In this work we investigate opportunities offered by telematics and analytics to enable better informed, and more integrated, collaborative management decisions on construction sites. We focus on efficient refuelling of assets across construction sites. More specifically, we develop decision support models that, by leveraging data supplied by different assets, schedule refuelling operations by minimising the distance travelled by the bowser truck as well as fuel shortages. Motivated by a practical case study elicited in the context of a project we recently conducted at the C610 Systemwide Crossrail site, we introduce the Dynamic Bowser Routing Problem. In this problem the decision maker aims to dynamically refuel, by dispatching a bowser truck, a set of assets which consume fuel and whose location changes over time; the goal is to ensure that assets do not run out of fuel and that the bowser covers the minimum possible distance. We investigate deterministic and stochastic variants of this problem. To tackle deterministic variants, we introduce and contrast a bilinear programming model and a mixed-integer linear programming model. To tackle stochastic variants, by employing a new general purpose software library for stochastic modeling, we introduce a complete stochastic dynamic programming model as well as a novel heuristic we named "sample waning." We consider two stochastic variants of the problem in which asset locations or asset fuel consumptions are uncertain. We demonstrate the effectiveness of our approaches in the context of an extensive computational study designed around information and data collected at C610 Systemwide as well as supplied by our project partners.
Moving our attention to robotics, recently investigated stochastic collection and replenishment of agents motivated by use cases in mining and agricultural settings in which a replenishment agent transports a resource between a centralised replenishment point to agents using the resource in the field. They employ Gaussian approximations to quickly calculate the risk-weighted cost of a schedule; a branch and bound search then exploits these predictions to minimise the downtime of the agents. Previous works in this area mainly focused on scheduling the actions of the dedicated replenishment agent from a short-term and deterministic angle. Scenario 2 [see][p. 59] citeulike:14544091 present similarities to our setup; this emphasises the practical relevance of our study. However, our modeling and solution framework has the advantage of relying solely on MILP modeling and not on ad-hoc algorithms to predict future asset resource levels. Moreover, the discussion in @cite_2 assumes that uncertain parameters and variables are normally distributed, while our approach based on piecewise linearisation of loss functions does not require this assumption and can accommodate any distribution.
@cite_2
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The multi-armed bandit (MAB) problem features the classical tradeoff between exploration and exploitation. The input specifies several stochastic arms which evolve with each pull, and the goal is to maximize the expected reward after a fixed budget of pulls. The celebrated work of , surveyed in [8], presumes a condition on the arms called the martingale assumption. In [9], A. obtained an LP-based 1 48-approximation for the problem with the martingale assumption removed. We improve the algorithm to a 4 27-approximation, with simpler analysis. Our algorithm also generalizes to the case of MAB superprocesses with (stochastic) multi-period actions. This generalization captures the framework introduced by Guha and Munagala in [11], and yields new results for their budgeted learning problems. Also, we obtain a (1 2 -- e)-approximation for the variant of MAB where preemption (playing an arm, switching to another arm, then coming back to the first arm) is not allowed. This contains the stochastic knapsack problem of Dean, Goemans, and Vondrak in [6] with correlated rewards, where we are given a knapsack of fixed size, and a set of jobs each with a joint distribution for its size and reward. The actual size and reward of a job can only be discovered in real-time as it is being scheduled, and the objective is to maximize expected reward before the knapsack size is exhausted. Our (1 2 -- e)-approximation improves the 1 16 and 1 8 approximations in [9] for correlated stochastic knapsack with cancellation and no cancellation, respectively, providing to our knowledge the first tight algorithm for these problems that matches the integrality gap of 2. We sample probabilities from an exponential-sized dynamic programming solution, whose existence is guaranteed by an LP projection argument. We hope this technique can also be applied to other dynamic programming problems which can be projected down onto a small LP. In this paper, we investigate the problem of maximizing the throughput over a finite-horizon time period for a sensor network with energy replenishment. The finite-horizon problem is important and challenging because it necessitates optimizing metrics over the short term rather than metrics that are averaged over a long period of time. Unlike the infinite-horizon problem, the fact that inefficiencies cannot be made to vanish to infinitesimally small values, means that the finite-horizon problem requires more delicate control. The finite-horizon throughput optimization problem can be formulated as a convex optimization problem, but turns out to be highly complex. The complexity is brought about by the “time coupling property,” which implies that current decisions can influence future performance. To address this problem, we employ a three-step approach. First, we focus on the throughput maximization problem for a single node with renewable energy assuming that the replenishment rate profile for the entire finite-horizon period is known in advance. An energy allocation scheme that is equivalent to computing a shortest path in a simply-connected space is developed and proven to be optimal. We then relax the assumption that the future replenishment profile is known and develop an online algorithm. The online algorithm guarantees a fraction of the optimal throughput. Motivated by these results, we propose a low-complexity heuristic distributed scheme, called NetOnline, in a rechargeable sensor network. We prove that this heuristic scheme is optimal under homogeneous replenishment profiles. Further, in more general settings, we show via simulations that NetOnline significantly outperforms a state-of-the-art infinite-horizon based scheme, and for certain configurations using data collected from a testbed sensor network, it achieves empirical performance close to optimal. This thesis addresses the question of planning under uncertainty within a time-dependent changing environment. Original motivation for this work came from the problem of building an autonomous agent able to coordinate with its uncertain environment; this environment being composed of other agents communicating their intentions or non-controllable processes for which some discrete-event model is available. We investigate several approaches for modeling continuous time-dependency in the framework of Markov Decision Processes (MDPs), leading us to a definition of Temporal Markov Decision Problems. Then our approach focuses on two separate paradigms. First, we investigate time-dependent problems as processes and describe them through the formalism of Time-dependent MDPs (TMDPs). We extend the existing results concerning optimality equations and present a new Value Iteration algorithm based on piecewise polynomial function representations in order to solve a more general class of TMDPs. This paves the way to a more general discussion on parametric actions in hybrid state and action spaces MDPs with continuous time. In a second time, we investigate the option of separately modeling the concurrent contributions of exogenous events. This approach of modeling leads to the use of Generalized Semi-Markov Decision Processes (GSMDP). We establish a link between the general framework of Discrete Events Systems Specification (DEVS) and the formalism of GSMDP, allowing us to build sound discrete-event compatible simulators. Then we introduce a simulation-based Policy Iteration approach for explicit-event Temporal Markov Decision Problems. This algorithmic contribution brings together results from simulation theory, forward search in MDPs, and statistical learning theory. The implicit-event approach was tested on a specific version of the Mars rover planning problem and on a drone patrol mission planning problem while the explicit-event approach was evaluated on a subway network control problem. Many Stochastic Optimal Control (SOC) approaches rely on samples to either obtain an estimate of the value function or a linearisation of the underlying system model. However, these approaches typically neglect the fact that the accuracy of the policy update depends on the closeness of the resulting trajectory distribution to these samples. The greedy operator does not consider such closeness constraint to the samples. Hence, the greedy operator can lead to oscillations or even instabilities in the policy updates. Such undesired behaviour is likely to result in an inferior performance of the estimated policy. We reuse inspiration from the reinforcement learning community and relax the greedy operator used in SOC with an information theoretic bound that limits the ‘distance’ of two subsequent trajectory distributions in a policy update. The introduced bound ensures a smooth and stable policy update. Our method is also well suited for model-based reinforcement learning, where we estimate the system dynamics model from data. As this model is likely to be inaccurate, it might be dangerous to exploit the model greedily. Instead, our bound ensures that we generate new data in the vicinity of the current data, such that we can improve our estimate of the system dynamics model. We show that our approach outperforms several state of the art approaches on challenging simulated robot control tasks.