Distributed Multi-Ant Colony System Algorithm Using Raspberry Pi Cluster for Travelling Salesman Problem

Alobaedy and Fazea Iraqi Journal of Science, 2022, Vol. 63, No. 9, pp: 4067-4078 DOI: 10.24996/ijs.2022.63.9.35 _________________________________ *Email: new.technology@hotmail.com 4067 Distributed Multi-Ant Colony System Algorithm using Raspberry Pi Cluster for Travelling Salesman Problem Mustafa Muwafak Alobaedy 1 *, Ali A. Khalaf 2 , Yousef Fazea 3 1 School of Information & Communication Technology, HELP University, Kuala Lumpur, Malaysia 2 Computer Science Department, College of Science, University of Baghdad, Baghdad, Iraq 3 Department of Computer & Information Technology, Marshall University, 1 John Marshall Drive, Huntington, WV 25755, USA Received: 25/10/2021 Accepted: 27/4/2022 Published: 30/9/2022 Abstract The traveling salesman problem is addressed in this paper by introducing a distributed multi-ant colony algorithm that is implemented on a Raspberry Pi cluster. The implementation of a master and eight workers, each running on Raspberry Pi nodes, is the central component of this novel technique. Each worker is responsible for managing their own colony of ants, while the master coordinates communications among workers’ nodes and assesses the most optimal approach. To put the newly built cluster through its paces, several datasets of traveling salesman problem are used to test the created cluster. The findings of the experiment indicate that a single board computer cluster, which makes use of multi-ant colony algorithm, is a viable alternative for distributed computing. This approach's extensibility options are extensively discussed as well. Keywords: Metaheuristic Algorithm, Single-Board Computing Cluster, Combinatorial Optimization problem, Distributed Computing, Distributed Algorithm. 1. Introduction The Ant Colony System (ACS) algorithm has been successfully applied in a wide range of combinatorial optimization problems [1]. The mechanism of the ACS algorithm is inspired by the natural behavior of biological ant colonies [2][3]. The ACS algorithm is built on notation of the reinforcement learning concept [4]. It uses ants as agents to manipulate environment via use of pheromone trails to find the shortest path. In every iteration cycle, each ant builds up a new solution step by step using exploitation and exploration mechanisms. Simultaneously, each ant reduces the pheromone from the path it uses to dissuade the next ant from utilizing the same path, causing the following ants to explore other paths (solutions). The determined as the best path so far among all the ants is labeled by applying pheromone to the edges of that path. In the subsequent iteration, the ants are drawn to search in the solution space near the previous best path in the succeeding iteration [5], [6]. The ACS algorithm may be implemented in a number of ways, including single or multi colonies [2]. Despite the fact that the ACS algorithm has been successfully implemented sequentially in a variety of domains, little attention has been paid to distributed multi-ant colony implementation [7]. Therefore, ACS algorithm could be a promising candidate for parallelization. ISSN: 0067-2904 Alobaedy and Fazea Iraqi Journal of Science, 2022, Vol. 63, No. 9, pp: 4067-4078 8604 In this paper, the Multi Ant Colony System (MACS) which comprises of Raspberry Pi cluster with nodes (workers), is used to investigate distributed multi ant colony based on coarsegrained approach. Each node represents an entire ant colony and a master node has been deployed to coordinate the workers activities. MACS is an iterative technique in which the colonies transfer their solution to the master node for evaluation after each iteration. Using the 3-opt approach, the master node will choose the optimal option for further improvement. If the improved solution outperforms the previous best so far solution, then it will be preserved. If the stop condition is not met, the master node will apply a global pheromone update; if it is met, the algorithm will terminate the iteration and display the final solution. Consequently, the created cluster’s performance was tested and evaluated using dataset token from traveling salesmen problem. The findings show that the Raspberry Pi cluster achieved a significant performance across three datasets. Thus, the proposed cluster could be scaled to a wide range of combinatorial optimization problems and could be expanded to any number of workers. Therefore, the proposed cluster is an important contribution to the body of knowledge. The following sections outline the structure of this paper. Section 2 presents an overview on the Raspberry Pi. Section 3 presents the classifications of Raspberry Pi cluster applications based on their functionalities. Section 4 discusses the methodology used. Then the findings are discussed in Section 5. Section 6 presents the conclusion and future directions. 2. Raspberry Pi Overview The Raspberry Pi (RPi) was initially developed by the Raspberry Pi Foundation to encourage the teaching of computer science and basic electronic courses in developing countries [8][9]. RPi gained popularity after researchers and practitioners found that it is a useful and practical device for a variety of applications including robotics, weather monitoring, and smart homes [10]–[12]. The RPi is depicted in Figure 1. It is a single-board computer with dimensions of approximately 8.8 x 5.8 x 1.8 cm. The RPi can run a Linux-based operating system (OS), known as Raspberry Pi OS, which comes with three options: Lite; desktop; and desktop with recommended software. In addition, the RPi can also support third-party OS as well, e.g., Raspbian, RISC OS, Windows IOT Core, and etc. Figure 1-Raspberry Pi 4 Model B dimensions The RPi comes in a variety of hardware models with varying memory, networks, and processing capabilities. Table 1 summarizes some of the features of several RPi models [13][14]. At the time of writing, the latest model of the RPi, released in 2019, is the Raspberry Pi 4 Model B which offers a processing speed of 1.5 GHz (quad-core), up to 8 GB memory, Alobaedy and Fazea Iraqi Journal of Science, 2022, Vol. 63, No. 9, pp: 4067-4078 8604 SD card support, GPIO, Wi-Fi, LAN Gigabit Ethernet, 4 USB, and two micro-HDMI ports (support up to 4 Kp 60). The RPi is therefore a useful and practical choice for a low-cost computing cluster capable of successfully solving small and medium-scale problems. Table 1- Comparison between Raspberry Pi models Model Release Date CPU Memory Network Raspberry Pi 4 B 2019 Quad-core (1.5GHz) 2, 4, 8 GB Gigabit Ethernet, Wireless and Bluetooth Raspberry Pi 3 A+ 2018 Quad-core (1.4GHz) 512MB Wireless and Bluetooth Raspberry Pi 3 B+ 2018 Quad-core (1.4GHz) 1GB Gigabit Ethernet, Wireless and Bluetooth Raspberry Pi 3 B 2016 Quad-core (1.2GHz) 1GB Wireless LAN / 100 Base Ethernet Raspberry Pi 2 B 2015 Quad-core (900MHz) 1GB 100 Base Ethernet Raspberry Pi 1 Model A+ 2014 Single core (700MHz) 512MB No Raspberry Pi 1 Model B+ 2014 Single core (700MHz) 512MB 100 Base Ethernet Raspberry Pi Zero W 2017 Single core (1GHz) 512MB Wireless LAN / Bluetooth Raspberry Pi Zero 2015 Single core (1GHz) 512MB No 3. Classification of Raspberry Pi Cluster Applications Figure 2 depicts the graphical representation of the taxonomy categorization of RPi application-oriented based. The taxonomy classification of RPi cluster applications was developed by conducting an extensive literature analysis of the existing literature. Alobaedy and Fazea Iraqi Journal of Science, 2022, Vol. 63, No. 9, pp: 4067-4078 8606 Figure 2-Mind-map of domains identified in Raspberry Pi cluster applications Alobaedy and Fazea Iraqi Journal of Science, 2022, Vol. 63, No. 9, pp: 4067-4078 8604 Data Analytics Data analytics requires high-performance computing in a data center to process intensive computing tasks such as classification and visualization. A viable alternative to an expensive data center is a Hadoop cluster using single-board computing such as the RPi. Despite its lowpower processors, it is possible to use RPi in big data analytics by combining it with several RP is in a cluster [15]. RPi cluster technology is applied in various types of data analytics applications such as big data, data mining, and visualization. Open-source software such as Message Passing Interface (MPI), Hadoop, Spark, and Yet Another Resource Negotiator (YARN) can be run from RPi cluster [16]–[19]. RPi cluster was implemented to process tourists’ data collected from Facebook, Twitter, Foursquare, and Instagram APIs to generate a heatmap [17]. The heatmap displays the tourists’ geolocations, comments, and attractions. A RPi cluster has similar capabilities as fully functional servers for big data and video streaming applications in centers [18]. In addition, RPi cluster is used in data mining to solve classification problems using the K- Means algorithm in big data [16]. RPi clusters are expected to play a prominent role in data analytics for small organizations. Education The idea behind creating the RPi device was to encourage students to learn programming and to develop their interest in computer science concepts, especially for students in developing countries [8], [9]. In higher education, teaching subjects such as High-Performance Computing (HPC), cluster and distributed computing with hands-on experience is very limited due to the high cost of the equipment [20]. Since the low cost of RPi makes it a viable option to be incorporated into the curriculum, RPi cluster has since been introduced in practical HPC education activities [19]–[21]. RPi clusters are also used as dedicated parallel computing hardware for each student, instead of students having to share hardware [22]. With the benefits of remote access, RPi cluster enables students to build their own File Systems in User Space (FUSE), and gain experience of using a low-cost remote laboratory [23], [24]. In addition, RPi cluster can potentially be extended into a mini supercomputer [25], [26], that can be used for education and research as a high-performance computer. The advantages of low cost, mobility, size, weight, and ambient cooling might change the way parallel and distributed computing is taught. Image Processing RPi cluster with open-source libraries such as Hadoop and OpenCV could play a pivotal role in image processing e.g. feature points extraction system using Speeded Up Robust Features (SURF) algorithm [27], face recognition [28], image stacking [29], edge detection [30], [31], image analysis [32], ray tracing [33], image conversion [34], image recognition [35], Fourier transform [36] and image classification [37]. Moreover, a RPi cluster can extend its capability in image processing by adding a GPU [38]. Cloud Technology RPi cluster has been implemented in two types of cloud technology: computing and storage. RPi cloud computing was developed using Nextcloud, an open-source client-server software [39]. To overcome the lack of computing power of the RPi, a cloud computing environment was developed using 300 nodes; this effectively demonstrated that RPi could be an inexpensive and green alternative for cloud computing in research [40]. RPi cloud has the potential to provide various cloud layers such as cloud stack, resource virtualization, and network for the educational environment [41]. Furthermore, the RPi hardware and the crowdsourcing platform could support the development of crowd cloud: a crowdsourced system for cloud infrastructure, cloud platform, and cloud software services [42]. A naïve model of HPC as a service was implemented using the RPi cluster in [43]. Moreover, RPi cluster has the capability to be used as cloud storage to provide real-time applications [44]. Alobaedy and Fazea Iraqi Journal of Science, 2022, Vol. 63, No. 9, pp: 4067-4078 8604 Miscellaneous Applications We found several additional applications of RPi clusters in other domains such as anomaly detections in the smart grid [45], power management [46], genome pattern matching in biological computation [47], patients monitoring systems in health care [48], and load balancing methods in webservers [49]. 4. Methodology for Distributed Multi-Ant Colony System Algorithm In this investigation, we employed a Raspberry Pi cluster with one master and eight worker nodes. As indicated in Figure 3, the cluster is linked via a switch that supports one-gigabit connection. Figure 3- Raspberry Pi cluster network topography The application was developed with the C#.NET framework and the Mono open-source library. The experiments were carried out utilizing eleven symmetric Travelling Salesman Problem (TSP) datasets, each of which reflects a different size and complexity of the work environment. Undermaster node coordination, each worker was implemented as a complete ant colony using the Ant Colony System (ACS) algorithm. Each ant colony node was populated with eight ants, which were chosen by following a pilot experiment to determine the optimal number of ants. The master node begins by identifying the local network's linked workers, then begins reading the TSP dataset for the initialization phase, which includes calculating distance, creating initial pheromone, and generating the initial solution. The master node begins delivering tasks and basic information to the workers at this stage. Using the pheromone matrix obtained from the master, each worker begins looking for the optimum solution and applying local pheromone updates. The worker will communicate the best solution to the master node once it achieves the stop condition. The master node will assess the solutions received from the worker nodes and choose the best one. The master node used the 3-Opt local search method to get the best solution. If the best employee’s solution is better than the previous solution, it will be saved as the best so far solution. If the termination condition is fulfilled, the master node applies a global pheromone update, and the entire process is replayed using the updated pheromone matrix. The procedure will be ended if the termination condition is satisfied, and the best solution so far will be shown. The process flow for master and worker nodes is depicted in Figure 4. Alobaedy and Fazea Iraqi Journal of Science, 2022, Vol. 63, No. 9, pp: 4067-4078 8604 Figure 4-Master and workers process flow for Raspberry Pi cluster. Developing ACS for Raspberry Pi Cluster This study implemented Raspberry Pi nodes as a computing cluster that consists of a master node and eight worker nodes. The procedure begins with the master node connecting the workers through IP address as shown in Figure 5. The next phase will be carried out once the connection has been established.  Read TSP instances  Initialize distance using Euclidian distance, which generates a symmetric initial distance matrix ).  Initialize heuristic where is the distance from city to city .  Initialize the pheromone matrix using the nearest neighbor approach .  Initialize a place holder for best so far solution ̂ .  Master sends the initial information to each worker. Alobaedy and Fazea Iraqi Journal of Science, 2022, Vol. 63, No. 9, pp: 4067-4078 8608 procedure ACS master List of Workers IP Address Read TSP Dataset Initial Distance Heuristic Initial Pheromone ̂ Initial best so far, a solution While termination condition is not met: Send Initial Information to ̂ starts ACS algorithm (Figure No) While not all solution received from do: Wait for Solution End-While Select the Best Iteration Solution Implement 3-opt ( if ̂ then ̂ end-if Apply Global Update Pheromone End-While Display ̂ End-procedure Figure 5-Master implementation for TSP using Raspberry Pi nodes based on Distributed ACS algorithm. The master node's primary responsibility is to set up the relevant parameters, such as distance, heuristic, and pheromone, and then transfer that information to the worker nodes for processing. Worker nodes are in charge of determining the optimal solution. Using the pseudorandom proportional rule [8], each worker implements eight ants to find the optimal solution. In addition, as illustrated in Figure 6, employees perform local pheromone updates throughout solution construction and global pheromone updates to the best so far solution in the colony. Procedure ACS-Worker Receive Initial Information to ̂ Initialize the number of ants While (Termination condition not met) Do For Do: Construct new solution Apply local pheromone update End For Apply Global pheromone update Update best found solution End-While End-procedure Figure 6-Worker’s implementation for TSP using Raspberry Pi nodes based on Distributed ACS algorithm. Alobaedy and Fazea Iraqi Journal of Science, 2022, Vol. 63, No. 9, pp: 4067-4078 8604 Experiment Design and Datasets The experiment was conducted using symmetric TSP datasets obtained from the TSPLIB library [9]. Each dataset contains a different number of cities and some of them have been provided with optimum paths. TSP is a problem of finding the shortest tour starting from any city, visiting every city one time only and going back to the starting city. Formally, TSP is a fully connected graph , where represents the cities and represents the connections. Each connection ( is assigned with distance value between ( . In this study, we have implemented an asymmetric TSP where . The problem can be formulated mathematically as shown in equation 1: ∑ (1) Finding the shortest path in TSP is classified as an optimization problem that requires a metaheuristic algorithm such as Genetic Algorithm (GA), Simulated Annealing (SA), and Ant Colony Optimization [10]. We have selected eleven TSP datasets for experiments, each experiment conducted 30 times to obtain the best, worse, mean, and standard deviation. Some datasets have optimal solutions provided from the source while others do not have. ACS Parameters Table 2 provides the parameters for the implemented ACS. Table 2-ACS Parameters Parameters for All Datasets No of Ant Colony 8 No of Ants in each Colony 8 Initial Pheromone 1 / (8 * nn (Nearest-neighbor)) No of Iterations 20 (Main ACS) x 100 (Sub-ACS) Alpha (α) 1 Beta (β) 2 Raw (ρ) 0.1 Zeta (ξ) 0.1 q0 0.9 5. Results and Discussion Various studies conducted experiments using TSP datasets indicate that metaheuristic algorithms have different performances on the deferent dataset. [5] presented the results of TSP using ant colony optimization algorithms such as Ant System (AS), Max-Min Ant System (MMAS), and Ant Colony System (ACS). In our study, we have implemented the ACS algorithm in the Raspberry Pi cluster based on distributed ant colonies. We have obtained the optimum traveling distance for three instances. Table 3 and Figure 7 present the experiments results (consider this instead- results of the experiment.) Alobaedy and Fazea Iraqi Journal of Science, 2022, Vol. 63, No. 9, pp: 4067-4078 8600 Table 3-Results of DMACO using eleven TSP datasets No Dataset Best Worst Mean SD Optimum 1 eil51 426 437 431.17 2.28 426 2 att48 33522 34063 33772.00 161.75 33522 3 eil76 538 552 547.37 2.81 538 4 st70 681 692 687.07 3.36 675 5 d198 15922 16100 16025.80 43.14 * 6 eil101 640 652 644.97 3.47 629 7 kroA100 21512 22124 21814.50 160.87 21282 8 rat99 1223 1259 1243.17 8.35 * 9 rat195 2047 2085 2068.63 9.40 * 10 rat783 10853 10950 10903.36 28.49 * 11 pcb442 52645 53321 53034.93 183.15 50778 *Not provided in the original dataset. Figure 7- DMACO using eleven TSP datasets The findings reveal that in three datasets, namely eil51, att48, and eil76, the Raspberry Pi cluster was able to reach the best answer. Despite the small number of optimal outcomes found in this study, the standard deviation values demonstrate that the worst values are near to the mean values, indicating that cluster performance is consistent across most datasets. The findings show that a single board computing device like the Raspberry Pi is a good alternative for a low-cost, small-scale cluster to handle optimization issues like TSP. 6. Limitations RPi cluster demonstrate very good performance in small and medium scale datasets. However, RPi cluster is not practical for large scale datasets due to the long processing time required to solve such problems. 7. Conclusion In this experiment, we have proved that a single board computer may be used as a processing unit in a computing cluster. Therefore, TSP datasets and the ACS technique were used to test the constructed cluster. We also demonstrated that each Raspberry Pi may be configured as a self-contained worker with master coordination. Experiments indicates that the Raspberry Pi cluster is appropriate for small and medium-sized challenges. We have also included the 0%20%40%60%80%100% eil51 att48 eil76 st70 d198 eil101 kroA100 rat99 rat195 rat783 pcb442 Datasets DMACO using eleven TSP datasets BestWorstMeanOptimum Alobaedy and Fazea Iraqi Journal of Science, 2022, Vol. 63, No. 9, pp: 4067-4078 8600 network topology, process flow, and implementation pseudocode. The Raspberry Pi cluster might be used for a variety of combinatorial optimization problems, allowing for future study and development. Acknowledgment The authors would like to thank the Computer Science Department, College of Science, University of Baghdad. References [1] B. Chandra Mohan and R. Baskaran, “A survey: Ant Colony Optimization based recent research and implementation on several engineering domain,” Expert Syst. Appl., vol. 39, no. 4, pp. 4618– 4627, 2012, doi: https://doi.org/10.1016/j.eswa.2011.09.076. [2] M. Dorigo and T. 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