Finding the K shortest hyperpaths

Nielsen, Lars Relund; Andersen, Kim Allan; Pretolani, Daniele

doi:10.1016/j.cor.2003.11.014

Cited by 52 publications

(53 citation statements)

References 19 publications

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“…Hence using recent efficient algorithms for finding the K shortest hyperpaths, Nielsen et al [21,24], we have that the K best policies can be found in O (M K) time.…”

Section: Discussionmentioning

confidence: 99%

“…The algorithm from Nielsen et al [24] findπ using procedure SHTacyclic each time a pair is selected form the candidate set. Moreover, in the branching operation, each hyperpathπ i is found using procedure SHTacyclic on subhypergraphH i .…”

Section: Shtacyclic(o H)mentioning

confidence: 99%

“…Recently, a general algorithm for finding the K minimum weight hyperpaths has been presented in Nielsen, Andersen, and Pretolani [24] and in Nielsen, Pretolani, and Andersen [21] the complexity of the algorithm is lowered. Algorithms for ranking solutions are useful 1 Dynamic programming and Markov processes since practical problems often include constraints which are hard to specify formally or hard to optimize.…”

Section: Introductionmentioning

confidence: 99%

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Finding the K best policies in a finite-horizon Markov decision process

Nielsen¹,

Kristensen²

2006

European Journal of Operational Research

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Directed hypergraphs represent a general modelling and algorithmic tool, which have been successfully used in many different research areas such as artificial intelligence, database systems, fuzzy systems, propositional logic and transportation networks. However, modelling Markov decision processes using directed hypergraphs has not yet been considered.In this paper we consider finite-horizon Markov decision processes (MDPs) with finite state and action space and present an algorithm for finding the K best deterministic Markov policies. That is, we are interested in ranking the first K deterministic Markov policies in non-decreasing order using an additive criterion of optimality. The algorithm uses a directed hypergraph to model the finite-horizon MDP. It is shown that the problem of finding the optimal policy can be formulated as a minimum weight hyperpath problem and be solved in linear time, with respect to the input data representing the MDP, using different additive optimality criteria.

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“…Hence using recent efficient algorithms for finding the K shortest hyperpaths, Nielsen et al [21,24], we have that the K best policies can be found in O (M K) time.…”

Section: Discussionmentioning

confidence: 99%

Section: Shtacyclic(o H)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Finding the K best policies in a finite-horizon Markov decision process

Nielsen¹,

Kristensen²

2006

European Journal of Operational Research

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“…Extensions have since been studied, including k-shortest hyperpaths (4,5) and the one-to-one hyperpath (6). For a transit schedule-based network (7-13), Nguyen et al proposed a hyperpath that uses the logit model (14), extending the hyperpath concept beyond the traditional application to frequency-based transit assignment.…”

Section: Hyperpaths In Network Based On Transit Schedulesmentioning

confidence: 99%

Hyperpaths in Network Based on Transit Schedules

Noh

Hickman

Khani

2012

Transportation Research Record: Journal of the Transportation R

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with a link-to-link connector that captures both the feasibility and the cost of making a connection between the scheduled links. In this way, separate links for boarding and alighting behavior are not necessary (as might be needed in a node-based representation). Instead, the hyperlink includes the cost for each transfer between two consecutive links and can have a separate cost for each transfer movement, which differs from when a hyperlink cost is on the existing hyperpath.A transit schedule network represented in a link-based scheme gives the same result as node-based models. Each scheduled vehicle trip between two consecutive stops is represented as a single transit schedule link, with a route and a mode. This is called a link-based time-expanded (LBTE) network. Because a basic search unit is along a link and in the link-to-link connections, it is not necessary to expand a physical stop to multiple stops, representing the same stop at different points in time [a diachronic graph (8)]. Thus for network representation, the benefit of the LBTE is twofold: passenger boarding and alighting behavior is represented on a hyperlink, instead of through separate boarding and alighting hyperlinks, and the network size is much smaller than a node-based time-expanded transit schedule network.Because of its efficiency in network representation and its flexibility in representing transit passenger behavior, a logit-based hyperpath choice model is proposed for use on an LBTE transit schedule network. It is assumed that passengers have a preferred arrival time (PAT) at the destination, and thus a backward hyperpath search model is introduced. Because of different perceptions of the generalized cost of travel for each passenger, each hyperlink is managed by a logit-type function for the choice set of schedule alternatives. The proposed hyperpath search model is expected to give more strategic alternatives for passengers on the transit schedule network.This study defines the link-based hyperlink, its cost, and the resulting hyperpath structure. An LBTE transit schedule network compatible with this definition is proposed, along with a weighting function for both deterministic and stochastic assignment cases. A label-correcting algorithm is provided to solve for the bounded optimal assignment. These algorithms were applied to a transit test network. REPRESENTATION OF NETWORK FOR LINK-BASED HYPERPATH DefinitionsGallo et al. define a hyperlink by using e = [t(e), h(e)], where t(e) is the tail node subset of hyperlink e and h(e) is the head node subset of hyperlink e (15). Each hyperlink is represented in the form (node-link-node). Instead, this paper introduces a (link-to-link) Hyperpaths in Network Based on Transit SchedulesHyunsoo Noh, Mark Hickman, and Alireza Khani The use of hyperpaths in public transportation was conceptualized by Nguyen et al. (1), Nguyen and Pallottino (2), and Spiess and Florian (3). Extensions have since been studied, including k-shortest hyperpaths (4, 5) and the one-to-one hyperpath (6). For a transit ...

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“…Directed hypergraphs represent a general modeling and algorithmic tool, which has been used in many different research areas such as artificial intelligence, database systems, fuzzy systems, propositional logic, and transportation networks [8,25,27]. For a general overview on directed hypergraphs see [1].…”

Section: Illustrating An Mdp Using a Directed Hypergraphmentioning

confidence: 99%

Embedding a state space model into a Markov decision process

2010

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In agriculture Markov decision processes (MDPs) with finite state and action space are often used to model sequential decision making over time. For instance, states in the process represent possible levels of traits of the animal and transition probabilities are based on biological models estimated from data collected from the animal or herd.State space models (SSMs) are a general tool for modeling repeated measurements over time where the model parameters can evolve dynamically.In this paper we consider methods for embedding an SSM into an MDP with finite state and action space. Different ways of discretizing an SSM are discussed and methods for reducing the state space of the MDP are presented. An example from dairy production is given.

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Finding the K shortest hyperpaths

Cited by 52 publications

References 19 publications

Finding the K best policies in a finite-horizon Markov decision process

Finding the K best policies in a finite-horizon Markov decision process

Hyperpaths in Network Based on Transit Schedules

Embedding a state space model into a Markov decision process

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