An efficient exact approach for the constrained shortest path tour problem

Ferone, Daniele; Festa, Paola; Guerriero, Francesca

doi:10.1080/10556788.2018.1548015

Cited by 23 publications

(4 citation statements)

References 18 publications

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“…Therefore, many approaches have been formed to find the best solution to solve the problem [16]. The TSP is a method that pays attention to the distance between cities (nodes) by passing and calculating the weight values between them and then looking for the distance or the smallest value [17], [18].…”

Section: Introductionmentioning

confidence: 99%

Design and Implementation of the Shortest Path Navigation in Samosir District using Branch and Bound Algorithm

Chandra,

Arifin Prasetyo

2024

J. RESTI (Rekayasa Sist. Teknol. Inf.)

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Samosir has a wide area and several tourist attractions, making it difficult for visitors to explore the island. Not knowing the route can make the journey less fun and waste time. In general, tourists seek to know the fastest path to a tourist location to save time and money while on vacation. As a result, we require an application that will offer directions to the shortest path. This research aims to develop a web-based application that may display a map of the shortest travel to a tourist site. This website will display a map that marks from the origin point to the destination point. The Branch and Bound algorithm is used to determine the shortest path. The Python libraries OSMnx, Folium, and NetworkX modify paths and show a route map with OpenStreetMap. The error value of the distance between the branch, bound algorithm, and Google Maps is used to get the RMSE accuracy value. The RMSE value is 3.02 and MAPE value is 0.0023 indicating that the application produced already has a good implementation prototype. Furthermore, there is no significant distinction between the appearance of maps implementing OpenStreetMap and Google Maps

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Section: Introductionmentioning

confidence: 99%

Design and Implementation of the Shortest Path Navigation in Samosir District using Branch and Bound Algorithm

Chandra,

Arifin Prasetyo

2024

J. RESTI (Rekayasa Sist. Teknol. Inf.)

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“…Traditional methods for the shortest pathfinding problem, such as Dijkstra's [12], Floyd-Warshall [13], and Bellman-Ford algorithms, deliver the optimal solution in a reasonable time but are not able to handle stochastic distance distributions and complex constraints. The exact mixed-integer linear or quadratic programming technique [14] can be an option in multiple cases because it supports the integration of constraints, but is sensitive to stochastic parameters and the size of the problem [15]. There are successful results in applying machine learning (ML) tools to improve the performance of branch & bound method by optimizing the plane cuts.…”

Section: Introductionmentioning

confidence: 99%

Generally Applicable Q-Table Compression Method and Its Application for Constrained Stochastic Graph Traversal Optimization Problems

Kegyes,

Kummer,

Süle

et al. 2024

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We analyzed a special class of graph traversal problems, where the distances are stochastic, and the agent is restricted to take a limited range in one go. We showed that both constrained shortest Hamiltonian pathfinding problems and disassembly line balancing problems belong to the class of constrained shortest pathfinding problems, which can be represented as mixed-integer optimization problems. Reinforcement learning (RL) methods have proven their efficiency in multiple complex problems. However, researchers concluded that the learning time increases radically by growing the state- and action spaces. In continuous cases, approximation techniques are used, but these methods have several limitations in mixed-integer searching spaces. We present the Q-table compression method as a multistep method with dimension reduction, state fusion, and space compression techniques that project a mixed-integer optimization problem into a discrete one. The RL agent is then trained using an extended Q-value-based method to deliver a human-interpretable model for optimal action selection. Our approach was tested in selected constrained stochastic graph traversal use cases, and comparative results are shown to the simple grid-based discretization method.

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“…The authors showed that the Hamiltonian Path Problem [3] can be polynomially reduced to the CSPTP and that the CSPTP belongs to the NP ‐hard class. The CSPTP was further studied in de Andrade and Saraiva [1] and Ferone et al [15]. These two works independently proposed two similar mathematical models for the problem.…”

Section: Introductionmentioning

confidence: 99%

The constrained forward shortest path tour problem: Mathematical modeling and GRASP approximate solutions

et al. 2020

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This paper deals with the Constrained Forward Shortest Path Tour Problem, an NP‐complete variant of the Forward Shortest Path Tour Problem. Given a directed weighted graph G = (V, A), where the set of nodes V is partitioned into clusters T1, …, TN, the aim is determining a shortest path between two given nodes, s and d, with the properties that clusters must be visited according to a given order, and each arc can be crossed at most once. We introduce a mathematical formulation of the problem, and a reduction procedure to reduce the number of variables involved in the model. Furthermore, we propose a Greedy Randomized Adaptive Search Procedure (GRASP) algorithm to solve large instances of the problem. Computational tests show that the reduction procedure is very effective and its application significantly speeds up the resolution of the model. Moreover, the computational results certify the effectiveness of GRASP that often finds the optimal solution and, in general, provides quickly high‐quality sub‐optimal solutions.

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An efficient exact approach for the constrained shortest path tour problem

Cited by 23 publications

References 18 publications

Design and Implementation of the Shortest Path Navigation in Samosir District using Branch and Bound Algorithm

Design and Implementation of the Shortest Path Navigation in Samosir District using Branch and Bound Algorithm

Generally Applicable Q-Table Compression Method and Its Application for Constrained Stochastic Graph Traversal Optimization Problems

The constrained forward shortest path tour problem: Mathematical modeling and GRASP approximate solutions

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