, which are local search algorithms. Such population- based algorithms generally possess a heightened capability for solution exploration and evasion of local optima. The second factor is MPSO-GI’s hyper-heuristic approach, which incorporates various LLLHs, including the 5 types of LLHs. This not only magnifies the diversity of the search but often leads to enhanced solutions. In a direct comparison of SA and HC, SA appeared less adept at exploiting solutions. This observa- tion was substantiated by the ”average” results, where SA often lagged behind HC. However, in more extensive datasets like Mumford0, Mumford1, and Mumford2, especially in the operation cost aspect, HC, which typ- A comparison of meta-heuristic and hyper-heuristic algorithms in solving ... (Ahmad Muklason)
  • 8. 2930 r ISSN: 2252-8938 ically accepts superior solutions, seemed more susceptible to local optima. As a result, in these datasets, its solutions were occasionally outpaced by those of the SA algorithm. Table 2. Comparison results of proposed method Fitness function Methods Statistics Dataset Mandl4 Mandl6 Mandl7 Mandl8 Mumford0 Mumford1 Mumford2 Cp HC Best 18 15 16 10 15 34 70 Average 29.95 26.3 27.9 24.75 35.9 52.7 81.1 Worst 44 45 43 41 50 63 89 Std Dev 8.20 8.77 7.18 8.09 8.93 10.71 5.79 SA Best 15 27 19 16 19 54 76 Average 23.7 29.3 29.7 18.3 40.3 66 83.2 Worst 35 43 44 38 66 73 89 Std Dev 5.3 5.3 9.1 9.3 10.5 9.5 6.8 MPSO-GI Best 8 9 8 7 17 45 72 Average 15 16.35 17.25 19.65 30 60.35 79.35 Worst 30 24 35 45 39 68 83 Std Dev 4.22 3.5 9.31 9.91 6.85 8.31 3.47 Co HC Best 53 90 107 113 117 1074 3624 Average 73.7 108.55 131.05 151.9 641.95 1106.55 3791.25 Worst 101 157 172 195 1158 1158 3948 Std Dev 12.63 16.13 16.02 24.53 497.45 33.99 153.16 SA Best 69 99 107 135 394 1033 3867 Average 70.3 105 128.44 180.9 410.3 1112.5 3955.66 Worst 100 145 166 195 430 1203 4012 Std Dev 10.3 17.3 17.2 22.32 33.21 60.58 40.05 MPSO-GI Best 41 53 68 61 340 903 3905 Average 47.25 77.55 99.55 125.95 400.5 1013.3 3946.8 Worst 61 101 145 196 440 1106 4002 Std Dev 6.91 12.74 21.21 38.13 31.01 50.84 37.77 3.2. Comparison with previous studies In this section, the results of the three algorithms are compared to those of two previous studies. The comparison results are presented in Table 3 and Figures 3 to 4. The results indicate that, on small datasets such as Mandl4, Mandl6, Mandl7, and Mandl8, the MPSO-GI algorithm performed better overall than the algorithms in the previous studies. The MPSO-GI algorithm produced worse solutions only on the Mandl7 and Mandl8 datasets in the operator cost aspect. On the other hand, the NH-EO and SS-GD algorithms performed significantly better on larger datasets such as Munford0, Munford1, and Munford2. The significant difference in performance, particularly on larger datasets, can be attributed to a number of factors. According to Ahmed et al. [18], the algorithm development involved a larger number of LLHs and a more complex LLH selection strategy, as well as a larger number of iterations run. In contrast, this study had to limit the number of iterations due to our time constraints. According to Mumford [17], a larger number of iterations were also employed, which led to better results on larger datasets. Table 3. Comparison results with several previous studies Dataset Fitness HC SA MPSO-GI NH-EO SS-GD Mandl4 Cp 18 15 8 10.57 10.48 Co 53 69 41 63 63 Mandl6 Cp 15 27 9 10.27 10.18 Co 90 99 53 63 63 Mandl7 Cp 16 19 8 10.22 10.1 Co 107 107 68 63 63 Mandl8 Cp 10 16 7 10.17 10.08 Co 113 135 61 63 63 Mumford0 Cp 15 19 17 16.05 14.09 Co 117 394 340 111 94 Mumford1 Cp 34 54 45 24.79 21.69 Co 1074 1033 903 568 403 Mumford2 Cp 70 76 72 28.65 25.19 Co 3624 3867 3905 2244 1330 Int J Artif Intell, Vol. 13, No. 3, September 2024: 2923–2933
  • 9. Int J Artif Intell ISSN: 2252-8938 r 2931 Mandl4 Mandl6 Mandl7 Mandl8 Mumford0 Mumford1 Mumford2 Dataset 0 10 20 30 40 50 60 70 Cost Passenger HC SA MPSO-GI NH-EO SS-GD Figure 3. Comparison results of cost passanger Mandl4 Mandl6 Mandl7 Mandl8 Mumford0 Mumford1 Mumford2 Dataset 0 500 1000 1500 2000 2500 3000 3500 4000 Cost Operator HC SA MPSO-GI NH-EO SS-GD Figure 4. Comparison results of cost operator 4. CONCLUSION In this study, a comprehensive comparison of algorithms tailored for the UTRP was conducted, with a distinct focus on the novel hyper-heuristic approach via MPSO-GI. Evaluations were benchmarked against datasets, with a particular emphasis on smaller datasets which posed unique challenges and opportunities. Empirical findings revealed that the newly introduced MPSO-GI algorithm, with its hyper-heuristic approach, consistently outperformed traditional metaheuristic techniques such as SA and HC. It’s noteworthy to mention the significant influence of iteration count on the algorithmic outcomes, an aspect that warrants further explo- ration. Looking ahead, our research trajectory will encompass a broader analysis involving larger datasets to test the scalability of the MPSO-GI algorithm. Additionally, delving deeper into performance determinants across varying algorithms and synergizing with other heuristic methodologies for the UTRP will be pivotal components of our forthcoming investigations. REFERENCES [1] A. Koźlak and D. Wach, “Causes of traffic congestion in urban areas. Case of Poland,” SHS Web of Conferences, vol. 57, 2018, doi: 10.1051/shsconf/20185701019. A comparison of meta-heuristic and hyper-heuristic algorithms in solving ... (Ahmad Muklason)
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Mumford, “Research on the urban transit routing problem (bus routing),” Structure, vol. 2, 2017. BIOGRAPHIES OF AUTHORS Ahmad Muklason Assistant Professor at Data Engineering and Business Intelligence Lab., Department of Information Systems, Faculty of Intelligent Electrical, Electronic Engineering and Informatics, Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia. Received his doctoral degree from School of Computer Sciences, The University of Nottingham, UK, in 2017; Master of Science degree of Computer and Information Sciences Department, Universiti Teknologi Petronas, Malaysia, in 2009; and Bachelor of Computer Science from Institut Teknologi Sepuluh Nopember, Surabaya in 2006. He can be contacted at email: mukhlason@is.its.ac.id. Int J Artif Intell, Vol. 13, No. 3, September 2024: 2923–2933
  • 11. Int J Artif Intell ISSN: 2252-8938 r 2933 Shof Rijal Ahlan Robbani IT Officer at Application Management & Operation Division, PT Bank Rakyat Indonesia. He recieved Master of Computer Science in Information Systems Degree from the Department of Information Systems, Faculty of Intelligent Electrical, Electronic Engineer- ing and Informatics, Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia. Graduated from Information Systems Department, University of Airlangga, Surabaya Indonesia. He can be contacted at email: robbirobbani@gmail.com. Edwin Riksakomara Assistant Professor at Data Engineering and Business Intelligence Lab., Department of Information Systems, Faculty of Intelligent Electrical, Electronic Engineering and Informatics, Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia. Received his Master of Engineering degree and Bachelor of Computer Science from Institut Teknologi Sepuluh Nopember, Surabaya Indonesia. He can be contacted at email: erk@is.its.ac.id. I Gusti Agung Premananda received his master degree from Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia in 2021 in information systems; and Bachelor of Computer Science from Institut Teknologi Sepuluh Nopember, Surabaya in 2019. Presently he is taking the doctoral program in Institut Teknologi Sepuluh Nopember, Surabaya, Indonesia in 2021 in information sys- tems. He can be contacted at email: igustiagungpremananda@gmail.com. A comparison of meta-heuristic and hyper-heuristic algorithms in solving ... (Ahmad Muklason)