Stochastic Vehicle Routing with Recourse

We study the classic Vehicle Routing Problem in the setting of stochastic optimization with recourse. StochVRP is a two-stage optimization problem, where demand is satisfied using two routes: fixed and recourse. The fixed route is computed using only a demand distribution. Then after observing the demand instantiations, a recourse route is computed -- but costs here become more expensive by a factor lambda. We present an O(log^2 n log(n lambda))-approximation algorithm for this stochastic routing problem, under arbitrary distributions. The main idea in this result is relating StochVRP to a special case of submodular orienteering, called knapsack rank-function orienteering. We also give a better approximation ratio for knapsack rank-function orienteering than what follows from prior work. Finally, we provide a Unique Games Conjecture based omega(1) hardness of approximation for StochVRP, even on star-like metrics on which our algorithm achieves a logarithmic approximation.Comment: 20 Pages, 1 figure Revision corrects the statement and proof of Theorem 1.

Tour recommendation for groups

Consider a group of people who are visiting a major touristic city, such as NY, Paris, or Rome. It is reasonable to assume that each member of the group has his or her own interests or preferences about places to visit, which in general may differ from those of other members. Still, people almost always want to hang out together and so the following question naturally arises: What is the best tour that the group could perform together in the city? This problem underpins several challenges, ranging from understanding people’s expected attitudes towards potential points of interest, to modeling and providing good and viable solutions. Formulating this problem is challenging because of multiple competing objectives. For example, making the entire group as happy as possible in general conflicts with the objective that no member becomes disappointed. In this paper, we address the algorithmic implications of the above problem, by providing various formulations that take into account the overall group as well as the individual satisfaction and the length of the tour. We then study the computational complexity of these formulations, we provide effective and efficient practical algorithms, and, finally, we evaluate them on datasets constructed from real city data

Informative Path Planning in Random Fields via Mixed Integer Programming

We present a new mixed integer formulation for the discrete informative path planning problem in random fields. The objective is to compute a budget constrained path while collecting measurements whose linear estimate results in minimum error over a finite set of prediction locations. The problem is known to be NP-hard. However, we strive to compute optimal solutions by leveraging advances in mixed integer optimization. Our approach is based on expanding the search space so we optimize not only over the collected measurement subset, but also over the class of all linear estimators. This allows us to formulate a mixed integer quadratic program that is convex in the continuous variables. The formulations are general and are not restricted to any covariance structure of the field. In simulations, we demonstrate the effectiveness of our approach over previous branch and bound algorithms

Planning Algorithms for Multi-Robot Active Perception

A fundamental task of robotic systems is to use on-board sensors and perception algorithms to understand high-level semantic properties of an environment. These semantic properties may include a map of the environment, the presence of objects, or the parameters of a dynamic field. Observations are highly viewpoint dependent and, thus, the performance of perception algorithms can be improved by planning the motion of the robots to obtain high-value observations. This motivates the problem of active perception, where the goal is to plan the motion of robots to improve perception performance. This fundamental problem is central to many robotics applications, including environmental monitoring, planetary exploration, and precision agriculture. The core contribution of this thesis is a suite of planning algorithms for multi-robot active perception. These algorithms are designed to improve system-level performance on many fronts: online and anytime planning, addressing uncertainty, optimising over a long time horizon, decentralised coordination, robustness to unreliable communication, predicting plans of other agents, and exploiting characteristics of perception models. We first propose the decentralised Monte Carlo tree search algorithm as a generally-applicable, decentralised algorithm for multi-robot planning. We then present a self-organising map algorithm designed to find paths that maximally observe points of interest. Finally, we consider the problem of mission monitoring, where a team of robots monitor the progress of a robotic mission. A spatiotemporal optimal stopping algorithm is proposed and a generalisation for decentralised monitoring. Experimental results are presented for a range of scenarios, such as marine operations and object recognition. Our analytical and empirical results demonstrate theoretically-interesting and practically-relevant properties that support the use of the approaches in practice