A minmax regret version of the time-dependent shortest path problem

2018 ◽  
Vol 270 (3) ◽  
pp. 968-981 ◽  
Author(s):  
Eduardo Conde ◽  
Marina Leal ◽  
Justo Puerto
Keyword(s):  
Shortest Path ◽  
Shortest Path Problem ◽  
Time Dependent ◽  
Minmax Regret

Dynamic Discretization Discovery Algorithms for Time-Dependent Shortest Path Problems

2021 ◽  
Author(s):  
Edward Yuhang He ◽  
Natashia Boland ◽  
George Nemhauser ◽  
Martin Savelsbergh
Keyword(s):  
Lower Bound ◽  
Travel Time ◽  
Shortest Path ◽  
Optimal Path ◽  
Upper Bounds ◽  
Shortest Path Problem ◽  
Time Dependent ◽  
Time Interval ◽  
Shortest Path Problems ◽  
Discovery Algorithms

Finding a shortest path in a network is a fundamental optimization problem. We focus on settings in which the travel time on an arc in the network depends on the time at which traversal of the arc begins. In such settings, reaching the destination as early as possible is not the only objective of interest. Minimizing the duration of the path, that is, the difference between the arrival time at the destination and the departure from the origin, and minimizing the travel time along the path from origin to destination, are also of interest. We introduce dynamic discretization discovery algorithms to efficiently solve such time-dependent shortest path problems with piecewise linear arc travel time functions. The algorithms operate on partially time-expanded networks in which arc costs represent lower bounds on the arc travel time over the subsequent time interval. A shortest path in this partially time-expanded network yields a lower bound on the value of an optimal path. Upper bounds are easily obtained as by-products of the lower bound calculations. The algorithms iteratively refine the discretization by exploiting breakpoints of the arc travel time functions. In addition to time discretization refinement, the algorithms permit time intervals to be eliminated, improving lower and upper bounds, until, in a finite number of iterations, optimality is proved. Computational experiments show that only a small fraction of breakpoints must be explored and that the fraction decreases as the length of the time horizon and the size of the network increases, making the algorithms highly efficient and scalable. Summary of Contribution: New data collection techniques have increased the availability and fidelity of time-dependent travel time information, making the time-dependent variant of the classic shortest path problem an extremely relevant problem in the field of operations research. This paper provides novel algorithms for the time-dependent shortest path problem with both the minimum duration and minimum travel time objectives, which aims to address the computational challenges faced by existing algorithms. A computational study shows that our new algorithm is indeed significantly more efficient than existing approaches.

scholarly journals The dynamic shortest path problem with time-dependent stochastic disruptions

2018 ◽  
Vol 92 ◽  
pp. 42-57 ◽  
Author(s):  
Derya Sever ◽  
Lei Zhao ◽  
Nico Dellaert ◽  
Emrah Demir ◽  
Tom Van Woensel ◽  
...  
Keyword(s):  
Shortest Path ◽  
Shortest Path Problem ◽  
Time Dependent

scholarly journals An evolutionary solution for multimodal shortest path problem in metropolises

2010 ◽  
Vol 7 (4) ◽  
pp. 789-811 ◽  
Author(s):  
Rahim Abbaspour ◽  
Farhad Samadzadegan
Keyword(s):  
Evolutionary Algorithm ◽  
Shortest Path ◽  
Urban Areas ◽  
Shortest Path Problem ◽  
Experimental Results ◽  
Time Dependent ◽  
Research Focus ◽  
Problem Of Time ◽  
Optimum Path

This paper addresses the problem of time-dependent shortest multimodal path in complex and large urban areas. This problem is one of the important and practical problems in several fields such as transportation, and recently attracts the research focus due to developments in new application areas. An adapted evolutionary algorithm, in which chromosomes with variable lengths and particularly defined evolutionary stages were used, was employed to solve the problem. The proposed solution was tested over the dataset of city of Tehran. The evaluation consists of computing shortest multimodal path between 250 randomly selected pairs of origins and destination points with different distances. It was assumed that three modes of walking, bus, and subway are used to travel between points. Moreover, some tests were conducted over the dataset to illustrate the robustness of method. The experimental results and related indices such as convergence plot show that the proposed algorithm can find optimum path according to applied constraints.

The Constrained Reliable Shortest Path Problem in Stochastic Time-Dependent Networks

2021 ◽  
Author(s):  
Matthias Ruß ◽  
Gunther Gust ◽  
Dirk Neumann
Keyword(s):  
Shortest Path ◽  
Shortest Paths ◽  
Shortest Path Problem ◽  
Time Dependent ◽  
Stochastic Time

Finding Shortest Paths That Are Reliable and Satisfy Constraints on Time-Dependent Weights

scholarly journals The ε-Approximation of the Time-Dependent Shortest Path Problem Solution for All Departure Times

2019 ◽  
Vol 8 (12) ◽  
pp. 538
Author(s):  
František Kolovský ◽  
Jan Ježek ◽  
Ivana Kolingerová
Keyword(s):  
Travel Time ◽  
Relative Error ◽  
Shortest Path ◽  
Main Idea ◽  
Shortest Path Problem ◽  
Time Dependent ◽  
Time Interval ◽  
Problem Solution ◽  
Maximum Relative Error ◽  
Time Analysis

In this paper, the shortest paths search for all departure times (profile search) are discussed. This problem is called a time-dependent shortest path problem (TDSP) and is suitable for time-dependent travel-time analysis. Particularly, this paper deals with the ε -approximation of profile search computation. The proposed algorithms are based on a label correcting modification of Dijkstra’s algorithm (LCA). The main idea of the algorithm is to simplify the arrival function after every relaxation step so that the maximum relative error is maintained. When the maximum relative error is 0.001, the proposed solution saves more than 97% of breakpoints and 80% of time compared to the exact version of LCA. Furthermore, the runtime can be improved by other 15% to 40% using heuristic splitting of the original departure time interval to several subintervals. The algorithms we developed can be used as a precomputation step in other routing algorithms or for some travel time analysis.

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