we consider biobjective shortest path problems in networks with fuzzy arc lengths. considering the available studies for single objective shortest path problems in fuzzy networks, using a distance function for comparison of fuzzy numbers, we propose three approaches for solving the biobjective prob- lems. the rst and second approaches are extensions of the labeling method to solve the sing...

In this paper, I propose a new methodology to find the bicriteria shortest path from the source to the sink node of a network of queues under the steady-state condition. I assume the number of servers in each service station settled in a node of the network is either one or infinity. Moreover, the arc lengths are mutually independent random variables. First, I propose a method to transform each...

We extend the traditional framework of POMDPs to model resource consumption inducing a hard constraint on the behaviour of the model. Resource levels increase and decrease with transitions, and the hard constraint requires that the level remains positive in all steps. We present an algorithm for solving POMDPs with resource levels, developing on existing POMDP solvers. Our second contribution i...

In this paper, we tackle the problem of risk-averse route planning in a transportation network with time-dependent and stochastic costs. To solve this problem, we propose an adaptation of the A* algorithm that accommodates any risk measure or decision criterion that is monotonic with first-order stochastic dominance. We also present a case study of our algorithm on the Manhattan, NYC, transport...

We consider a stochastic extension of the loop-free shortest path problem with adversarial rewards. In this episodic Markov decision problem an agent traverses through an acyclic graph with random transitions: at each step of an episode the agent chooses an action, receives some reward, and arrives at a random next state, where the reward and the distribution of the next state depend on the act...

Research in efficient methods for solving infinite-horizon MDPs has so far concentrated primarily on discounted MDPs and the more general stochastic shortest path problems (SSPs). These are MDPs with 1) an optimal value function V ∗ that is the unique solution of Bellman equation and 2) optimal policies that are the greedy policies w.r.t. V ∗. This paper’s main contribution is the description o...

The importance of a node in a directed graph can be measured by its PageRank. The PageRank of a node is used in a number of application contexts – including ranking websites – and can be interpreted as the average portion of time spent at the node by an infinite random walk. We consider the problem of maximizing the PageRank of a node by selecting some of the edges from a set of edges that are ...

We consider partially observable Markov decision processes (POMDPs) with a set of target states and positive integer costs associated with every transition. The traditional optimization objective (stochastic shortest path) asks to minimize the expected total cost until the target set is reached. We extend the traditional framework of POMDPs to model energy consumption, which represents a hard c...

We consider online learning in a special class of episodic Markovian decision processes, namely, loop-free stochastic shortest path problems. In this problem, an agent has to traverse through a finite directed acyclic graph with random transitions while maximizing the obtained rewards along the way. We assume that the reward function can change arbitrarily between consecutive episodes, and is e...

We consider a stochastic shortest path problem with associative criteria in which for each node of a graph we choose a probability distribution over the set of successor nodes so as to reach a given target node optimally. We formulate such a problem as an associative Markov decision processes. We show that an optimal value function is a unique solution to an optimality equation and find an opti...