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Traveling Salesman Problem (TSP) is a basic and one of the most important transportation problems in operational logistics. It is also known in the literature as a Chinese postman problem or single vehicle routing problem. TSP can be shortly described as follows. Vehicle starting from the selected city must visit a set of another cities exactly onc...
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... of connections between all graph's vertices and it is called Hamiltonian cycle in graph theory. Therefore, we can say that TSP route is feasible, if it is a Hamiltonian cycle (see Fig. 1). On the figure below there are shown all possible graph's edges for 8 nodes (includ- ing starting point P 0 ) -solid and dotted lines. On the next figure (see Fig. 2) there is shown infeasible TSP route -solid line. Vehicle starting route from point P 0 is visiting points: P 1 , P 5 , P 6 , P 7 (or: P 7 , P 6 , P 5 , P 1 ) and returns to point: P 0 . Nodes P 2 , P 3 , P 4 have been omitted. It means, that these points would have to be visited after restarting the route from point P 0 . This case ...
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... Ant colony algorithms, like most swarm intelligence algorithms, are based on the use of a population of potential solutions and are designed to solve complex combinatorial optimization problems, primarily finding the shortest path on graphs. Ant colony algorithms are used to solve problems of the TSP (Traveling Salesman Problem) [32] and QAP (Quadratic Assignment Problem) [33]. Quite a large number of different practical problems are reduced to these types of problems. ...
The article proposes on the information technology for determining vehicle route based on ant colony algorithms. The analysis of specialized software and information technologies for determining vehicle route was carried out. Existing information technologies for determining the route of vehicles are not able to find an accurate solution or require an unreasonably long time to find effective solutions. The relevance of the article is due to the great complexity and dimension of routing problems, as well as the emergence of its new verifications. In this regard, there is a need to develop new information technologies for solving problems of this class. The proposed information technology is based on ant colony algorithms. This information technology allows to reduce the time of searching for solutions in problems of large dimensions, and at the same time improve the quality of the solutions obtained. Information technology for determining the route of the vehicle will be considered in the form of a set of functions. This set of functions are related to each other in a certain way. This set of functions implement techniques, methods and methods that ensure the receipt, storage, processing, transmission and use of information regarding the route of the vehicle. In the paper, we will use the IDEF0. This is required for visualization and further formal representation of the structure and composition of the information technology for determining the route of the vehicle. We will present the Determining Route Information Technology in its entirety: the tuple and the sets. The top-level context diagram and. the upper child diagram top-level context diagram are presented. When determining the route of the vehicle, we will use ant algorithms. The main modifications of the classic ant colony algorithm are presented: Max-Min Ant System, Elitist Ant System, Q-ant system, Rank ant system, Ant Colony System, Fast Ant System, Antabu
... Der in [3] vorgestellte Ansatz modelliert neben der Hochspannungs-auch die Mittel-und Niederspannungsebene. Anhand realer Positionsdaten von Umspannwerken aus OSM werden Voronoi-Zellen gebildet, im Folgenden Mittelspannungsregionen genannt, die eindeutige geografische Flächen für jeweils ein Mittelspannungsnetz darstellen [7]. Anhand der in der Niederspannungsnetzgenerierung modellierten Ortsnetzstationen, der Straßeninfrastruktur und der Landnutzungsregionen aus OSM werden unter Anwendung des k-Means-Algorithmus [8], eines Verfahrens zur Lösung des Problem des Handlungsreisenden [9] und des Dijkstra-Algorithmus [10] Mittelspannungsnetze mit offener Ringstruktur gebildet. Für die Generierung von Niederspannungsnetzen werden zusätzlich Gebäudedaten aus OSM geladen und die Hausanschlüsse und Hausanschlussleitungen über die Distanz der Straßen zum Gebäudemittelpunkt berechnet. ...
... Für alle Ortsnetzstationen eines Clusters wird die Luftlinien-Distanz zum Umspannwerk berechnet und die zwei Ortsnetzstationen mit den geringsten Distanzen als Start-und End-Ortsnetzstation eines Ringes ausgewählt. Mit einem genetischen Algorithmus zur Lösung des Problems des Handlungsreisenden wird die Reihenfolge der Ortsnetzstationen in einem Ring mit den festgelegten Start-und Endortsnetzstationen initiiert [9]. Auftretende Überschneidungen einzelner Verbindungen werden über lokale Suchverfahren und Optimierungsverfahren aufgehoben [2], [13]. ...
Der stetige Zubau an dezentralen Erzeugungsanlagen, sowie die zunehmende Sektorenkopplung im Mobilitäts-und Wärmebereich, können zu zusätzlichen Belastungen für die Stromnetze führen. Die bei der Integration in das Verteilnetz entstehenden Herausforderungen werden bereits in zahlreichen Forschungsprojekten und Studien untersucht und Lösungsansätze in die Praxis überführt. Die Untersuchung dieser Herausforderungen erfordert dabei die Kenntnis über vorhandene Verteilnetzstrukturen, Erzeuger und Lasten. Für regionsabhängige Energiesystemanalysen können reale Netzmodelle von Verteilnetzbetreibern verwendet werden, die jedoch aufgrund von Datenschutzgründen nicht ohne Weiteres herausgegeben bzw. veröffentlicht werden. Eine weitere Möglichkeit ist die Nutzung von Referenznetzen [1], die eine Verallgemeinerung realer Stromnetze darstellen und sich somit nur bedingt für regionsabhängige Energiesystemanalysen eignen. Um das Problem fehlender Netz-, Last-und Erzeugungsdaten zu umgehen, wurden in den letzten Jahren Methodiken veröffentlicht, bei denen Verteilnetze auf Basis öffentlich verfügbarer Daten anhand geltender Richtlinien und Normen modelliert werden [2], [3]. Die recherchierten Ansätze beruhen jedoch auf verschiedenen Annahmen und betrachten die einzelnen Netzebenen in unterschiedlicher Detailtiefe. In diesem Paper wird daher ein Ansatz zur Modellierung regionaler Verteilnetzstrukturen auf Nieder-und Mittelspannungsebene mit Erzeugern und Lasten auf Basis öffentlich verfügbarer Daten vorgestellt, der auf den recherchierten Ansätzen aufbaut, diese kombiniert und um verschiedene Funktionen erweitert. Anhand der generierten Verteilnetze sollen zukünftig forschungsabhängige Fragestellungen beantwortet werden, wie z. B. die Untersuchung der Integration von elektrischen Landmaschinen im Forschungsprojekt Energy-4-Agri oder netzdienlicher Flexibilitäten im Forschungsprojekt flexess.
... Transporation is needed to guarantee the mobility of people and goods and as part of the economic system, transportation has an important function in national development [3]. The concept of TSP is described as follows: a salesman or a vehicle has a number of cities to visit with a distance of time between two cities and each city is visited only once (Hamiltonian cycle) and returns to the starting city then the total distance or time is minimized [4,5,6]. Distance is a key factor in transportation. ...
The subject of this research is distance and time of several city tour problems which known as traveling salesman problem (tsp). The goal is to find out the gaps of distance and time between two types of optimization methods in traveling salesman problem: exact and approximate. Exact method yields optimal solution but spends more time when the number of cities is increasing and approximate method yields near optimal solution even optimal but spends less time than exact methods. The task in this study is to identify and formulate each algorithm for each method, then to run each algorithm with the same input and to get the research output: total distance, and the last to compare both methods: advantage and limitation. Methods used are Brute Force (BF) and Branch and Bound (B&B) algorithms which are categorized as exact methods are compared with Artificial Bee Colony (ABC), Tabu Search (TS) and Simulated Annealing (SA) algorithms which are categorized as approximate methods or known as a heuristics method. These three approximate methods are chosen because they are effective algorithms, easy to implement and provide good solutions for combinatorial optimization problems. Exact and approximate algorithms are tested in several sizes of city tour problems: 6, 9, 10, 16, 17, 25, 42, and 58 cities. 17, 42 and 58 cities are derived from tsplib: a library of sample instances for tsp; and others are taken from big cities in Java (West, Central, East) island. All of the algorithms are run by MATLAB program. The results show that exact method is better in time performance for problem size less than 25 cities and both exact and approximate methods yield optimal solution. For problem sizes that have more than 25 cities, approximate method-Artificial Bee Colony (ABC) yields better time which is approximately 37% less than exact and deviates 0.0197% for distance from exact method. The conclusion is to apply exact method for problem size that is less than 25 cities and approximate method for problem size that is more than 25 cities. The gap of time will be increasing between two methods when sample size becomes larger.
... Mathematical programming of the TSP, first proposed by Dantzig in 1959 (Radoslaw, 2014), has attracted many scholars. In the initial period, people relied on precise algorithms to solve this problem, including the branch and bound algorithm, which controls the search process by constraining the boundaries; the linear programming algorithm, which seeks the cutting plane to converge to the optimal solution; and the dynamic programming algorithm, which is based on dynamic programming equations (Liang, 2000). ...
... Mathematical programming of the TSP, first proposed by Dantzig in 1959 (Radoslaw, 2014), has attracted many scholars. In the initial period, people relied on precise algorithms to solve this problem, including the branch and bound algorithm, which controls the search process by constraining the boundaries; the linear programming algorithm, which seeks the cutting plane to converge to the optimal solution; and the dynamic programming algorithm, which is based on dynamic programming equations (Liang, 2000). ...
... Moreover, to confirm that the solution obtained by solving the models proposed in this study is truly optimal and unaffected by any mistake in the solver package or programming code, several optimization studies employing the brute-force search method [18][19][20][21] were used as a baseline. The brute-force search method enumerates all possible candidate solutions and then checks whether each candidate satisfies the problem statement. ...
Develop a new optimization algorithm inspired by nature that can solve optimization problems in engineering, economics, research, etc. Metaheuristic algorithms are very useful to solve problems that are difficult to model mathematically, with many variables, complex interactions and many local optima, this type of algorithms work by iteratively searching for solutions in a large space of solutions, using heuristic rules to guide the search unlike exact methods, metaheuristic algorithms do not guarantee that the optimal solution is found, but if they are usually more efficient and scalable than exact methods.
У статті увага приділяється питанням транспортної логістики, а саме визначенню маршруту руху транспортних засобів при наявності заборонених зон (обмежень та ризиків). Метою статті є розробка методу визначення маршруту руху транспортних засобів при наявності заборонених зон. Проаналізовано види задач транспортної логістики та математичні методи їх вирішення. Запропоновано задачу визначення маршруту руху транспортних засобів розглядати в області теорії графів за допомогою алгоритмів ройового інтелекту. Обрано модифікований алгоритм мурашиної колонії. Результати роботи запропонованого методу протестовано та представлено на тестовому прикладі та на реальній мапі.
