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"Investor perlu memiliki strategi dalam menentukan harga opsi wajar untuk sebuah opsi. Salah satu strategi yang dapat digunakan adalah mempelajari model harga opsi Heston. Dalam model harga opsi diperlukan nilai-nilai parameter yang harus ditentukan terlebih dahulu melalui kalibrasi. Kalibrasi dapat dipandang sebagai masalah optimasi nonlinear, yakni dengan meminimumkan nilai fungsi objektif yang terkait. Algoritma Particle Swarm Optimization merupakan salah satu metode iteratif yang dapat digunakan dalam menentukan solusi masalah optimasi nonlinear. Selanjutnya hasil kalibrasi digunakan untuk menentukan harga wajar sebuah opsi. Data yang digunakan dalam penelitian ini adalah data 50 harga opsi pasar saham Apple Inc (AAPL). Berdasarkan hasil implementasi yang dilakukan, algoritma Particle Swarm Optimization menunjukkan kinerja yang cukup baik dalam aproksimasi nilai parameter model harga Opsi Heston.

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Investors should have a strategy to determine a fair price for an option. One of the strategy that can be applied is by studing the Heston option pricing model. In the option pricing model, there are some required parameter values that should be determined by using the calibration. The calibration can be considered as a nonlinear optimization problem by minimizing the value of a related objective function. Particle swarm optimization algorithm is one of iterative methods that can be used in the calibration of model?s parameters. Furthermore, the results of calibration can be used to determine the price of an option. The data used in this research is consist of 50 stock market option prices of Apple Inc. Based on the results the implementation, particle swarm optimization algorithm shows a good performance."

"Model Heston merupakan salah satu model yang sangat populer untuk menghitung harga opsi. Namun, keakuratan model tersebut sangat bergantung pada parameter model yang digunakan. Oleh karena itu, pemilihan model parameter sama pentingnya dengan model itu sendiri. Salah satu cara untuk menemukan parameter model Heston terbaik adalah dengan cara meminimumkan fungsi eror antara hara opsi model dengan harga opsi yang berlaku di pasar. Cara seperti ini disebut kalibrasi. Implementasi kalibrasi model Heston dengan algoritma differential evolution (DE) dapat dilakukan dengan enam langkah. Langkah pertama, yaitu menentukan data harga opsi yang digunakan. Langkah-langkah selanjutnya yaitu menentukan metode perhitungan model Heston, fungsi eror, variasi dan parameter kontrol DE, serta kondisi terminasinya. Langkah terakhir, DE diimplementasikan untuk mendapatkan parameter model. Hasil simulasi lima puluh kali kalibrasi pada data harga opsi artifisial menunjukan DE telah cukup baik dalam mengkalibrasi empat dari lima jenis data harga opsi yang digunakan. Lebih jauh lagi, kalibrasi menggunakan lima puluh data harga opsi saham Apple Inc juga memberikan hasil yang cukup baik.

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The Heston Model is one of the most popular model for option pricing. Yet, its accuracy is highly depend on choosing model parameters. Thus, choosing model parameters is important as the model itself. One way to choose the best model parameters is minimizing eror function between the model price and the market price. Such a way is called calibration. Calibrating Heston model with differential evolution (DE) algorithm can be implemented in six steps. First, decide the option price data used for calibration. Then, choose a method for evaluating option price by Heston Model, error function for calibration, variation and control parameter for DE, Also terminating condition of the algorithm. The last, Implement DE to get pameters of the model. The result of fifty times calibration with DE was good enough in four of five artifisial data used. Moreover, calibration using fifty option price of The Apple Inc data also show a good result."

"ABSTRACTThe characteristics of decentralization, diversification, and dynamics of outsourcing resources put forward higher requirements for the supplier selection in manufacturing enterprises. For buildingmaterials equipment manufacturing enterprises, due to the complex product structure, the demand for outsourcing resources is very large. The traditional method is difficult to meet the needs of current outsourcer evaluation and selection. In order to solve the problem, this paper establishes an outsourcing supplier selection model based on the quality, price, delivery time, reliability, and availibility of outsourced suppliers. And then, a hybrid supplier selection algorithm based on Analytic Hierarchy Process AHP and Particle Swarm Optimization PSO is designed in this paper. Finally, the model and algorithm with genetic algorithm GA and ant colony optimization ACO. The experimental results show that the model can effectively improve the effectiveness and reliability of outsourcing supplier selection."

"[Model Black-Scholes merupakan model pertama penentuan harga opsi. Terdapat asumsi-asumsi yang harus dipenuhi pada model Black-Scholes, salah satunya volatilitas yang konstan. Karena asumsi tersebut, maka nilai implied volatility berdasarkan model Black-Scholes akan sama untuk setiap harga opsi. Implied volatilty dipengaruhi oleh harga strike dan waktu jatuh tempo. Namun, pada skripsi ini, implied volatility dibatasi pada pengaruh harga strike saja dan hubungan antara implied volatility dengan harga strike diinterpretasikan dalam kurva smile. Bentuk kurva smile berbeda-beda tergantung pada data observasi nilai opsi di pasar dan bentuknya seperti senyum (smile), skew, atau smirk. Dengan mempelajari kurva smile, seorang investor dapat mempertimbangkan risiko berinvestasi opsi. Pada skripsi ini dibahas bagaimana cara menentukan implied volatility Heston yang diinterpretasikan dalam kurva smile. Untuk dapat menentukan implied volatility Heston, diperlukan harga opsi Heston yang disubstitusi ke model harga opsi Black-Scholes. Untuk memperoleh harga opsi Heston, dilakukan penurunan harga opsi saham Heston berdasarkan model pergerakan harga saham Heston. Kemudian, dengan menghitung beberapa nilai implied volatility Heston yang diperoleh dengan menggunakan harga strike yang berbeda, dapat dibentuk kurva smile Heston. Hasil analisis kurva smile dari implied volatility Heston menggunakan data Anglo American Shares dengan selang harga strike dan tingkat bunga bebas risiko yang berbeda serta waktu jatuh tempo yang tetap adalah sebuah kurva smile yang berbentuk smirk.

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Black-Scholes model is the first option pricing model. There are some assumptions that need to be satisfied in Black-Scholes model, one of them is the constant volatility. Because of that assumption, implied volatility from Black-Scholes model will be same for all option price. Implied volatility depends on strike price and time to maturity. However, in this skripsi, implied volatility is bounded by strike price only and the relation between implied volatility and strike price is interpreted in smile curve. The shapes of smile curve is vary through observed option price effect and its shape looks like smile, skew, or smirk. With studying smile curve, an investor can consider the risk of investing an option. This skripsi will study how to determine Heston implied volatility which is interpreted in smile curve. Heston option price which is substituted to Black-Schole model is needed to determine Heston implied volatility. For that purpose, deriving Heston option pricing model based on Heston stock price model is needed to be done. Then, by calculating some of implied volatilities that have different strike price, smile curve can be made. The analysis result of Anglo American Shares data with different in Strike Price interval and risk-free rates but same in maturity time (1 year) is a smirk shaped smile curve.;Black-Scholes model is the first option pricing model. There are some assumptions that need to be satisfied in Black-Scholes model, one of them is the constant volatility. Because of that assumption, implied volatility from Black-Scholes model will be same for all option price. Implied volatility depends on strike price and time to maturity. However, in this skripsi, implied volatility is bounded by strike price only and the relation between implied volatility and strike price is interpreted in smile curve. The shapes of smile curve is vary through observed option price effect and its shape looks like smile, skew, or smirk. With studying smile curve, an investor can consider the risk of investing an option. This skripsi will study how to determine Heston implied volatility which is interpreted in smile curve. Heston option price which is substituted to Black-Schole model is needed to determine Heston implied volatility. For that purpose, deriving Heston option pricing model based on Heston stock price model is needed to be done. Then, by calculating some of implied volatilities that have different strike price, smile curve can be made. The analysis result of Anglo American Shares data with different in Strike Price interval and risk-free rates but same in maturity time (1 year) is a smirk shaped smile curve.;Black-Scholes model is the first option pricing model. There are some assumptions that need to be satisfied in Black-Scholes model, one of them is the constant volatility. Because of that assumption, implied volatility from Black-Scholes model will be same for all option price. Implied volatility depends on strike price and time to maturity. However, in this skripsi, implied volatility is bounded by strike price only and the relation between implied volatility and strike price is interpreted in smile curve. The shapes of smile curve is vary through observed option price effect and its shape looks like smile, skew, or smirk. With studying smile curve, an investor can consider the risk of investing an option. This skripsi will study how to determine Heston implied volatility which is interpreted in smile curve. Heston option price which is substituted to Black-Schole model is needed to determine Heston implied volatility. For that purpose, deriving Heston option pricing model based on Heston stock price model is needed to be done. Then, by calculating some of implied volatilities that have different strike price, smile curve can be made. The analysis result of Anglo American Shares data with different in Strike Price interval and risk-free rates but same in maturity time (1 year) is a smirk shaped smile curve., Black-Scholes model is the first option pricing model. There are some assumptions that need to be satisfied in Black-Scholes model, one of them is the constant volatility. Because of that assumption, implied volatility from Black-Scholes model will be same for all option price. Implied volatility depends on strike price and time to maturity. However, in this skripsi, implied volatility is bounded by strike price only and the relation between implied volatility and strike price is interpreted in smile curve. The shapes of smile curve is vary through observed option price effect and its shape looks like smile, skew, or smirk. With studying smile curve, an investor can consider the risk of investing an option. This skripsi will study how to determine Heston implied volatility which is interpreted in smile curve. Heston option price which is substituted to Black-Schole model is needed to determine Heston implied volatility. For that purpose, deriving Heston option pricing model based on Heston stock price model is needed to be done. Then, by calculating some of implied volatilities that have different strike price, smile curve can be made. The analysis result of Anglo American Shares data with different in Strike Price interval and risk-free rates but same in maturity time (1 year) is a smirk shaped smile curve.]"

"Pendistribusian BBM di Region Ambon memiliki tantangan berupa terbatasnya akses transportasi melalui jalur darat dikarenakan kondisi geografis yang terdiri dari pulau-pulau sehingga pendistribusain menjadi rumit dan mengalami keterlambatan penyaluran BBM. Sehingga diperlukakn rute distribusi yang optimal untuk memastikan penyaluran BBM tidak terlambat dan tidak ada kelangkaan BBM. Penelitian ini mengimplementasikan metode optimasi dengan mempergunakan algoritma Genetika dan Particle Swarm Optimization untuk pemilihan rute distribusi dengan tujuan meminimalisir jarak tempuh. Data jarak mil laut antar pelabuhan, kecepatan kapal pada tiap pelabuhan diolah menjadi sebuah model Asymmetric Travelling Salesman Problem (ATSP). Penerapan dua algoritma yaitu : Algorima Genetika dan particle swarm optimization dipergunakan untuk menyelesaikan model ATSP yang dibuat dengan fungsi objektif jarak tempuh yang seminimum mungkin. Variasi pada destinasi awal/akhir dari pemilihan rute juga dilakukan sebagai parameter uji tambahan dari setiap algoritma. Hasil penelitian menunjukkan bahwa algoritma genetika memberikan rute terpendek dan efisien dibandingkan particle swarm optimization pada setiap pemilihan rute yang dilakukan. Hal ini membuktikan bahwa algoritma genetika lebih efektif dalam menentukan rute pendistribusian BBM yang lebih pendek dan efisien.

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The distribution of BBM in the Ambon Region has challenges in the form of limited access to transportation via land routes due to geographical conditions consisting of islands so that distribution becomes complicated and delays fuel distribution. So that an optimal distribution route is needed to ensure the distribution of fuel is not late and there is no shortage of fuel. This study implements an optimization method using the Genetic Algorithm and Particle Swarm Optimization for the selection of distribution routes with the aim of minimizing the distance traveled. Nautical mile distance data between ports, ship speed at each port is processed into an Asymmetric Traveling Salesman Problem (ATSP) model. The application of two algorithms, namely: Genetic Algorithm and particle swarm optimization is used to solve the ATSP model which is made with the objective function of the distance traveled as minimal as possible. Variations in the initial/final destination of the route selection are also performed as additional test parameters of each algorithm. The results showed that the genetic algorithm provides the shortest and most efficient route compared to particle swarm optimization for each route selection made. This proves that the genetic algorithm is more effective in determining the shorter and more efficient fuel distribution route."

"Energi listrik telah menjadi suatu kebutuhan esensial untuk menunjang kehidupan manusia. Rencana Usaha Penyediaan Tenaga Listrik Tahun 2021-2030 menyebutkan bahwa akan terjadi peningkatan jumlah pelanggan mencapai 24.4 juta dengan persentase pertumbuhan listrik sebesar 4.9% di Indonesia, sehingga penyedia tenaga listrik harus mampu memenuhinya secara efisien. Salah satu faktor yang memengaruhi efisiensi suatu sistem tenaga listrik adalah terjadinya rugi-rugi daya aktif pada saat penyaluran listrik dari pembangkit menuju pelanggan. Hal ini tidak dapat dihindari, namun dapat diminimalisasi dengan melakukan optimisasi aliran daya reaktif pada sistem berupa pengaturan magnitude tegangan terminal generator, posisi tap transformator, dan keluaran dari sumber daya reaktif. Optimisasi aliran daya reaktif merupakan permasalahan yang kompleks karena tidak konveks, memiliki variabel kontinyu dan diskrit, serta memiliki banyak nilai optimum lokal maupun global sehingga dibutuhkan algoritma perhitungan cerdas yang mampu menemukan solusi nilai optimum global dari fungsi tujuan, meskipun terdapat variabel diskrit didalamnya. Penelitian ini memanfaatkan algoritma particle swarm optimization (PSO) dalam menyelesaikan permasalahan optimisasi aliran daya reaktif yang diuji di Sistem RIS dengan mengatur magnitude tegangan terminal generator bermode kontrol tegangan dan/atau posisi tap transformator yang dilengkapi On Load Tap Changer. Hasil dari penilitian ini berupa penurunan total rugi-rugi daya aktif saluran transmisi dari kondisi awal pada Sistem RIS sebesar 20.13% saat mengatur tegangan terminal generator, 8.62% saat mengatur posisi tap transformator yang dilengkapi On Load Tap Changer, dan 13.18% saat mengatur keduanya.

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Electricity has become an essential need to support human life. The Electricity Supply Business Plan for 2021-2030 states that there will be an increase in the number of customers up to 24.4 million with a percentage growth of 4.9% in Indonesia, so electricity providers must be able to meet it efficiently. One of the factors affecting the efficiency of a power system is the occurrence of active power losses during the transmission of electricity from the generator to the customers. This cannot be avoided but can be minimized by optimizing reactive power flow in the system, such as setting the terminal voltage magnitude of the generator, the tap position of the transformer, and the output of reactive power sources. Reactive power flow optimization is a complex problem because it is non-convex, has continuous and discrete variables, and has many local and global optimum values, requiring intelligent calculation algorithms that can find the global optimum value solution of the objective function, even though there are discrete variables in it. This research utilizes the particle swarm optimization (PSO) algorithm to solve the optimization of reactive power flow problem tested in the RIS system by controlling the voltage magnitude of the generator terminal and/or the tap position of the transformer equipped with an On-Load Tap Changer. The results of this study are a decrease in the total active power losses on transmission lines of the RIS system by 20.13% when adjusting the generator terminal voltage magnitude, 8.62% when adjusting the tap position of the transformer equipped with an On-Load Tap Changer, and 13.18% when adjusting both."

"Komunikasi mmWave merupakan komunikasi yang menjanjikan dan menarik bagi kalangan akademik dan industri karena ketersediaan spektrum yang berlimpah, akan tetapi spektrum mmWave mmiliki karakteristik kanal propagasi yang buruk. Teknik beamforming dengan perarahan yang tinggi menjadi solusi yang efektif untuk hal tersebut. Penggunaan teknik tersebut memiliki masalah waktu tunda yang tinggi dalam mekanisme initial access (IA). Hal ini dapat berdampak pada kinerja yang buruk untuk dapat mendukung implementasinya di teknologi komunikasi saat ini, yaitu 5G low end-to-end latency. Metode meta-heuristic dengan menggunakan algoritma Genetic Algorithm (GA) merupakan salah satu metode yang telah dilakukan untuk menyelsaikan permaslahan tersebut. Namun, kinerja yang dihasilkan belum cukup baik dan masih dilakukan penelitian untuk menghasilkan peningkatan kinerja waktu tunda terbaik dengan meninjau pada algoritma berbasis alam. Pada penelitian ini, kami melakukan perancangan dan penentuan suatu algoritma berdasarkan algoritma berbasis alam yang memiliki kinerja lebih baik dari GA yang telah dilakukan untuk kasus IA pada komunikasi mmWave. Algoritma yang telah dirancang dan ditentukan adalah algoritma hybrid genetic algorithm and particle swarm optimization (HGAPSO). Hasil kinerja algoritma tersebut menunjukkan nilai kapasitas terbaik (Gbit/s) dan waktu tunda yang cukup rendah (jumlah iterasi) dibandingkan algoritma GA yang telah diajukan dan particle swarm optimization (PSO). Oleh karena itu, dapat disimpulkan bahwa HGAPSO merupakan algoritma yang memiliki kinerja lebih baik dari GA yang telah diajukan dan dapat menjadi algoritma alternatif untuk kasus IA pada komunikasi mmWave.

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MmWave communication is a promising and attractive communication for academic and industry because of the abundant available spectrum, but mmWave spectrum has poor propagation channel characteristics. High beamforming technique is an effective solution for the problem. The technique has a high delay in the initial access (IA) mechanism. This can have an impact on bad performance to be able to support its implementation in current communication technology, namely 5G low end-to-end latency. The meta-heuristic method using the Genetic Algorithm (GA) is one of the methods that have been used to solve the IA problem. However, the performance result is not good enough and research is still being carried out to produce the best delay time performance improvement by using nature inspired algorithms. In this research, we design and determine an algorithm based on nature inspired algorithms that have better performance than the GA that has been proposed for the IA case in mmWave communication. The algorithm that has been designed and determined are the hybrid genetic algorithm and particle swarm optimization (HGAPSO). The performance of the algorithm shows the best capacity value (Gbit/s) and the delay time is quite low (number of iterations) compared to the GA algorithm that has been proposed and particle swarm optimization (PSO). Therefore, it can be concluded that HGAPSO is an algorithm that has better performance than the GA that has been proposed and can be alternative algorithm for the IA case in mmWave communication."

"Isi tesis ini mengenai pembuatan simulator 3D dari algoritma pencarian Particle Swarm Optimization untuk pencarian banyak sumber asap dengan menggunakan Open Dynamics Engine dan mengenai Dynamic Niche-PSO yang adalah algoritma baru sebagai modifikasi algoritma MPSO dari penelitian sebelumnya [1]. Versi simulator 2D untuk PSO ini telah dibuat penelitian sebelumnya ini. Pemodelan fisik 3D ini bertujuan untuk mengurangi gap antara perangkat lunak dan perangkat keras di dunia nyata.Salah satu bab adalah bab yang menjelaskan pembuatan model robot, asap dan sumbernya, dan medan dengan Open Dynamics Engine. Dilanjutkan dengan bab tentang cara pemakaian GUI simulator ini.Algoritma Dynamic Niche-PSO yang diajukan pada penelitian ini bertujuan untuk memperbaiki kelemahan algoritma PSO sebelumnya dimana 2 niche (kelompok agen) atau lebih masih ada kemungkinan untuk menuju sumber asap yang sama. Pada Dynamic Niche-PSO ini diperkenalkan robot baru, yaitu robot utama yang mempunyai arca ketertarikan. Pada Dynamic Niche-PSO ini juga robot netral dan bermuatan dapat berpindah keanggotaan dari satu niche ke niche yang lain apabila memasuki arca ketertarikan atau attract area dari robot utama niche yang lain ini.

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The contents of this thesis are the development of 3D simulator for visualizing Particle Swarm Optimization algorithm for multi odor source localization using Open Dynamics Engine, and Dynamic Niche-PSO as modification of MPSO algorithm from previous research [1]. The 2D version of this MPSO is made in previous research. This 3D modeling has a purpose to reducegap between Software and Hardware in the real world.

One of chapters is explaining about how to make the model of robots, plumes and its sources, and field with Open Dynamics Engine. Continued with chapter explaining about how to use the GUI of this simulator.

Dynamic Niche-PSO algorithm proposed in this research has a purpose to refine the weakness of previous algorithm where 2 niches (group of agents) or more still have a probability to move toward the same odor source. There is newly introduced robot in this Dynamic Niche-PSO algorithm called main robot which has an attract area. In this Dynamic Niche-PSO also a neutral robot or a charge robot could become a member of another niche if it entered the attract area of main robot of this other niche."

" PSS (Power system stabilizer) telah digunakan secara luas untuk memperbaiki stabilitas sistem tenaga listrik modern. Dalam makalah ini diusulkan perancangan sistematik PSS dengan Particle Swarm Optimization (PSO) sebagai metode optimasi penalaan parameter PSS. Penalaan parameter PSS dilakukan untuk mendapatkan sistem tenaga listrik yang stabil dan teredam secara optimal. Kriteria optimal yang digunakan dalam proses penalaan parameter adalah indeks performansi Integral of Time multiplied by Absolute Error (ITAE). Performansi dariPSS ini diujikan pada sistem tenaga listrik mesin tunggal dibawah gangguan kecil, kondisi beban dan parameter tertentu. Hasil analisa nilaieigen dan simulasi menunjukkan bahwa osilasi sistem tenaga listrik dapat teredam secara optimal melalui penalaan PSS berbasis PSO ini. Hasil simulasi juga menunjukkan bahwa performansi dinamik PSS berbasis PSO lebih baik dibandingkan PSS yang ditala secara konvensional.

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AbstractPower system stabilizer (PSS) have been extensively used in modern power system for enhancing stability of the system. This paper presents a new systematic approach for the design of power systemstabilizer using PSO (Particle Swarm Optimization). The proposed approach employs PSO search for optimal setting of PSS parameters. The optimal criteria of the Integral of Time multiplied by AbsoluteError (ITAE) is used to search optimal setting. The performance of the proposed PSS under small disturbances, loading conditions and system parameters is tested. The eigenvalue analysis and simulationresults show the effectiveness of the PSO based PSS to damp out the system oscillations. It is found that the dynamic performance with the PSO based PSS shows improved results, over conventionally tunedPSS."

"Traveling Salesman Problem (TSP) adalah masalah mencari jalur terpendek untuk mengunjungi setiap simpul tepat satu kali kecuali simpul awal kunjungan jika diberikan himpunan simpul yang harus dikunjungi. Tiga modifikasi dilakukan pada skripsi ini untuk menyelesaikan masalah TSP dengan menggabungkan metode Ant Colony Optimization (ACO), Particle Swarm Optimization (PSO) dan 3-Opt Algorithm. ACO digunakan untuk mencari solusi TSP, PSO digunakan untuk mencari nilai paremeter terbaik 𝛼 dan 𝛽 yang digunakan pada ACO, dan 3-Opt digunakan untuk mengurangi total jarak tempuh solusi yang didapat dari ACO. Pada modifikasi pertama, 3-Opt digunakan untuk mengurangi total jarak tempuh dari solusi terbaik yang didapatkan setiap iterasi. Pada modifikasi kedua, 3-Opt digunakan untuk mengurangi total jarak tempuh seluruh solusi yang didapatkan pada setiap iterasi. Pada modifikasi ketiga, 3-Opt digunakan untuk mengurangi total jarak tempuh seluruh solusi yang berbeda yang didapatkan pada setiap iterasi.Hasil modifikasi diuji menggunakan 6 benchmark problems yang diambil dari TSPLIB dengan menghitung besarnya galat relatif terhadap best known solution dan running time percobaan. Setiap masalah diselesaikan dengan 10 kali percobaan, dengan masing-masing percobaan menggunakan 10 agen dan 50 iterasi. Hasil implementasi menunjukkan modifikasi pertama tidak memberikan hasil yang memuaskan, modifikasi kedua memberikan hasil yang memuaskan namun dengan running time yang cukup besar, serta modifikasi ketiga memberikan nilai galat yang tidak jauh berbeda dengan modifikasi kedua namun dengan running time yang jauh lebih kecil.

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The Traveling Salesman Problem (TSP) is the problem of finding a shortest tour which visits all the vertices exactly once, except the first vertex, given a set of vertices. This thesis discusses three modification to solve TSP by combining Ant Colony Optimization (ACO), Particle Swarm Optimization (PSO) and 3-Opt Algorithm. ACO is used to find the solution of TSP, PSO is used to find the best value of parameters α and β that are used in ACO, and 3-Opt is used to reduce the total of tour length from the solution obtained by ACO. In the first modification, 3-Opt is used to reduce the total of tour length from the best solution obtained at each iteration. In the second modification, 3-Opt is used to reduce the total of tour length from the entire solutions obtained at each iteration. In the third modification, 3-Opt is used to reduce the total of tour length from different solutions obtained at each iteration.Results were tested using 6 benchmark problems taken from TSPLIB by calculating the relative error to the best known solution and the running time. Every problem was solved with 10 trials, where each trial uses 10 agents and 50 iterations. The implementation results showed the first modification did not provide satisfactory results, the second modification gave a satisfactory result, but the running time was quite large, and the third modification gave errors that were close to the second one but with smaller running time."