Toll Pricing and Heterogeneous Users

2005 ◽  
Vol 1923 (1) ◽  
pp. 28-36 ◽  
Author(s):  
Hani S. Mahmassani ◽  
Xuesong Zhou ◽  
Chung-Cheng Lu
Keyword(s):  
Shortest Path ◽  
Large Scale ◽  
Approximation Error ◽  
Computation Time ◽  
Time Dependent ◽  
Approximation Schemes ◽  
Value Of Time ◽  
Solution Quality ◽  
Shortest Path Problems ◽  
Toll Pricing

This paper presents both exact and approximation algorithms for finding extreme efficient time-dependent shortest paths for use with dynamic traffic assignment applications to networks with variable toll pricing and heterogeneous users (with different value of time preferences). A parametric least-generalized cost path algorithm is presented to determine a complete set of extreme efficient time-dependent paths that simultaneously consider travel time and cost criteria. However, exact procedures may not be practical for large networks. For this reason, approximation schemes are devised and tested. Based on the concept of ε-efficiency in multiobjective shortest path problems, a binary search framework is developed to find a set of extreme efficient paths that minimize expected approximation error, with the use of the underlying value of time distribution. Both exact and approximation schemes (along with variants) are tested on three actual traffic networks. The experimental results indicate that the computation time and the size of the solution set are jointly determined by several key parameters such as the number of time intervals and the number of nodes in the network. The results also suggest that the proposed approximation scheme is computationally efficient for large-scale bi-objective time-dependent shortest path applications while maintaining satisfactory solution quality.

scholarly journals A Fissile Ripple Spreading Algorithm to Solve Time-Dependent Vehicle Routing Problem via Coevolutionary Path Optimization

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Wen Xu ◽  
JiaJun Li
Keyword(s):  
Vehicle Routing ◽  
Shortest Path ◽  
Traffic Congestion ◽  
Path Optimization ◽  
Time Dependent ◽  
Optimization Approach ◽  
Routing Problem ◽  
Shortest Path Problems ◽  
Travelling Time ◽  
Logistics Delivery

The time-dependent vehicle routing problems have lately received great attention for logistics companies due to their crucial roles in reducing the time and economic costs, as well as fuel consumption and carbon emissions. However, the dynamic routing environment and traffic congestions have made it challenging to make the actual travelling trajectory optimal during the delivery process. To overcome this challenge, this study proposed an unconventional path optimization approach, fissile ripple spreading algorithm (FRSA), which is based on the advanced structure of coevolutionary path optimization (CEPO). The objective of the proposed model is to minimize the travelling time and path length of the vehicle, which are the popular indicators in path optimization. Some significant factors usually ignored in other research are considered in this study, such as congestion evolution, routing environment dynamics, signal control, and the complicated correlation between delivery sequence and the shortest path. The effectiveness of the proposed approach was demonstrated well in two sets of simulated experiments. The results prove that the proposed FRSA can scientifically find out the optimal delivery trajectory in a single run via global research, effectively avoid traffic congestion, and decrease the total delivery costs. This finding paves a new way to explore a promising methodology for addressing the delivery sequence and the shortest path problems at the same time. This study can provide theoretical support for the practical application in logistics delivery.

scholarly journals Space-time clustering-based method to optimize shareability in real-time ride-sharing

PLoS ONE ◽  
2022 ◽  
Vol 17 (1) ◽  
pp. e0262499
Author(s):  
Negin Alisoltani ◽  
Mostafa Ameli ◽  
Mahdi Zargayouna ◽  
Ludovic Leclercq
Keyword(s):  
Real Time ◽  
Large Scale ◽  
Computation Time ◽  
Clustering Method ◽  
Matching Problem ◽  
Solution Quality ◽  
Mobility Service ◽  
Ride Sharing ◽  
Large Scale Problems ◽  
Spatio Temporal

Real-time ride-sharing has become popular in recent years. However, the underlying optimization problem for this service is highly complex. One of the most critical challenges when solving the problem is solution quality and computation time, especially in large-scale problems where the number of received requests is huge. In this paper, we rely on an exact solving method to ensure the quality of the solution, while using AI-based techniques to limit the number of requests that we feed to the solver. More precisely, we propose a clustering method based on a new shareability function to put the most shareable trips inside separate clusters. Previous studies only consider Spatio-temporal dependencies to do clustering on the mobility service requests, which is not efficient in finding the shareable trips. Here, we define the shareability function to consider all the different sharing states for each pair of trips. Each cluster is then managed with a proposed heuristic framework in order to solve the matching problem inside each cluster. As the method favors sharing, we present the number of sharing constraints to allow the service to choose the number of shared trips. To validate our proposal, we employ the proposed method on the network of Lyon city in France, with half-million requests in the morning peak from 6 to 10 AM. The results demonstrate that the algorithm can provide high-quality solutions in a short time for large-scale problems. The proposed clustering method can also be used for different mobility service problems such as car-sharing, bike-sharing, etc.

scholarly journals A Multilevel Simplification Algorithm for Computing the Average Shortest-Path Length of Scale-Free Complex Network

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Guoyong Mao ◽  
Ning Zhang
Keyword(s):  
Complex Network ◽  
Shortest Path ◽  
Path Length ◽  
Large Scale ◽  
Computation Time ◽  
Scale Free Network ◽  
Original Network ◽  
Memory Space ◽  
Scale Free ◽  
Free Network

Computing the average shortest-path length (ASPL) of a large scale-free network needs much memory space and computation time. Based on the feature of scale-free network, we present a simplification algorithm by cutting the suspension points and the connected edges; the ASPL of the original network can be computed through that of the simplified network. We also present a multilevel simplification algorithm to get ASPL of the original network directly from that of the multisimplified network. Our experiment shows that these algorithms require less memory space and time in computing the ASPL of scale-free network, which makes it possible to analyze large networks that were previously impossible due to memory limitations.

scholarly journals Parallel Implementation of Non-slicing Floorplans with MPI and OpenMP

2021 ◽  
Author(s):  
Oluvaseun Owojaiye
Keyword(s):  
Message Passing ◽  
Large Scale ◽  
Message Passing Interface ◽  
Parallel Implementation ◽  
Computation Time ◽  
Sequential Algorithm ◽  
Design Stage ◽  
Single Chip ◽  
Solution Quality ◽  
Early Design Stage

Advancement in technology has brought considerable improvement to processor design and now manufacturers design multiple processors on a single chip. Supercomputers today consists of cluster of interconnected nodes that collaborate together to solve complex and advanced computation problems. Message Passing Interface and Open Multiprocessing are the popularly used programming models to optimize sequential codes by parallelizing them on the different multiprocessor architecture that exist today. In this thesis, we parallelize the non-slicing floorplan algorithm based on Multilevel Floorplanning/placement of large scale modules using B*tree (MB*tree) with MPI and OpenMP on distributed and shared memory architectures respectively. In VLSI (Very Large Scale Integration) design automation, floorplanning is an initial and vital task performed in the early design stage. Experimental results using MCNC benchmark circuits show that our parallel algorithm produced better results than the corresponding sequential algorithm; we were able to speed up the algorithm up to 4 times, hence reducing computation time and maintaining floorplan solution quality. On the other hand, we compared both parallel versions; and the OpenMP results gave slightly better than the corresponding MPI results.

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 Microcomputer-based algorithms for large scale shortest path problems

1986 ◽  
Vol 13 (2-3) ◽  
pp. 183-206 ◽  
Author(s):  
Darwin D. Klingman ◽  
Robert F. Schneider
Keyword(s):  
Shortest Path ◽  
Large Scale ◽  
Shortest Path Problems

scholarly journals Quality-Oriented Study on Mapping Island Model Genetic Algorithm onto CUDA GPU

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 318 ◽  
Author(s):  
Xue Sun ◽  
Ping Chou ◽  
Chao-Chin Wu ◽  
Liang-Rui Chen
Keyword(s):  
Genetic Algorithm ◽  
Execution Time ◽  
Large Scale ◽  
Parallel Architecture ◽  
Computation Time ◽  
Search Space ◽  
Island Model ◽  
Process Unit ◽  
Np Hard ◽  
Solution Quality

Genetic algorithm (GA), a global search method, has widespread applications in various fields. One very promising variant model of GA is the island model GA (IMGA) that introduces the key idea of migration to explore a wider search space. Migration will exchange chromosomes between islands, resulting in better-quality solutions. However, IMGA takes a long time to solve the large-scale NP-hard problems. In order to shorten the computation time, modern graphic process unit (GPU), as highly-parallel architecture, has been widely adopted in order to accelerate the execution of NP-hard algorithms. However, most previous studies on GPUs are focused on performance only, because the found solution qualities of the CPU and the GPU implementation of the same method are exactly the same. Therefore, it is usually previous work that did not report on quality. In this paper, we investigate how to find a better solution within a reasonable time when parallelizing IMGA on GPU, and we take the UA-FLP as a study example. Firstly, we propose an efficient approach of parallel tournament selection operator on GPU to achieve a better solution quality in a shorter amount of time. Secondly, we focus on how to tune three important parameters of IMGA to obtain a better solution efficiently, including the number of islands, the number of generations, and the number of chromosomes. In particular, different parameters have a different impact on solution quality improvement and execution time increment. We address the challenge of how to trade off between solution quality and execution time for these parameters. Finally, experiments and statistics are conducted to help researchers set parameters more efficiently to obtain better solutions when GPUs are used to accelerate IMGA. It has been observed that the order of influence on solution quality is: The number of chromosomes, the number of generations, and the number of islands, which can guide users to obtain better solutions efficiently with moderate increment of execution time. Furthermore, if we give higher priority on reducing execution time on GPU, the quality of the best solution can be improved by about 3%, with an acceleration that is 29 times faster than the CPU counterpart, after applying our suggested parameter settings. However, if we give solution quality a higher priority, i.e., the GPU execution time is close to the CPU’s, the solution quality can be improved up to 8%.

Reliable Shortest Path Problems in Stochastic Time-Dependent Networks

2013 ◽  
Vol 18 (2) ◽  
pp. 177-189 ◽  
Author(s):  
Bi Yu Chen ◽  
William H. K. Lam ◽  
Agachai Sumalee ◽  
Qingquan Li ◽  
Mei Lam Tam
Keyword(s):  
Shortest Path ◽  
Time Dependent ◽  
Shortest Path Problems ◽  
Stochastic Time

Time-Dependent Shortest Path Problems with Penalties and Limits on Waiting

2020 ◽  
Author(s):  
Edward He ◽  
Natashia Boland ◽  
George Nemhauser ◽  
Martin Savelsbergh
Keyword(s):  
Computational Complexity ◽  
Polynomial Time ◽  
Shortest Path ◽  
Complexity Analysis ◽  
Fundamental Problem ◽  
Algorithm Design ◽  
Weather Conditions ◽  
Time Dependent ◽  
Shortest Path Problems ◽  
The Right

Waiting at the right location at the right time can be critically important in certain variants of time-dependent shortest path problems. We investigate the computational complexity of time-dependent shortest path problems in which there is either a penalty on waiting or a limit on the total time spent waiting at a given subset of the nodes. We show that some cases are nondeterministic polynomial-time hard, and others can be solved in polynomial time, depending on the choice of the subset of nodes, on whether waiting is penalized or constrained, and on the magnitude of the penalty/waiting limit parameter. Summary of Contributions: This paper addresses simple yet relevant extensions of a fundamental problem in Operations Research: the Shortest Path Problem (SPP). It considers time-dependent variants of SPP, which can account for changing traffic and/or weather conditions. The first variant that is tackled allows for waiting at certain nodes but at a cost. The second variant instead places a limit on the total waiting. Both variants have applications in transportation, e.g., when it is possible to wait at certain locations if the benefits outweigh the costs. The paper investigates these problems using complexity analysis and algorithm design, both tools from the field of computing. Different cases are considered depending on which of the nodes contribute to the waiting cost or waiting limit (all nodes, all nodes except the origin, a subset of nodes…). The computational complexity of all cases is determined, providing complexity proofs for the variants that are NP-Hard and polynomial time algorithms for the variants that are in P.

scholarly journals Shortest-Path Optimization of Ship Diesel Engine Disassembly and Assembly Based on AND/OR Network

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Deng-Zhi Chen ◽  
Chen Wei ◽  
Guo-Ling Jia ◽  
Zhi-Hua Hu
Keyword(s):  
Diesel Engine ◽  
Shortest Path ◽  
Large Scale ◽  
Random Search ◽  
Computing Time ◽  
Graph Model ◽  
Mixed Integer ◽  
Mixed Integer Linear Program ◽  
Optimal Sequence ◽  
Solution Quality

Ship diesel engine disassembly and assembly (SDEDA) is essential for ship inspection and maintenance and navigation safety. The SDEDA consists of various machinery parts and operations. It is crucial to develop a system of SDEDA operations to improve the efficiency of disassembly and assembly (D&A). Considering the “AND” and “OR” relations (modeled as links) among the D&A operations (modeled as nodes), an “AND/OR” network is developed to extend a specialized graph model for the D&A sequencing problem in the context of education and training. Then, we devised a mixed-integer linear program (MILP) to optimize the SDEDA sequence based on the AND/OR network. Considering the flow balance in the AND/OR network, we developed exact algorithms and random search algorithms using breadth-first, branch cut and depth-first strategies to minimize the cost of the shortest path that represents an optimal sequence of D&A operations. To the best of our knowledge, it is the first try to formulate the D&A operations by an extended network model. Numerical experiments show that the proposed algorithms are practical for solving large-scale instances with more than 2000 D&A operations. The breadth-first shortest-path algorithm outperforms the MILP solver from the perspective of solution quality and computing time, and all developed algorithms are competitive in terms of computing time.

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