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Finding the k shortest hyperpaths
"... The K shortest paths problem has been extensively studied for many years. Efficient methods have been devised, and many practical applications are known. Shortest hyperpath models have been proposed for several problems in different areas, for example in relation with routing in dynamic networks. Ho ..."
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Cited by 19 (3 self)
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The K shortest paths problem has been extensively studied for many years. Efficient methods have been devised, and many practical applications are known. Shortest hyperpath models have been proposed for several problems in different areas, for example in relation with routing in dynamic networks. However, the K shortest hyperpaths problem has not yet been investigated. In this paper we present procedures for finding the K shortest hyperpaths in a directed hypergraph. This is done by extending existing algorithms for K shortest loopless paths. Computational experiments on the proposed procedures are performed, and applications in transportation, planning and combinatorial optimization are discussed.
Finding the K best policies in finitehorizon Markov decision processes. Submitted
, 2004
"... 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 ..."
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Cited by 3 (2 self)
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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 finitehorizon Markov decision processes (MDPs) with finite state and action space and present an algorithm for finding the K best policies. That is, we are interested in ranking the first K policies in nondecreasing order using an additive criterion of optimality. The algorithm uses a directed hypergraph to model the finitehorizon 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.
Embedding a State Space Model Into a Markov Decision Process
, 2009
"... 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 ..."
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Cited by 2 (1 self)
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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.
Finding the K best policies in a finitehorizon Markov decision process
, 2005
"... 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 ..."
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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 finitehorizon 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 nondecreasing order using an additive criterion of optimality. The algorithm uses a directed hypergraph to model the finitehorizon 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. Keywords: Finitehorizon Markov decision processes, stochastic dynamic programming, directed hypergraphs, hyperpaths, K best policies. 1
Timeadaptive and historyadaptive multicriterion routing in stochas tic, timedependent
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Bicriterion shortest paths in stochastic timedependent networks
"... In recent years there has been a growing interest in using stochastic timedependent (STD) networks as a modelling tool for a number of applications within such areas as transportation and telecommunications. It is known that an optimal routing policy does not necessarily correspond to a path, but ..."
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In recent years there has been a growing interest in using stochastic timedependent (STD) networks as a modelling tool for a number of applications within such areas as transportation and telecommunications. It is known that an optimal routing policy does not necessarily correspond to a path, but rather to a timeadaptive strategy. In some applications, however, it makes good sense to require that the routing policy should correspond to a loopless path in the network, that is, the timeadaptive aspect disappears and a priori route choice is considered. In this paper we consider bicriterion a priori route choice in STD networks, i.e. the problem of finding the set of efficient paths. Both expectation and minmax criteria are considered and a solution method based on the twophase method is devised. Experimental results reveal that the full set of efficient solutions can be determined on rather large test instances, which is in contrast to the timeadaptive case.
Research Unit of Statistics and Decision Analysis
, 2005
"... We present some reoptimization techniques for computing (shortest) hyperpath weights in a directed hypergraph. These techniques are exploited to improve the worstcase computational complexity (as well as the practical performance) of an algorithm finding the K shortest hyperpaths in acyclic hypergr ..."
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We present some reoptimization techniques for computing (shortest) hyperpath weights in a directed hypergraph. These techniques are exploited to improve the worstcase computational complexity (as well as the practical performance) of an algorithm finding the K shortest hyperpaths in acyclic hypergraphs. Keywords: Network programming, Directed hypergraphs, K shortest hyperpaths, Reoptimization. 1
unknown title
, 2005
"... Finding the K best policies in a finitehorizon Markov decision process ..."
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unknown title
"... Abstract—Many exist studies always use Markov decision processes (MDPs) in modeling optimal route choice in stochastic, timevarying networks. However, taking many variable traffic data and transforming them into optimal route decision is a computational challenge by employing MDPs in real transport ..."
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Abstract—Many exist studies always use Markov decision processes (MDPs) in modeling optimal route choice in stochastic, timevarying networks. However, taking many variable traffic data and transforming them into optimal route decision is a computational challenge by employing MDPs in real transportation networks. In this paper we model finite horizon MDPs using directed hypergraphs. It is shown that the problem of route choice in stochastic, timevarying networks can be formulated as a minimum cost hyperpath problem, and it also can be solved in linear time. We finally demonstrate the significant computational advantages of the introduced methods. Keywords—Markov decision processes (MDPs), stochastic timevarying networks, hypergraphs, route choice. I.