An Anytime Algorithm for Chance Constrained Stochastic Shortest Path Problems and Its Application to Aircraft Routing

Hong, Sungkweon; Lee, Sang Uk; Huang, Xin; Khonji, Majid; Alyassi, Rashid; Williams, Brian

doi:10.1109/icra48506.2021.9561229

Cited by 14 publications

(8 citation statements)

References 29 publications

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“…1 provides a pictorial illustration of the SSP And-Or (search) graph. Not that unlike And-Or search trees obtained by history enumeration algorithms (see, e.g., [13]), with such representation, a node may have multiple parents, leading to significant reduction in the search space. The objective function and the constraint's left hand side can be written recursively using Bellman equation as…”

Section: Problem Definitionmentioning

confidence: 99%

“…However, due to partial observability, these methods require an enumeration of histories, making the solution space exponentially large with respect to the planning horizon. To speed up the computation, [13] provides an anytime algorithm using a Lagrangian relaxation method for CC-SSP and CC-POMDP that returns feasible sub-optimal solutions and gradually improves the solution's optimality when sufficient time is permitted. Unfortunately, the solution space is represented as an And-Or tree of all possible history trajectories, causing the algorithm to slow down as we increase the planning horizon.…”

Section: Introductionmentioning

confidence: 99%

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A Fully Polynomial Time Approximation Scheme for Fixed-Horizon Constrained Stochastic Shortest Path Problem under Local Transitions

Khonji¹

2022

Preprint

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The fixed-horizon constrained stochastic shortest path problem (C-SSP) is a formalism for planning in stochastic environments under certain operating constraints. Chance-Constrained SSP (CC-SSP) is a variant that allows bounding the probability of constraint violation, which is desired in many safety-critical applications. This work considers an important variant of (C)C-SSP under local transition, capturing a broad class of SSP problems where state reachability exhibit a certain locality. Only a constant number of states can share some subsequent states. (C)C-SSP under local transition is NP-Hard even for a planning horizon of two. In this work, we propose a fully polynomial-time approximation scheme for (C)C-SSP that computes (near) optimal deterministic policies. Such an algorithm is the best approximation algorithm attainable in theory.

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Section: Problem Definitionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A Fully Polynomial Time Approximation Scheme for Fixed-Horizon Constrained Stochastic Shortest Path Problem under Local Transitions

Khonji¹

2022

Preprint

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“…In this section, we introduce a recently developed anytime algorithm for C-SSPs in [13] which we use as a subroutine in our proposed method. The algorithm has two stages where the first stage finds a Lagrangian dual solution of a C-SSP and then the second stage incrementally closes a duality gap, if there is any.…”

Section: B Anytime Algorithm For C-sspsmentioning

confidence: 99%

“…Note that the Lagrangian function value and incumbent cost at any time set lower and upper bounds on the optimal cost of the C-SSP, respectively. We refer to [13] for the details of the anytime algorithm.…”

Section: B Anytime Algorithm For C-sspsmentioning

confidence: 99%

Hierarchical Constrained Stochastic Shortest Path Planning via Cost Budget Allocation

Hong¹,

Williams²

2022

Preprint

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Stochastic sequential decision making often requires hierarchical structure in the problem where each highlevel action should be further planned with primitive states and actions. In addition, many real-world applications require a plan that satisfies constraints on the secondary costs such as risk measure or fuel consumption. In this paper, we propose a hierarchical constrained stochastic shortest path problem (HC-SSP) that meets those two crucial requirements in a single framework. Although HC-SSP provides a useful framework to model such planning requirements in many real-world applications, the resulting problem has high complexity and makes it difficult to find an optimal solution fast which prevents user from applying it to real-time and risk-sensitive applications. To address this problem, we present an algorithm that iteratively allocates cost budget to lower level planning problems based on branch-and-bound scheme to find a feasible solution fast and incrementally update the incumbent solution. We demonstrate the proposed algorithm in an evacuation scenario and prove the advantage over a state-of-the-art mathematical programming based approach.

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“…More concretely, the contributions and roadmap of this paper can be summarized as follows: Through rigorous analytical scrutiny, the probabilistic constraints in MCC-SSP are proved reducible to equivalent linear ones in ILP (Theorem 1). More importantly, the ILP formulation features polynomial number of variables and constraints when the number of agents per interaction is small, thereby improving upon the stateof-the-art designed for the single agent case [16], [17]. 3) Drawing on MCC-SSP formalism, Sec.…”

Section: Introductionmentioning

confidence: 99%

Multi-Agent Chance-Constrained Stochastic Shortest Path with Application to Risk-Aware Intelligent Intersection

Khonji¹,

Alyassi²,

Merkt³

et al. 2022

Preprint

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In transportation networks, where traffic lights have traditionally been used for vehicle coordination, intersections act as natural bottlenecks. A formidable challenge for existing automated intersections lies in detecting and reasoning about uncertainty from the operating environment and human-driven vehicles. In this paper, we propose a risk-aware intelligent intersection system for autonomous vehicles (AVs) as well as human-driven vehicles (HVs). We cast the problem as a novel class of Multi-agent Chance-Constrained Stochastic Shortest Path (MCC-SSP) problems and devise an exact Integer Linear Programming (ILP) formulation that is scalable in the number of agents' interaction points (e.g., potential collision points at the intersection). In particular, when the number of agents within an interaction point is small, which is often the case in intersections, the ILP has a polynomial number of variables and constraints. To further improve the running time performance, we show that the collision risk computation can be performed offline. Additionally, a trajectory optimization workflow is provided to generate risk-aware trajectories for any given intersection. The proposed framework is implemented in CARLA simulator and evaluated under a fully autonomous intersection with AVs only as well as in a hybrid setup with a signalized intersection for HVs and an intelligent scheme for AVs. As verified via simulations, the featured approach improves intersection's efficiency by up to 200% while also conforming to the specified tunable risk threshold.

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An Anytime Algorithm for Chance Constrained Stochastic Shortest Path Problems and Its Application to Aircraft Routing

Cited by 14 publications

References 29 publications

A Fully Polynomial Time Approximation Scheme for Fixed-Horizon Constrained Stochastic Shortest Path Problem under Local Transitions

A Fully Polynomial Time Approximation Scheme for Fixed-Horizon Constrained Stochastic Shortest Path Problem under Local Transitions

Hierarchical Constrained Stochastic Shortest Path Planning via Cost Budget Allocation

Multi-Agent Chance-Constrained Stochastic Shortest Path with Application to Risk-Aware Intelligent Intersection

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