i LAPORAN AKHIR PENELITIAN UNGGULAN ITS DANA ITS 2020 Pengembangan Model Traveling Salesman Problem & Vehicle Routing Problem dan Algoritma Generik Berbasis Hyper-heuristics Untuk Menyelesaikan Permasalahan Optimasi Operasi dan Penjadwalan Public Transport di Kota Surabaya dalam Kerangka Kerja Intelligent Transport Systems Tim Peneliti : Ahmad Muklason, S.Kom., M.Sc., Ph.D. (Departemen Sistem Informasi/FT-EIC/ITS) Dra. Nuri Wahyuningsih, M.Kes. (Departemen Sains Aktuaria/FSAD/ITS) Raras Tyasnurita, S.Kom., M.BA, Ph.D. (Departemen Sistem Informasi/FT-EIC/ITS) Retno Aulia Vinarti, S.Kom., M.Kom, Ph.D. (Departemen Sistem Informasi/FT-EIC/ITS) DIREKTORAT RISET DAN PENGABDIAN KEPADA MASYARAKAT INSTITUT TEKNOLOGI SEPULUH NOPEMBER SURABAYA 2020 Sesuai Surat Perjanjian Pelaksanaan Penelitian No: 800/PKS/ITS/2020
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i
LAPORAN AKHIR
PENELITIAN UNGGULAN ITS
DANA ITS 2020
Pengembangan Model Traveling Salesman Problem & Vehicle Routing
Problem dan Algoritma Generik Berbasis Hyper-heuristics Untuk
Menyelesaikan Permasalahan Optimasi Operasi dan Penjadwalan Public
Transport di Kota Surabaya dalam Kerangka Kerja Intelligent Transport
Systems
Tim Peneliti :
Ahmad Muklason, S.Kom., M.Sc., Ph.D. (Departemen Sistem Informasi/FT-EIC/ITS)
Raras Tyasnurita, S.Kom., M.BA, Ph.D. (Departemen Sistem Informasi/FT-EIC/ITS)
Retno Aulia Vinarti, S.Kom., M.Kom, Ph.D. (Departemen Sistem Informasi/FT-EIC/ITS)
DIREKTORAT RISET DAN PENGABDIAN KEPADA MASYARAKAT
INSTITUT TEKNOLOGI SEPULUH NOPEMBER
SURABAYA
2020
Sesuai Surat Perjanjian Pelaksanaan Penelitian No: 800/PKS/ITS/2020
i
Daftar Isi
Daftar Isi .......................................................................................................................................................... i
Daftar Tabel .................................................................................................................................................... ii
Daftar Gambar ............................................................................................................................................... iv
Daftar Lampiran .............................................................................................................................................. v
BAB I RINGKASAN ..................................................................................................................................... 1
BAB II HASIL PENELITIAN ........................................................................................................................ 2
BAB VI HASIL DAN PEMBAHASAN ........................................................................................................ 2
4.1 Data Uji Coba .................................................................................................................................. 2
4.2 Lingkungan Uji Coba ........................................................................................................................ 2
4.3 Hasil Solusi Awal.............................................................................................................................. 3
4.4 Hasil Uji Coba Algoritma Artificial Bee Colony ...................................................................................... 8
4.5.1 Perbandingan dengan Solusi Awal ........................................................................................... 19
4.5.2 Perbandingan dengan Algoritma Nearest Neighbour ................................................................... 20
4.5.3 Perbandingan dengan Algoritma Genetik .................................................................................... 20
4.5.4 Perbandingan dengan Algoritma Simulated Annealing ............................................................... 24
BAB III STATUS LUARAN ........................................................................................................................ 28
BAB IV KENDALA PELAKSANAAN PENELITIAN .............................................................................. 30
BAB V RENCANA TINDAK LANJUT PENELITIAN .............................................................................. 31
BAB VI DAFTAR PUSTAKA ..................................................................................................................... 32
BAB VII LAMPIRAN .................................................................................................................................. 33
LAMPIRAN 1 Tabel Daftar Luaran ............................................................................................................. 34
ii
Daftar Tabel
Tabel 4. 1 Spesifikasi Perangkat Keras ............................................................................................................ 2
Tabel 4. 2 Spesifikasi Perangkat Lunak............................................................................................................ 2
Tabel 4. 3 Hasil Solusi Awal ............................................................................................................................. 3
Tabel 4. 4 Hasil Solusi Akhir........................................................................................................................... 14
iii
Tabel 4.1 Spesifikasi Perangkat Keras 2
Tabel 4.2 Spesifikasi Perangkat Lunak ............................................................. Error! Bookmark not defined.
Tabel 3 Status Luaran .................................................................................................................................... 28
iv
Daftar Gambar
Gambar 4. 1 Uji Coba Parameter Limit pada Dataset 6 .................................................................................. 9
Gambar 4. 2 Uji Coba Parameter Limit pada Dataset 11 ................................................................................ 9
Gambar 4. 3 Uji Coba Parameter Limit pada Dataset 14 ................................................................................ 9
Gambar 4. 4 Uji Coba Parameter FoodSource pada Dataset 6 ..................................................................... 10
Gambar 4.5 Gambar 4. 5 Uji Coba Parameter FoodSource pada Dataset 11 ............................................... 10
Gambar 4. 6 Uji Coba Parameter FoodSource pada Dataset 14 ................................................................... 11
Gambar 4. 7 Running Time Parameter FoodSource ..................................................................................... 11
Gambar 4. 8 Uji Coba Jumlah Iterasi pada Dataset 6 .................................................................................... 11
Gambar 4. 9 Uji Coba Jumlah Iterasi pada Dataset 11 .................................................................................. 12
Gambar 4. 10 Uji Coba Jumlah Iterasi pada Dataset 14 ................................................................................ 12
Gambar 4. 11 Uji Coba LLH pada Dataset 6 .................................................................................................. 13
Gambar 4. 12 Uji Coba LLH pada Dataset 11 ................................................................................................ 13
Gambar 4. 13 Uji Coba LLH pada Dataset 14 ................................................................................................ 13
Gambar 4. 14 Perbandingan Solusi Awal dan Solusi Akhir ........................................................................... 19
Gambar 4. 15 ................................................................................................................................................. 20
Gambar 4. 16 Perbandingan Algoritma ABC dan NN .................................................................................... 20
Gambar 4. 17 Perbandingan Algoritma ABC dan GA .................................................................................... 21
Gambar 4. 18 Perbandingan Algoritma ABC dan GA .................................................................................... 21
Gambar 4. 19 Box Plot Dataset 1 dan 2 ........................................................................................................ 22
Gambar 4. 20 Box Plot Dataset 3 dan 4 ........................................................................................................ 22
Gambar 4. 21 Box Plot Dataset 5 dan 6 ........................................................................................................ 22
Gambar 4. 22 Box Plot Dataset 7 dan 8 ........................................................................................................ 23
Gambar 4. 23 Box Plot Dataset 9 dan 10 ...................................................................................................... 23
Gambar 4. 24 Box Plot Dataset 11 dan 12 .................................................................................................... 23
Gambar 4. 25 Box Plot Dataset 13 dan 14 .................................................................................................... 24
Gambar 4. 26 Perbandingan Algoritma ABC dan SA ..................................................................................... 24
Gambar 4. 27 Perbandingan Algoritma ABC dan SA ..................................................................................... 25
Gambar 4. 28 Box Plot Dataset 3 dan 4 ........................................................................................................ 25
Gambar 4. 29 Box Plot Dataset 5 dan 6 ........................................................................................................ 26
Gambar 4. 30 Box Plot Dataset 7 dan 8 ........................................................................................................ 26
Gambar 4. 31 Box Plot Dataset 9 dan 10 ...................................................................................................... 26
Gambar 4. 32 Box Plot Dataset 11 dan 12 .................................................................................................... 27
Gambar 4. 33 Box Plot Dataset 13 dan 14 .................................................................................................... 27
v
Daftar Lampiran
1. Paper Publikasi
1
BAB I RINGKASAN
Kemacetan lalu lintas adalah masalah umum di kota-kota besar di seluruh kota besar. Selain dengan
penyediaan moda transportasi masal yang bagus, untuk mengatasi masalah kemacetan diperlukan
sistem manajemen transportasi yang bagus juga. Penelitian ini bertujuan untuk mengembangkan
model Traveling Salesman Problem (TSP) dan Vehicle Routing Problem (VRP) untuk memodelkan
permasalahan manajemen transportasi di kota Surabaya, khususnya yang berkaitan dengan optimasi
operasional dan penjadwalan moda transportasi umum masal terintegrasi yang direncanakan akan
dibangun di kota Surabaya. Selain pembuatan model, untuk menyelesaiakan model permasalahan,
dalam penelitian ini akan diusulkan algoritma generik dengan menggunakan pendekatan hyper-
heuristics. Dari sisi keilmuwan, kontribusi ilmiah yang diharapkan dari penelitian ini adalah
diperolehnya data set dan pengembangan model baru untuk TSP dan VRP yang telah dibuktikan
sebagai permasalahan yang Non-deterministic Polynomial (NP), i.e. NP-hard, dimana belum
diketahui adanya algoritma esak yang mempu menyelesaikan dalam waktu polynomial. Data set
dan model baru ini diharapkan dapat mendorong penelitian algoritma lebih lanjut oleh peneliti
lainya khususnya di bidang kecerdasan buatan dan riset operasi. Dari sisi manfaat praktis, luaran
dari penelitian ini diharapkan dapat menghasilkan piranti lunak cerdas yang dapat membantu dalam
manajemen transportasi masal terintegrasi dalam kerangka kerja Intelligent Transport System (ITS)
di kota-kota besar di Indonesia, khususnya di kota Surabaya.
Kata Kunci: Traveling Salesman Problem, Vehicle Routing Problem, Intelligent Transport
System, Hyper-heuristics
2
Ringkasan penelitian berisi latar belakang penelitian,tujuan dan tahapan metode
penelitian, luaran yang ditargetkan, kata kunci
BAB II HASIL PENELITIAN
BAB VI
HASIL DAN PEMBAHASAN
Pada bab ini akan menjelaskan mengenai hasil uji coba dan analisis terhadap hasil solusi yang
diperoleh dari implementasi Algoritma ABC dan perbandingannya dengan beberapa algoritma
lain seperti NN, GA dan SA.
4.1 Data Uji Coba
Data yang digunakan sebagai uji coba adalah dataset TSP dari Traveling Salesman Competition
(TSC) 2.0 yang digunakan langsung dalam penelitian tugas ini.
4.2 Lingkungan Uji Coba
Pada subbab Lingkungan Uji Coba ini akan menjelaskan terkait lingkungan pengujian dalam
melakukan implementasi penelitian terkait optimasi rute rencana perjalanan dengan pesawat pada
studi kasus TSC 2.0. Spesifikasi perangkat keras yang digunakan dalam implementasi ditunjukkan
pada Error! Reference source not found..
Tabel 4. 1 Spesifikasi Perangkat Keras
Perangkat Keras Spesifikasi
Jenis Laptop Dell Inspiron 7559
Processor Intel(R) Core(TM) i7-6700HQ 2.6GHz
RAM 16 GB
Hard Disk Drive 1000 GB
Untuk spesifikasi perangkat lunak yang digunakan dalam pengerjaan penelitian ini ditunjukkan
pada Error! Reference source not found..
Tabel 4. 2 Spesifikasi Perangkat Lunak
Perangkat Lunak Fungsi
Windows 10 64 bit Sistem Operasi
Netbeans 8.2 Implementasi Algoritma
Microsoft Excel 2016 Pengolahan Hasil Uji Coba
Microsoft Word 2016 Penulisan Laporan
3
4.3 Hasil Solusi Awal
Pembuatan solusi awal dilakukan dengan cara menentukan secara acak urutan tur kota dari daftar
kota yang telah dilakukan seleksi sebelumnya. Jika ditemukan solusi yang tidak layak maka urutan
kota akan kembali diacak hingga ditemukan solusi yang layak. Tabel 4.3 menunjukan solusi yang
dihasilkan pada solusi awal beserta biaya yang dibutuhkan.
Abstract—In the literature, almost all optimization problems in NP-hard class are solved by meta-heuristics approach. However, this approach has the drawback of requiring tuning parameters for each different problem domain and different instances of the same problem. This approach is considered less effective in resolving these problems. Therefore, a new approach is needed, namely the hyper-heuristics approach that is able to solve cross-domain problems. Hyper-heuristic is one of the approximate search methods which is able to provide solutions to NP-hard problems in polynomial time, as well as giving fairly good and acceptable results. This method has two properties of search space, namely the selection of LLH and the acceptance of solutions (move acceptance). This approach works in barrier domains rather than directly working in problem domains. With these properties, hyper-heuristic is able to solve problems in different domains. In addition, hyper-heuristics has a learning mechanism through feedback from previously generated solutions. This final project tries to apply a hyper-heuristic algorithm in six combinatorial optimization problem domains, namely SAT, Bin Packing, Flow Shop, Personnel Scheduling, TSP, and VRP. The method that will be used in this final project is Self Adaptive - Great Deluge (SAD-GED). The Self Adaptive mechanism is used to make LLH selection to be used, while the Great Deluge is used in determining the acceptance of solutions (move acceptance) in a hyper-heuristic framework. The application of the SAD-GED algorithm is expected to be able to provide better results than the existing algorithm used previously, namely Simple Random - Simulated Annealing.
Optimization is a method of finding feasible and optimal solutions from a collection of solutions that have been identified [1]. Optimization plays a role in minimizing or maximizing the value of the objective function in each problem. There are various optimization problems such as sat, flow shop, timetabling, vehicle routing problem, bin packing, and traveling salesman problem where trying to find the shortest distance, from one location to another [2]. These problems can be included in the NP-hard class where optimal solutions are difficult to obtain because of the complexity of the problem.
In solving increasingly complex problems, we need algorithms that are able to provide solutions with relatively fast time. Approximate algorithms such as heuristics, meta-heuristics, and hyper-heuristics are choices in solving these problems. The approximate algorithm provides a solution that does not guarantee the most optimal, but is quite good and relatively fast (polynomial).
Meta-heuristic is one method that is able to select and modify heuristics to produce new solutions or change current solutions into other solutions [3]. For many combinatorial problems, this method becomes very powerful and provides a flexible method. However, this method has drawback, unable to adapt well to the changes in the structure of problems or even instance of problems that are different from the same structure.
Unlike Hyper-heuristics, this method is a high-level methodology which combine multiple low-level heuristics (LLH) and problem instances effectively so it provides solutions in cross-domain problems. In other words, this method can determine which low level heuristic will be used and determine whether to accept the solution produced by LLH (move acceptance) or not. This method works in a heuristic workspace so there is no need to know a specific understanding of the problem to be solved. So that, hyper-heuristic is more general in solving hard combinatorial optimization problems because it does not depend on the problem parameters [4]. This study tries to apply the Hyper-heuristic Self Adaptive Learning Great Deluge (SADGED) method in solving cross domain optimization problems. The problem to be solved refers to the HyFlex framework where there are six problem domains, satisfiability (SAT), one dimensional bin packing, permutation flow shop, personnel scheduling, traveling salesman problem (TSP), and vehicle routing problem (VRP). Later, the results obtained from the method will be compared with the Simple Random Simulated Annealing (SRSA) algorithm which acts as a comparison method so that it can measure the performance of the algorithm that has been applied
II. LITERATURE STUDY
A. Combinatorial Optimization
The problem of combinatorial optimization is a problem that exists in the fields of machinery, planning, and industry that can be modeled in the form of minimizing or maximizing costs on limited discrete variables. [5]. In the optimization problem, there is a value of the objective function which will be maximized and minimized according to the objectives to be achieved based on the existing constraints.
B. Meta-heuristic
Meta-heuristics are the main strategies that guide and modify other heuristics to produce solutions outside of optimal local search. This method describes the entire search process, such as which heuristics will be used, even the criteria for accepting solutions. For many combinatorial problems, this method becomes very powerful and provides a flexible method. Meta-heuristics are mostly inspired by natural processes or science, such as the Simulated Annealing method, Taboo Search, Genetic Algorithm, and so on [3].
Meta-heuristics will succeed in optimizing the problem if it can strike a balance between exploration (diversification) and exploitation (intensification) so that it depends on parameter values [6]. Exploitation is needed to identify parts of the search for solutions with good quality results. The classification of solutions resulting from this process can be either single or plural solutions. This approach relies on parameter values so that it is less able to adapt to changes in problem structures or even different problem instances with the same structure.
C. Hyper-heuristic
Hyper-heuristic includes a collection of approaches which aim to automate, which usually combines with machine learning techniques, the process involves selecting and combining simple heuristics or creating new heuristics from existing heuristic components in order to solve optimization problems [6]. Hyper-heuristic is a methodology that can provide a solution that is not too optimal, but a fairly good and acceptable solution. the main purpose of hyper-heuristics is to create a general design method, which can provide a feasible solution based on the use of LLH.
Hyper-heuristic is a learning algorithm if it uses feedback from the solution search process. Based on the feedback dimension, there are 3 divisions of learning types. Online learning, learning is done when the algorithm is solving problems. Offline learning, which is collecting knowledge in the form of rules and programs, from a collection of training instances that are expected to generalize to resolve events that are not visible [7]. As for No-learning, Hyperheurisik does not do learning. Hyper-heuristic has a general structure consisting of high-level and low-level parts. low level heuristic is a heuristic that will be chosen which is a representation of the problem, evaluation function and initial solution related to the problem so that each problem has a different LLH collection [1]. As for the high level,
it has LLH selection mechanism (to determine new solutions) and move acceptance (determine whether to accept the solution or not).
III. METHOD
A. Problem Identification
This study aims to apply a hyper-heuristic method that is able to provide optimal results (fitness) for each problem domain contained in the HyFlex framework. Each problem contained in HyFlex has different problem characteristics so that the LLH
Fig. 1. The Design of Algorithm Flowchart for Self Adaptive Learning Great Deluge
contained in each problem is also different. Hyper-heuristics must be able to recognize every LLH and use LLH for every problem. Applying the right high level heuristic method is expected to be able to choose LLH appropriately and provide a good solution in each problem domain. this hyper-heuristic
development focuses on selection of pertubative LLH based on single point search (one solution result) [8].
B. Literature Study
At this stage a literature study is carried out related to the material that will be used as a research reference. Literature studies include concepts that will be applied in research.
C. Desain The Algorithm
At this stage the hyper-heuristic is developed as a high-level heuristic strategy that is in accordance with the problem that has been defined. At this stage the method will be described in the selection of LLH and the mechanism for accepting solutions.
In this study, the high level strategy applied to hyper-heuristics is a combination of self adaptive learning and great deluge (SADGED). The self adaptive learning method is used as LLH selection in solving problems, while the great deluge is used as a mechanism of move acceptance in obtaining new solutions resulting from the implementation of LLH in each problem domain. This mechanism will accept a better solution or below the parameter B value limit in the great deluge method at each predetermined iteration. SADGED algorithm design can be seen in Figure 1.
In this study, the LLH series (low level heuristic) used is LLH which is available in the HyFlex framework. low level heuristic is a collection of heuristics on HyFlex which is used to generate solutions so that the objective function of the solution can be known in solving problems. In HyFlex, LLH used are grouped into four types, namely mutation, ruin-recreate, local search, and crossover [9].
Fig. 2. The calculation of minimum and median value that is better than SRSA based on the trial results of the percentage of desired value based on the initial solution
The self adaptive learning method plays a role in determining the amount of LLH that will be used by the method to find the value of objective functions, this study uses the number of LLH limits as provided in the HyFlex framework. The value of the desired value variable is set to 10 percent of the initial solution value. The initial level parameter value or the solution acceptance factor is set the same as the initial solution value, while the value of the decay rate or temperature reducing factor is set based on the reduction in the initial value of the solution with the desired value, then divided by the number of iterations
[10]. Self adaptive learning plays a role in selecting LLH which produces the best value. When all the selected LLHs have been used, the algorithm will fill in the LLH that will be used with a composition of 75% of LLH that produces values that can be accepted by the move acceptance method, while the remaining 25% of LLH is in the problem domain [11].
D. Implementation
This stage is the implementation phase of the algorithm design in the hyper-heuristic Flexible (HyFlex) framework. Implementation is the stage of development of algorithm design into the program language. This stage starts from the preparation of tools to the implementation of the program.
The implementation is done on a 3.2 Ghz core i5 processor and 4096 MB of memory. The algorithm design will be implemented in the HyFlex framework using the NetBeans IDE 8.2 application. implementation is done by calling the method contained in the chesc.jar library.
E. Trial
Algorithm testing tries to find the optimal solution for the six problem domains in the HyFlex framework. A trial was conducted to find out how the performance of the algorithm that had been built on six problem domains, namely satisfaction, one-dimensional bin packing, permutation flow shop, personnel scheduling, traveling salesman problem, and vehicle routing problem.
Fig. 3. The scenario of testing methods that will be used in the HyFlex framework.
Based on the results of testing the desired value parameters in the self-adaptive learning great deluge method, the most optimal value obtained is 10 percent of the value of the initial solution. The trial is conducted by comparing the median and minimum values of the results of the execution. From Figure 2, the desired value of 10 percent provides a fairly stable number of solutions compared to other trial values. The value obtained is a percentage of the initial solution value. Meanwhile, the use of LLH length in the SADGED method is adjusted to the number of LLH contained in each problem domain.
In Figure 3 the method trial scenario, the algorithm is run by entering some required input data. Furthermore, the framework will search for solutions based on predefined input data. After the final criteria for running the algorithm are completed, the framework will return the value of the best solution resulting from the search process Simple Random Simulated Annealing Algorithm and Great Deluge Self Adaptive Learning are applied in six problem domains contained in the HyFlex framework. In each problem domain, there are five instances that have been determined in the trial process so that the total instances used are 30 instances. Each instance is tested 31 times with a time of 60000 milliseconds. From the data the results of the execution are calculated the best value (minimum), first quartile, median, third quartile, maximum value, and average that will be used as a comparison value for each method
IV. RESULTS AND DISCUSSION
The trials were conducted 31 times on six problem domains with 5 instances of each problem. In conducting trials, performance measurements are carried out by comparing the SADGED method with SRSA. Performance testing is done by doing three comparisons. First, comparing the distribution of data from the results of the method execution on some statistical data, namely the minimum value (fitness), the first quartile, median, third quartile, and the maximum value of the value of the objective function. This test uses the calculation of values and points and visualization of boxplot diagrams from the statistical data obtained. Second, comparing the median values obtained to measure the concentration of values in the data. Third, make a comparison of the minimum values obtained from the method execution results.
A. Comparison of Data Distribution
Comparison of data distribution is done by calculating based on statistical values such as minimum value, first quartile, median, third quartile, and maximum value and visualization of values against the boxplot diagram. The objective function value data from the comparison of two methods that give smaller values will get one point. The maximum point in one problem domain is 25 while the overall point of the problem domain is 150. Methods that get a greater value are said to be superior to other methods. The results of calculations and boxplot diagrams of the two methods can be seen as follows: • In the SAT problem domain, SADGED has better
performance compared to SRSA. The SADGED method excels at the five instances tested and gets 25 points.
• In the bin packing problem domain, the SADGED algorithm lost 17 points from the SRSA algorithm with the acquisition of 21 values for SRSA and 4 for SADGED. The SADGED algorithm is only able to outperform one instance and lose to the other four instances.
• In the flowshop problem domain, SADGED is only able to excel at two instances namely instance 1 and instance 8, while losing to the remaining three instances. The defeat of the SADGED algorithm is not significant where
it gets 12 points, while SRSA gets 13 points. The difference between the two methods is only 1 point and won by SRSA.
• In the personnel scheduling problem domain, SADGED excels in three instances, namely instance 5, instance 10, and instance 11, while losing to the other two. The SADGED algorithm is 5 points ahead of SRSA with 16 points.
• In the tsp problem domain, SADGED excels in all five instances by getting a value of 21, which is 19 points ahead of SRSA who gets a value of 4.
• In the vrp problem domain, SAGDED excels in the five instances tested and scores 25 points.
Based on the calculation of points that have been done, the SADGED method excels in four problem domains and gets 56 points compared to SRSA. The SADGED method gets 103 points from all 30 instances tested compared to SRSA which only gets 47 points.
Fig. 4. The comparison of median score graph of great deluge self adaptive learning method with simple random simulated annealing.
B. Comparison of Median Values
Comparison of the median value is done to measure the centralization of the results of the method execution. This second measurement uses the FIFA ball method by looking at the value of the median in each instance. the algorithm that is considered to be won will be given a value of three, then for a balanced algorithm will get a value of one and the losing algorithm will get an empty value. The method is considered to win if the total value of the changes obtained is positive and is considered losing if it is negative.
Based on the test results in Figure 4, SADGED won in four problem domains, namely sat, personnel scheduling, tsp, and vrp. However, this method loses to two other problem domains, namely Bin Packing and Flowshop. This indicates that the SADGED algorithm is not able to provide better results in the two problem domains when compared to the SRSA algorithm, which suffered quite a lot of losses. Performance testing graph can be seen below.
Fig. 5. The Rank of Hyper-heuristic methods used is based on the Formula One system.
Figure 5 shows the testing using the Formula One system for both methods, the first rank obtained by the SADGED method with a score of 50 points from the total score that can be obtained by 60 points. The SADGED method gets a percentage point of 83% with an average of points gained in each instance of 1.6 points. Furthermore, the second rank obtained by the SRSA method with the acquisition of a score of 40 points from a total score of 60 points. This method gets a percentage point of 67% with an average point on each instance of 1.3 points.
C. Comparison of Minimum Values
The comparison of minimum values is performed on 30 instances of data with 31 executions. Comparisons at this stage use the FIFA ball system. This system provides a rating of three points for the method that is considered to win, a value of one in the draw method, as well as an empty value on the losing method or produce a worse value than the other methods. a method that gives a better percentage change value will get points of 3 in each problem domain. The purpose of this comparison is to test the performance of the strategies implemented in solving domain traffic optimization problems.
Based on the graph in Figure 6, the minimum SADGED score overall wins in four problem domains, namely SAT, Personnel Scheduling, TSP, and VRP. However, in the problem domain the Bin Packing and Flowshop SADGED method is unable to compete with SRSA. In the domain of the flowshop problem, the SADGED defeat is not too significant, the percentage of changes obtained is 0.71%. The most significant defeat was found in the Bin Packing problem domain where only one instance could win to reach the minimum value with a percentage change of 78.69%.
Although in this work, the hyper-heuristics was tested over 6 problem domains only, but hyper-heuristics also works for other problems. For example, similar works using hyper-heuristics by the can be found in [12], [13], and [14] in which the hyper-heuristics was used for solving examination timetabling problem. On the other hand, in [15] the hyper-heuristics was used to solve orienteering problem.
CONCLUSIONS
Based on the results of trials and analysis of the results that have been carried out, the following conclusions can be drawn:
• The combination of Great Deluge's Self Adaptive Learning is able to give better results compared to the Simple Random Simulated Annealing algorithm. SADGED is able to provide better results in four problem domains, namely SAT, Bin Packing, TSP, and VRP based on the results of trials conducted on the HyFlex framework.
• The SADGED method used is not good enough in finding optimal solutions to the Bin Packing problem. SADGED is only able to provide optimal solutions to one of the five instances tested in the problem domain. This method gets a significant reduction in percentage change of 78% when seen from the minimum value and 92% in the median value.
• Although there was a decrease in the flowshop problem domain, the decrease that occurred was not very significant. SADGED is able to provide an optimal solution for two instances in the problem domain being tested. When viewed from the minimum side of the decline obtained by 0.71%, while providing an optimal solution for three instances when viewed from the median value with a percentage change of 0.02%.
• Based on the test results using the Formula One system, the SADGED method has a better performance compared to the SRSA algorithm. This can be seen from the percentage of performance score obtained by 83% with 50 points from a total of 60 points tested in 30 instances in six different problem domains. The SADGED method is 16% superior to the SRSA method as a comparison algorithm that gets a percentage point of 67%.
In subsequent studies, experiments can be conducted in determining the parameters of the number of LLH limits used in finding optimal objective function values in the Self Adaptive Learning method. With the determination of the right amount, it is expected to be able to provide better results in finding optimal solutions, especially for the Bin Packing and Flowshop problem domains.
Fig. 6. The comparison graph of the minimum score of the great deluge self-adaptive learning method with simple random simulated annealing
REFERENCES
[1] S. S. Choong, L. P. Wong, and C. P. Lim, “Automatic design of
hyper-heuristic based on reinforcement learning,” Inf. Sci. (Ny)., vol. 436–437, pp. 89–107, 2018.
[2] C. Rego, D. Gamboa, F. Glover, and C. Osterman, “Traveling salesman problem heuristics: Leading methods, implementations and latest advances,” Eur. J. Oper. Res., vol. 211, no. 3, pp. 427–441, 2011.
[3] E. K. Burke and G. Kendall, Search Methodologies, 2nd ed. . [4] J. D. Walker, “Design of Vehicle Routing Problem Domains for a
Hyper-Heuristic Framework,” 2015. [5] P. Franq, “Optimization Problem,” Paul Otlet Institute, 2012.
[6] I. Boussaïd, J. Lepagnot, and P. Siarry, “A survey on optimization metaheuristics,” Inf. Sci. (Ny)., vol. 237, pp. 82–117, 2013.
[7] E. K. Burke et al., “A Classification of Hyper-heuristic Approaches,” 2009.
[8] E. K. Burke et al., “Hyper-heuristics: A survey of the state of the art,” J. Oper. Res. Soc., vol. 64, no. 12, pp. 1695–1724, 2013.
[9] E. Burke, T. Curtois, M. Hyde, G. Ochoa, and J. A. Vazquez-Rodriguez, “HyFlex: A Benchmark Framework for Cross-domain Heuristic Search,” no. January, 2011.
[10] R. A.-M. Nabeel, “Hybrid genetic algorithms with great deluge for course timetabling,” IJCSNS Int. J. Comput. Sci. Netw. Secur., vol. 10, no. 4, pp. 283–288, 2010.
[11] Q. Pan, M. F. Tasgetiren, P. N. Suganthan, and T. J. Chua, “A discrete artificial bee colony algorithm for the lot-streaming flow shop scheduling problem,” Inf. Sci. (Ny)., vol. 181, no. 12, pp. 2455–2468, 2011.
[12] Muklason, A., Bwananesia, P.C., YT, S.H., Angresti, N.D. and Supoyo, V.A., 2018, October. Automated Examination Timetabling Optimization Using Greedy-Late Acceptance-Hyperheuristic Algorithm. In 2018 International Conference on Electrical Engineering and Computer Science (ICECOS), pp. 201-206.
[13] Kusumawardani, D., Muklason, A., & Supoyo, V. A. (2019, July). Examination Timetabling Automation and Optimization using Greedy-Simulated Annealing Hyper-heuristics Algorithm. In 2019 12th International Conference on Information & Communication Technology and System (ICTS) pp 1-6
[14] Muklason, A., Syahrani, G.B. and Marom, A., 2019. Great Deluge Based Hyper-heuristics for Solving Real-world University Examination Timetabling Problem: New Data set and Approach. Procedia Computer Science, 161, pp.647-655.
[15] Yoga, I. Wayan AK, Arif Djunaidy, Wiwik Anggraeni, Ahmad Muklason, Faizal Mahananto, Edwin Riksakomara, Nisa D. Angresti, Hidayatul YT Sasmi, and Vicha Azthanty Supoyo. "Advanced Traveler Information Systems: Itinerary Optimisation Using Orienteering Problem Model and Genetic Algorithm." In 2018 International Conference on Information Technology Systems and Innovation (ICITSI), pp. 454-459.
Ahmad Mukhlason, S.Kom, M.Sc, Ph.D
PRESENTER
Route Optimization of Airplane Travel Plans Using the Tabu-Simulated Annealing Algorithm to Solve
the Traveling Salesman Challenge 2.0 Edwin Dwi Ahmad
Department of Information Systems Institut Teknologi Sepuluh Nopember
Abstract— Traveling Salesman Problem (TSP) has been
emerged as NP-hard problem in which there is no exact algorithm that can solve it in polynomial time. There has been an increasing interest in implementing TSP to find the shortest travel route where the trip starts from a city and must end in the same city as the departure city in a condition that every city has to be visited exactly once. Another important feature of TSP is to find travel routes with the lowest possible cost. This paper investigates a new variant of TSP to solve airplane travel plans problem in the Travelling Salesman Challenge (TSC) 2.0. A hybrid Tabu Search and Simulated Annealing was used to solve the problem. The results show that the proposed algorithm can solve the problem and outperforms great deluge algorithm, i.e. 48.54% vs 41.33% measured by the improvement from the initial solution.
Traveling Salesman Problem (TSP) is a problem faced by a salesman where the salesman must visit all cities. The salesman must start his journey from a city and must return to his departure city [1]. The expected result on the TSP is to find the shortest route that can be taken to visit each city that has been provided, with the condition that all cities must be visited once in each trip [2]. Besides being used to find the shortest travel route, TSP is also used to find travel routes with the least total cost [3].
TSP represents a classic problem in combinatorial optimization and is classified as NP-hard problem, which means a problem is difficult to solve in a polynomial time. The computational complexity in TSP will increase along with the increasing number of cities [2]. There have been some recent studies that solve the TSP problem using heuristic algorithms, such as simulated annealing, ant colony optimization and tabu search [4].
In 2018, there was a competition, Travelling Salesman Challenge (TSC) 2.0, raising the use of TSP in addressing airplane travel plan problem. The expected outcome of TSC 2.0 is an itinerary route using the lowest possible cost. The route chosen must pass through all the available areas where each area consists of at least one city. However, if there is one area that has several cities then only one city may be visited. The selection of cities in each area in the planning of this travel route is free as long as conditions for visiting the entire area have been met.
Recent developments in the field of TSP have led to a renewed interest in using various kinds of approaches, such
as Hybrid Simulated Annealing and Tabu Search algorithms. Previous researches show that the combination of those algorithms can obtain optimal results, as well as overcome the weaknesses of each algorithm. Therefore, Tabu-Annealing Simulated is chosen in this study to increase population diversity in Gene-Expression and to improve global search. The result expected from this study is the algorithms used successfully outperform other heuristic algorithms in terms of finding the best solution for airplane itinerary route problem.
II. LITERATURE REVIEW
A. Travelling Salesman Problem
Traveling Salesman Problem (TSP) is one of the classic problems in combinatorial optimization that aims to find the shortest route in visiting all the cities on the tourist map [2]. The selected route starts from a city and must end in the same city as the departure city, and each city should only be visited once. Besides aiming to find the shortest route, the search for a trip route with a minimum total cost must also be considered in the TSP to save the travel budget.
The mathematical modelling of TSP are expressed in the following equation: 1 0 min∑ ∑ , 0 ≤ ≤ 1 , = 0, … , ∑ = 1, = 0, … , ∑ = 1, = 0, … , ∈ = 0, … , − + ≤ − 11 ≤ ≠ ≤
Equation (1) shows the decision variable in binary number where 1 represents travelling route from city i to city j, while 0 indicates the reversed route (from city j to city i). Equation (2) expresses the objective of TSP to minimize the cost with the shortest distance throughout airplane travel routes. The condition in which all cities must be visited no more than 0 is illustrated in equation (3), (4), and (5), while equation (6) and (7) describe the constraint that all cities are connected to a route chosen by the salesman by adding a dummy variable to check that there are no sub routes.
(1)
(2)
(3)
(4)
(5)
(6)
(7)
B. Travelling Salesman Challenge 2.0
Traveling Salesman Challenge (TSC) 2.0 is a competition organized by online travel company, Kiwi. The purpose of this competition is to solve problems in planning the route of travel by airplane. The trip must be done by visiting a city in the given areas where an area can consists of more than or equal to one city.
TSC 2.0 provides the following hard constraints that should be met during the formulation of the solution: 1) the journey must start from the pre-determined city, 2) each area must be visited exactly once, 3) there are one or more cities in the areas, while each salesman area must visit exactly one city, 4) every day salesmen must move from one area to another, 5) salesmen may only visit one area every day, 6) the salesman's journey to the next area must continue from the city in the area visited the day before, 7) the trip must end in the same area as the first departure area.
The dataset used in this study are taken from TSC 2.0 in which some attributes are already provided, such as number of areas, the first city point to start the trip, the list of airports, as well as the flight schedule and prices for each flight. Table I below illustrates the breakdown of TSC 2.0 dataset.
TABLE I. TSC 2.0 DATASET
Dataset Number of Areas
Number of Cities
Data Type
Dataset 1 10 10 Artificial
Dataset 2 10 15 Artificial
Dataset 3 13 38 Artificial
Dataset 4 40 99 Artificial
Dataset 5 46 138 Artificial
Dataset 6 96 192 Artificial
Dataset 7 150 300 Artificial
Dataset 8 200 300 Artificial
Dataset 9 250 250 Artificial
Dataset 10 300 300 Artificial
Dataset 11 150 200 Real
Dataset 12 200 250 Real
Dataset 13 250 275 Real
Dataset 14 300 300 Real
C. Hyper-Heuristic
Hyper-heuristic is a heuristic search method used to automate processes, usually using machine learning. Hyper-heuristic can also be interpreted as a collection of approaches used to combine several heuristic methods to solve several computational problems that have a high degree of difficulties [9]. The Hyper-heuristic was developed to increase the scope of problem solving to become more general and simpler.
Hyper-heuristic is different from metaheuristic where metaheuristic is mostly implemented in the search space for problem solutions. Meanwhile, hyper-heuristic is
implemented beyond search space in the form of solution space. Hyper-heuristic has no guarantee of success in finding the optimal solution. However, the tuning parameters in such method are done automatically, so it no longer requires manual tuning parameters [10].
D. Tabu-Search Algorithm
Tabu Search is one of the metaheuristic algorithms that applies local search methods to do mathematical optimization [11]. The basic principle of the Tabu Search algorithm is to prevent a solution that does not improve by utilizing memory space, which is a taboo list. Tabu Search will save the solutions that have been found and the solutions will as much as possible avoid the process of searching back to the candidate from the previous solution. The concept used in the tabu list is to use FIFO (first in first out) rules, which means that the earliest taboo solution will be replaced by a new solution [12]. Therefore, Tabu Search Algorithm can avoid the local optima solution.
E. Simulated Annealing Algorithm
Simulated Annealing is a metaheuristic algorithm that adopts the concept of steel expansion in physical theory [13]. In the simulated annealing algorithm, if the new solution is no more optimal than the initial solution, then the new solution will pass the control function [14]. The control function is expressed by the Boltzmann equation: =
where P is probability, e is exponential number, c is the difference in the evaluation of the objective function between the solution and the candidate solution, and t is the temperature parameter.
III. IMPLEMENTATION
A. Initial Route Formation
Initial solution is formed by taking the city as the initial route randomly according to the available flight schedules. In order to avoid routes that have no flight schedules in the next day, a graph is made which consists of cities and flight schedules. The initial route must meet all applicable constraints, and once it is formed then an optimization will be performed using the tabu-simulated annealing algorithm.
B. Implementation of Tabulated Simulated Annealing Algorithm
Tabu-simulated annealing algorithm is performed to get the optimum solution. After getting the initial solution, a low level heuristic is applied by conducting 2-city-swap, 3-city-swap, and 4-city swap, and 1-city-swap. A temporary solution then generated by choosing the low level heuristic result randomly.
The temporary solution obtained will go through the tabu-simulated annealing process. If the temporary solution is better than the initial solution, then the temporary solution is accepted as a new solution. However, if the temporary solution is worse than the initial solution, the Boltzmann equation will be accomplished. Temporary
solution is accepted as a new solution if the value of the Boltzmann equation is greater than the random value.
The tabu list will be administered if the temporary solution is worse than the initial solution by entering the low level heuristic result. However, it will be checked beforehand whether there are still slots in the tabu list. If the tabu list slot is full, its contents will be removed first. Low level heuristics that have entered into the tabu list will not be used again in the next process until it is out of the list.
A temporary solution can be accepted as a new solution if its cost is lower than the initial solution’s or provided the random value is greater than the value of the Boltzman equation, as well as the low level heuristic used is not included in the taboo list.
The pseudocode of tabu-simulated annealing is illustrated as follow:
Fig. 1. Pseudocode of Artifical Bee Colony Algorithm
C. Parameters Experiment
There are several parameters tested in the tabu-simulated annealing algorithm as stated in the Table II below.
TABLE II. ALGORITHM PARAMETERS
Parameters Description
LLH Number of low level heuristic used
T0 Initial temperature of simulated annealing algorithm
T1 Final temperature of simulated annealing algorithm
cr Cooling Rate
TL Length of list of tabu search algorithm solutions
IV. RESULTS & DISCUSSIONS
A. Optimization Result
The research is carried out through several scenarios to get the optimum solution. Table III shows a list of the scenarios where each of them is run 11 times for one dataset. Meanwhile, the dataset chosen in the experiment are the 1st , 6th, 11th, and 12th since those can represent the characteristics of the entire dataset.
TABLE III. ALGORTHM PARAMETERS EXPERIMENTS
Scenario T0 T1 cr TL
1 100 0.1 0.95 2
2 10000 0.1 0.9025 2
3 100000000 0.1 0.81450625 2
4 1000000000 0.1 0.9995 2
5 1000000000 0.1 0.9995 3
6 1000000000 0.1 0.999995 3
7 1000000000 0.1 0.9999995 3
8 1500000000 0.1 0.999995 3
9 1500000000 0.001 0.99999995 3
10 1500000000 0.001 0.999995 2
11 1000000000 0.1 0.9999995 2
12 1000000000 0.001 0.9999995 3
The experimental results of 1st to 12th scenarios are compared to find out the combination of parameters that produces the optimum value. On the other side, in order to obtain the right scenario, a weight is given for each dataset, then it is added up based on each scenario, so it can lead to the most optimal scenario.
The 1st and 6th dataset are given a weight of 1 while 11th st and 12th datasets are given a weight of 1.5. The output of each scenario represents airplane travelling cost and Fig. 2
below depicts the results of cost comparison among all scenarios i.e during scenario selection.
Fig. 2. The comparison of each scenario
According to the graph above, the most optimum result or the cheapest travelling cost is triggered by 6th scenario, accounting for 428,0989. Therefore, the senario is used to find out optimum solution for the entire dataset.
B. Comparison between Optimal and Initial Solution
In this section, optimization result in the previous section above is compared to the initial solution for examining the tabu-simulated annealing algorithm performance in providing a more optimum solution (as shown in Table IV). The parameters used in this section are obtained from the scenario experiment where initial temperature equals to 1,000,000,000, cooling rate is 0.9999995, the final temperature is 0.1, while the taboo list length made up 3 and 4 low-level heuristics.
TABLE IV. THE RESULT OF INITIAL AND FINAL SOLUTION
Dataset Initial Final Percentage
1 15,444 1,710 88.9%
2 1,498 1,498 0.0%
3 18,283 10,255 43.9%
4 57,140 20,317 64.4%
5 5,152 1,304 74.7%
6 12,968 4,239 67.3%
7 91,014 37,873 58.4%
8 17,528 10,414 40.6%
9 299,022 167,997 43.8%
10 376,472 135,590 64.0%
11 102,443 70,881 30.8%
12 145,963 94,873 35.0%
13 188,607 170,909 9.4%
14 229,867 207,373 9.8%
Mean 48.5%
It can be seen from Table IV that tabu-simulated annealing algorithm is able to optimize solution at the average of 48.5%, having 1st dataset as the largest percentage of optimization, whilst 2nd dataset is excluded it results no change.
C. Comparison with Other Algorithm
In order to ensure that tabu-simulated annealing algorithm provide best solution, it must be compared with other algorithm. During the research, great deluxe is used by running the algorithm 11 times with 46,051,691 iterations. The summary of comparison can be found in Table V and Fig.3.
Dataset
Tabu-Simulated Annealing Great Deluge
Best Average Best Average
1 1,396 1,710 1,431 3,727
2 1,498 1,498 1,498 1,498
3 9,751 10,255 10,118 11,121
4 19,299 20,317 19,683 22,124
5 1,128 1,304 1,525 1,873
6 3,759 4,239 5,354 5,956
7 35,565 37,873 38,588 39,793
8 7,718 10,414 9,198 11,399
9 144,419 167,997 167,291 183,655
10 122,088 135,590 158,551 172,350
11 66,939 91,008 73,181 81,354
12 91,008 94,873 103,641 109,146
13 164,764 170,909 170,116 178,626
14 204,185 207,373 211,069 221,194
Fig. 3. The comparison of optimal solution using T-SA and GD
0
50000
100000
150000
200000
1 2 3 4 5 6 7 8 9 10 11 12 13 14
Trav
ellin
g Co
st
T-SA GD
Based on the table and figure above, it can be confirmed that tabu-simulated annealing (T-SA) performs better than great deluge (GD) since T-SA allows lower travelling costs.
V. CONCLUSION
This paper set out to investigate how TSP solve airplane travel plan problems in the Travelling Salesman Challenge (TSC) 2. The obvious findings to emerge from this research are as follow:
1. By comparing initial solution and the final solution that has been done, it is known that the taboo-simulated annealing algorithm can improve the initial solution more optimally by an average of 48.54% considering 1st and 2nd dataset
2. In small and medium datasets, the performance of tabu-simulated annealing algorithm in producing optimal solutions is better than large sized datasets.
3. In the dataset included in the artificial data group i.e. 1st to 10th data, the performance of the taboo-simulated annealing algorithm is more optimal when compared to the real data group. The initial solution in the artificial dataset can be optimized with a percentage of 40.59% - 88.92%. Meanwhile, in the real dataset, the percentage generated is smaller (in the range of 9.38% - 35%).
4. In term of finding the optimal solution for the entire dataset, tabu-simulated annealing algorithm provides a better average than great deluge algorithm.
5. Changes in parameters made in this study can affect algorithm performance. However, the greater the value of the parameters used does not guarantee a more optimal solution.
VI. FURTHER RESEARCH
Further studies regarding the efficiency of TSP to solve similar problem as in this paper would be worthwhile if more dataset and more complex scenarios perform, so the result can be more accurate. Another improvement area is to fully accomplish all parameter combinations that perhaps can help to find the most influential parameters in producing an optimal solution. Furthermore, low level heuristics used in this study are limited to moves and swaps, so adding other ones will produce a more optimum solution.
REFERENCES
[1] A. A. Ismail and S. Herdjunanto, “Penerapan Algoritma Ant System dalam Menemukan Jalur Optimal pada Traveling Salesman Problem ( TSP ) dengan Kekangan Kondisi Jalan,” vol. 1, no. 3, pp. 1–6, 2012.
[2] Y. Wang, “The Hybrid Genetic Algorithm with two Local Optimization Strategies for Traveling Salesman Problem,” Comput. Ind. Eng., 2014.
[3] Kara, I. and Derya, T., “Formulations for Minimizing Tour Duration of the Traveling Salesman Problem with Time Windows”. Procedia Economics and Finance, vol. 26, no. 15, pp.1026-1034, 2015.
[4] A. Zhou, L. Zhu, B. Hu, S. Deng, Y. Song, and H. Qiu, “Traveling-Salesman-Problem Algorithm Based on Simulated Annealing and Gene-Expression Programming.”
[5] Y. Lin, Z. Bian, and X. Liu, Developing a Dynamic Neighborhood Structure for an Adaptive Hybrid Simulated Annealing – Tabu Search Algorithm to Solve the Symmetrical Traveling Salesman Problem. Elsevier B.V., 2016.
[6] X. Geng, Z. Chen, W. Yang, D. Shi, and K. Zhao, “Solving the traveling salesman problem based on an adaptive simulated annealing algorithm with greedy search,” Appl. Soft Comput. J., vol. 11, no. 4, pp. 3680–3689, 2011.
[7] S. Suwannarongsri and D. Puangdownreong, “Adaptive Tabu Search for Traveling Salesman Problems,” Int. J. Math. Comput. Simul., vol. 6, no. 2, pp. 274–281, 2012.
[8] G.B. Dantzig, D.R. Fulkerson, and S. M. Johnson, “Solution of a large-scale traveling salesman problem,” Oper. Res., vol. 2, p. 393, 1954.
[9] E. K. Burke, M. Hyde, G. Kendall, G. Ochoa, and E. Ozcan, “A Classification of Hyper-heuristic Approaches A Classification of Hyper-heuristic Approaches,” no. August 2016, 2010.
[10] E. K. Burke et al, “Hyper-heuristics: A survey of the state of the art,” J. Oper. Res. Soc., vol. 64, no. 12, pp. 1695–1724, 2013.
[11] S. E. E. Profile, “A hybrid simulated annealing-tabu search algorithm for the part selection and machine loading problems in flexible manufacturing systems,” no. March 2012, 2014.
[12] F. S. Hillier, Handbook of Metaheuristics, 2nd ed. Springer, 2010.
[13] R. W.Eglese, “Simulated annealing A tool for operational research.” European Journal of Operational Research 46, North-Holland, pp. 271–281, 1990.
[14] L. Ingber, “Simulated Annealing : Practice versus Theory,” vol. 18, no. 11, pp. 29–57, 1993.
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