Search results for "Shortest path problem"
showing 10 items of 32 documents
Optimal paths in weighted timed automata
2004
AbstractWe consider the optimal-reachability problem for a timed automaton with respect to a linear cost function which results in a weighted timed automaton. Our solution to this optimization problem consists of reducing it to computing (parametric) shortest paths in a finite weighted directed graph. We call this graph a parametric sub-region graph. It refines the region graph, a standard tool for the analysis of timed automata, by adding the information which is relevant to solving the optimal-reachability problem. We present an algorithm to solve the optimal-reachability problem for weighted timed automata that takes time exponential in O(n(|δ(A)|+|wmax|)), where n is the number of clock…
The Spanning Tree based Approach for Solving the Shortest Path Problem in Social Graphs
2016
Nowadays there are many social media sites with a very large number of users. Users of social media sites and relationships between them can be modelled as a graph. Such graphs can be analysed using methods from social network analysis (SNA). Many measures used in SNA rely on computation of shortest paths between nodes of a graph. There are many shortest path algorithms, but the majority of them suits only for small graphs, or work only with road network graphs that are fundamentally different from social graphs. This paper describes an efficient shortest path searching algorithm suitable for large social graphs. The described algorithm extends the Atlas algorithm. The proposed algorithm so…
Deviations in pedestrian itineraries in urban areas: a method to assess the role of environmental factors
2010
Walking has long been neglected in urban-mobility research, but it is now making its way into numerous studies using various approaches. Empirical data are often processed in well-known models of flow allocation to study the behaviour of pedestrians and to identify their preferences. However, these models assume that route choices are predetermined at the start of each trip and do not admit any possible intervening decision along these trips. We propose to overcome this limitation through a new method for the analysis of pedestrian behaviour. This method, which we call ‘deviation analysis’ consists of (1) identifying the intersections from which a pedestrian has chosen a route longer than …
MARL-Ped: A multi-agent reinforcement learning based framework to simulate pedestrian groups
2014
Abstract Pedestrian simulation is complex because there are different levels of behavior modeling. At the lowest level, local interactions between agents occur; at the middle level, strategic and tactical behaviors appear like overtakings or route choices; and at the highest level path-planning is necessary. The agent-based pedestrian simulators either focus on a specific level (mainly in the lower one) or define strategies like the layered architectures to independently manage the different behavioral levels. In our Multi-Agent Reinforcement-Learning-based Pedestrian simulation framework (MARL-Ped) the situation is addressed as a whole. Each embodied agent uses a model-free Reinforcement L…
Deep Q-Learning With Q-Matrix Transfer Learning for Novel Fire Evacuation Environment
2021
We focus on the important problem of emergency evacuation, which clearly could benefit from reinforcement learning that has been largely unaddressed. Emergency evacuation is a complex task which is difficult to solve with reinforcement learning, since an emergency situation is highly dynamic, with a lot of changing variables and complex constraints that makes it difficult to train on. In this paper, we propose the first fire evacuation environment to train reinforcement learning agents for evacuation planning. The environment is modelled as a graph capturing the building structure. It consists of realistic features like fire spread, uncertainty and bottlenecks. We have implemented the envir…
Finding k -dissimilar paths with minimum collective length
2018
Shortest path computation is a fundamental problem in road networks. However, in many real-world scenarios, determining solely the shortest path is not enough. In this paper, we study the problem of finding k-Dissimilar Paths with Minimum Collective Length (kDPwML), which aims at computing a set of paths from a source s to a target t such that all paths are pairwise dissimilar by at least \theta and the sum of the path lengths is minimal. We introduce an exact algorithm for the kDPwML problem, which iterates over all possible s-t paths while employing two pruning techniques to reduce the prohibitively expensive computational cost. To achieve scalability, we also define the much smaller set …
Online shortest paths with confidence intervals for routing in a time varying random network
2018
International audience; The increase in the world's population and rising standards of living is leading to an ever-increasing number of vehicles on the roads, and with it ever-increasing difficulties in traffic management. This traffic management in transport networks can be clearly optimized by using information and communication technologies referred as Intelligent Transport Systems (ITS). This management problem is usually reformulated as finding the shortest path in a time varying random graph. In this article, an online shortest path computation using stochastic gradient descent is proposed. This routing algorithm for ITS traffic management is based on the online Frank-Wolfe approach.…
Predicting Heuristic Search Performance with PageRank Centrality in Local Optima Networks
2015
Previous studies have used statistical analysis of fitness landscapes such as ruggedness and deceptiveness in order to predict the expected quality of heuristic search methods. Novel approaches for predicting the performance of heuristic search are based on the analysis of local optima networks (LONs). A LON is a compressed stochastic model of a fitness landscape's basin transitions. Recent literature has suggested using various LON network measurements as predictors for local search performance.In this study, we suggest PageRank centrality as a new measure for predicting the performance of heuristic search methods using local search. PageRank centrality is a variant of Eigenvector centrali…
The pruning-grafting lattice of binary trees
2008
AbstractWe introduce a new lattice structure Bn on binary trees of size n. We exhibit efficient algorithms for computing meet and join of two binary trees and give several properties of this lattice. More precisely, we prove that the length of a longest (resp. shortest) path between 0 and 1 in Bn equals to the Eulerian numbers 2n−(n+1) (resp. (n−1)2) and that the number of coverings is (2nn−1). Finally, we exhibit a matching in a constructive way. Then we propose some open problems about this new structure.
The shortest-path problem with resource constraints with -loop elimination and its application to the capacitated arc-routing problem
2014
Abstract In many branch-and-price algorithms, the column generation subproblem consists of computing feasible constrained paths. In the capacitated arc-routing problem (CARP), elementarity constraints concerning the edges to be serviced and additional constraints resulting from the branch-and-bound process together impose two types of loop-elimination constraints. To fulfill the former constraints, it is common practice to rely on a relaxation where loops are allowed. In a k-loop elimination approach all loops of length k and smaller are forbidden. Following Bode and Irnich (2012) for solving the CARP, branching on followers and non-followers is the only known approach to guarantee integer …