Constrained Task Assignment and Scheduling on Networks of Arbitrary Topology.

Abstract

This dissertation develops a framework to address centralized and distributed constrained task assignment and task scheduling problems. This framework is used to prove properties of these problems that can be exploited, develop effective solution algorithms, and to prove important properties such as correctness, completeness and optimality. The centralized task assignment and task scheduling problem treated here is expressed as a vehicle routing problem with the goal of optimizing mission time subject to mission constraints on task precedence and agent capability. The algorithm developed to solve this problem is able to coordinate vehicle (agent) timing for task completion. This class of problems is NP-hard and analytical guarantees on solution quality are often unavailable. This dissertation develops a technique for determining solution quality that can be used on a large class of problems and does not rely on traditional analytical guarantees. For distributed problems several agents must communicate to collectively solve a distributed task assignment and task scheduling problem. The distributed task assignment and task scheduling algorithms developed here allow for the optimization of constrained military missions in situations where the communication network may be incomplete and only locally known. Two problems are developed. The distributed task assignment problem incorporates communication constraints that must be satisfied; this is the Communication-Constrained Distributed Assignment Problem. A novel distributed assignment algorithm, the Stochastic Bidding Algorithm, solves this problem. The algorithm is correct, probabilistically complete, and has linear average-case time complexity. The distributed task scheduling problem addressed here is to minimize mission time subject to arbitrary predicate mission constraints; this is the Minimum-time Arbitrarily-constrained Distributed Scheduling Problem. The Optimal Distributed Non-sequential Backtracking Algorithm solves this problem. The algorithm is correct, complete, outputs time optimal schedules, and has low average-case time complexity. Separation of the task assignment and task scheduling problems is exploited here to ameliorate the effects of an incomplete communication network. The mission-modeling conditions that allow this and the benefits gained are discussed in detail. It is shown that the distributed task assignment and task scheduling algorithms developed here can operate concurrently and maintain their correctness, completeness, and optimality properties.