Chance-constrained Scheduling via Conflict-directed Risk Allocation

Temporal uncertainty in large-scale logistics forces one to trade off between lost efficiency through built-in slack and costly replanning when deadlines are missed. Due to the difficulty of reasoning about such likelihoods and consequences, a computational framework is needed to quantify and bound the risk of violating scheduling requirements. This work addresses the chance-constrained scheduling problem, where actions’ durations are modeled probabilistically. Our solution method uses conflict-directed risk allocation to efficiently compute a scheduling policy. The key insight, compared to previous work in probabilistic scheduling, is to decouple the reasoning about temporal and risk constraints. This decomposes the problem into a separate master and subproblem, which can be iteratively solved much quicker. Through a set of simulated car-sharing scenarios, it is empirically shown that conflict-directed risk allocation computes solutions nearly an order of magnitude faster than prior art does, which considers all constraints in a single lump-sum optimization

Solving optimal satisfiability problems through ClA*

Thesis (M.Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2002.Includes bibliographical references (p. 37-38).Real-world applications, such as diagnosis and embedded control, are increasingly being framed as OpSAT problems - problems of finding the best solution that satisfies a formula in propositional state logic. Previous methods, such as Conflict-directed A*, solve OpSAT problems through a weak coupling of A* search, used to generate optimal candidates, and a DPLL-based SAT solver, used to test feasibility. This paper achieves a substantial performance improvement by introducing a tightly coupled approach, Clause-directed A * (CIA *). ClA* simultaneously directs the search towards assignments that are feasible and optimal. First, satisfiability is generalized to state logic by unifying the DPLL satisfiability procedure with forward checking. Second, optimal assignments are found by using A* to guide variable splitting within DPLL. Third, search is directed towards feasible regions of the state space by treating all clauses as conflicts, and by selecting only assignments that entail more clauses. Finally, ClA* climbs towards the optimum by using a variable ordering heuristic that emulates gradient search. Empirical experiments on real-world and randomly-generated instances demonstrate an order of magnitude increase in performance over Conflict-directed A*.by Robert J. Ragno.M.Eng

Sound, Complete, Linear-Space, Best-First Diagnosis Search

Various model-based diagnosis scenarios require the computation of the most preferred fault explanations. Existing algorithms that are sound (i.e., output only actual fault explanations) and complete (i.e., can return all explanations), however, require exponential space to achieve this task. As a remedy, to enable successful diagnosis on memory-restricted devices and for memory-intensive problem cases, we propose RBF-HS, a diagnostic search method based on Korf's well-known RBFS algorithm. RBF-HS can enumerate an arbitrary fixed number of fault explanations in best-first order within linear space bounds, without sacrificing the desirable soundness or completeness properties. Evaluations using real-world diagnosis cases show that RBF-HS, when used to compute minimum-cardinality fault explanations, in most cases saves substantial space (up to 98 %) while requiring only reasonably more or even less time than Reiter's HS-Tree, a commonly used and as generally applicable sound, complete and best-first diagnosis search

Best-first Enumeration Based on Bounding Conflicts, and its Application to Large-scale Hybrid Estimation

With the rise of autonomous systems, there is a need for them to have high levels of robustness and safety. This robustness can be achieved through systems that are self-repairing. Underlying this is the ability to diagnose subtle failures. Likewise, online planners can generate novel responses to exceptional situations. These planners require an accurate estimate of state. Estimation methods based on hybrid discrete/continuous state models have emerged as a method of computing precise state estimates, which can be employed for either diagnosis or planning in hybrid domains. However, existing methods have difficulty scaling to systems with more than a handful of components. Discrete state estimation capabilities can scale to this level by combining best-first enumeration and conflict-directed search. Best-first methods have been developed for hybrid estimation, but the creation of conflict-directed methods has previously been elusive. While conflicts are used to learn from constraint violation, probabilistic hybrid estimation is relatively unconstrained. In this paper we present an approach to hybrid estimation that unifies best-first enumeration and conflict-directed search through the concept of "bounding" conflicts, an extension of conflicts that represent tighter bounds on the cost of regions of the search space. This paper presents a general best-first search and enumeration algorithm based on bounding conflicts (A*BC) and a hybrid estimation method based on this enumeration algorithm. Experiments show that an A*BC powered state estimator produces estimates faster than the current state of the art, particularly on large systems

Fast, approximate state estimation of concurrent probabilistic hybrid automata

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2013.This electronic version was submitted and approved by the author's academic department as part of an electronic thesis pilot project. The certified thesis is available in the Institute Archives and Special Collections.Cataloged from department-submitted PDF version of thesisIncludes bibliographical references (p. 73).It is an undeniable fact that autonomous systems are simultaneously becoming more common place, more complex, and deployed in more inhospitable environments. Examples include smart homes, smart cars, Mars rovers, unmanned aerial vehicles, and autonomous underwater vehicles. A common theme that all of these autonomous systems share is that in order to appropriately control them and prevent mission failure, they must be able to quickly estimate their internal state and the state of the world. A natural representation of many real world systems is to describe them in terms of a mixture of continuous and discrete variables. Unfortunately, hybrid estimation is typically intractable due to the large space of possible assignments to the discrete variables. In this thesis, we investigate how to incorporate conflict directed techniques from the consistency-based, model-based diagnosis community into a hybrid framework that is no longer purely consistency based. We introduce a novel search algorithm, A* with Bounding Conflicts, that uses conflicts to not only record infeasiblilities, but also learn where in the search space the heuristic function provided to the A* search is weak (possibly due to heavy to moderate sensor or process noise). Additionally, we describe a hybrid state estimation algorithm that uses this new search to perform estimation on hybrid discrete/continuous systems.by Eric Timmons.S.M

Enabling fast flexible planning through incremental temporal reasoning

Thesis (M. Eng.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2003.Includes bibliographical references (leaves 70-71).In order for a team of autonomous agents to successfully complete its mission, the agents must be able to quickly re-plan on the fly as unforeseen events arise in the environment. This requires temporally flexible plans that allow the agent to adapt to execution uncertainties by not overcommitting on time constraints, and a continuous planner that replans at any point when the current plan fails. To achieve both of these requirements, planners must have the ability to reason quickly about timing constraints. This thesis provides a fast incremental algorithm, ITC, for determining the temporal consistency of temporally flexible plans. Additionally, the temporal reasoning capability of ITC is able to return the conflict or the nature of the inconsistency to the planner, such that the planner can resolve inconsistencies quickly and intelligently. The ITC algorithm combines the speed of shortest-path algorithms known to network optimization with the spirit of incremental algorithms such as Incremental A* and those used within truth maintenance systems (TMS). The algorithm has been implemented and integrated into a temporal planner, called Kirk. It has demonstrated an order of magnitude speed increase on cooperative air vehicle scenarios.by I-hsiang Shu.M.Eng

Survey of Robot 3D Path Planning Algorithms

Robot 3D (three-dimension) path planning targets for finding an optimal and collision-free path in a 3D workspace while taking into account kinematic constraints (including geometric, physical, and temporal constraints). The purpose of path planning, unlike motion planning which must be taken into consideration of dynamics, is to find a kinematically optimal path with the least time as well as model the environment completely. We discuss the fundamentals of these most successful robot 3D path planning algorithms which have been developed in recent years and concentrate on universally applicable algorithms which can be implemented in aerial robots, ground robots, and underwater robots. This paper classifies all the methods into five categories based on their exploring mechanisms and proposes a category, called multifusion based algorithms. For all these algorithms, they are analyzed from a time efficiency and implementable area perspective. Furthermore a comprehensive applicable analysis for each kind of method is presented after considering their merits and weaknesses

Generalized conflict learning for hybrid discrete/linear optimization

Thesis (S.M.)--Massachusetts Institute of Technology, Dept. of Aeronautics and Astronautics, 2005.Includes bibliographical references (p. 73-76).Conflict-directed search algorithms have formed the core of practical, model-based reasoning systems for the last three decades. In many of these applications there is a series of discrete constraint optimization problems and a conflict-directed search algorithm, which uses conflicts in the forward search step to focus search away from known infeasibilities and towards the optimal solution. In the arena of model-based autonomy, discrete systems, like deep space probes, have given way to more agile systems, such as coordinated vehicle control, which must robustly control their continuous dynamics. Controlling these systems requires optimizing over continuous, as well as discrete variables, using linear and non-linear as well as logical constraints. This paper explores the development of algorithms for solving hybrid discrete/linear optimization problems that use conflicts in the forward search direction, generalizing from the conflict-directed search algorithms of model-based reasoning. We introduce a novel algorithm called Generalized Conflict-directed Branch and Bound (GCD-BB). GCD-BB extends traditional Branch and Bound (B&B), by first constructing conflicts from nodes of the search tree that are found to be infeasible or sub-optimal, and then by using these conflicts to guide the forward search away from known infeasible and sub-optimal states. We evaluate GCD-BB empirically on a range of test problems of coordinated air vehicle control. GCD-BB demonstrates a substantial improvement in performance compared to a traditional B&B algorithm, applied to either disjunctive linear programs or an equivalent binary integer program encoding.by Hui Li.S.M