Incremental Scheduling with Upper and Lowerbound Temporospatial Constraints

Responding quickly and efficiently to dynamic disturbances is a crucial challenge in domains such as manufacturing, aerial and underwater vehicle tasking, 16,18 and health care. In many cases, accurately capturing the complicated dependencies between tasks in these environments requires the use of upper and lowerbound temporal constraints (i.e, deadlines and wait constraints). However, optimally scheduling tasks related by upper and lowerbound temporal constraints is known to be NP-Hard. While exact solution techniques exist to efficiently schedule resources, these techniques are computationally intractable for problems of interest with fifty or more tasks and five agents. Furthermore, techniques that seek to improve scalability often attempt to distribute the scheduling problem amongst the agents, where each agent generates its own schedule. However, when agents must share unary-access resources (e.g., a spatial location that can be occupied by only one agent at a time), these techniques lose their advantage because the problems do not naturally lend themselves to decomposition. As a result, many techniques work by first finding an initial, though possibly infeasible, schedule through solving a relaxed version of the problem, and then repairing the schedule to resolve any constraint violations. Even with the advancement of robotic technology, human operators continue to play a critical role in both the supervision of the scheduling process as well as in direct task execution. Approximate solution techniques exist for scheduling against upper and lowerbound temporal constraints; however, these approaches construct a new schedule from scratch each time the algorithm is called. Assimilating a new schedule into an operators’ mental model every time a disturbance occurs during runtime is a challenging prospect. Gombolay et al. propose a fast, near-optimal solution technique that seeks to minimize the difference in the allocation of tasks to agents between the previous schedule and the revised schedule in response to a dynamic disturbance, but this minimization is balanced with schedule optimality. Researchers have proposed techniques that respond to runtime disturbances by incrementally updating the schedule as the disturbances arise. 9, 19,21 Bartak et al. consider resource constraints, but each task is assumed to be independent. Gallagher et al. develop incremental scheduling heuristics for tasks where task durations are decision variables, and the reward for executing a task is dependent upon its duration and when it is executed. Zweben et al. consider the problem of iteratively repairing a schedule (i.e., reducing the cost of exiting constraint violations) where tasks are related through soft, upper and lowerbound temporal constraints as well as resource constraints. We propose a set of computational techniques for incremental scheduling of multiple agents to complete a set of non-preemptive tasks with hard, upper and lowerbound temporal and spatial constraints. Specifically, we consider the scenario where an initial schedule is given and an additional task must be inserted in the schedule. This new task may have temporal and spatial dependencies with the previously scheduled tasks. We model this scheduling problem using a Simple Temporal Network (STN), where nodes represent scheduling events (i.e., the start and finish times of tasks), and edges represent temporal constraints relating events (e.g., task durations, wait constraints, and deadline constraints). Our investigation differs from previous work in that we are attempting to incrementally schedule non-preemptive tasks with complex dependencies (i.e., hard upper and lowerbound temporal and resource constraints). Work by Zweben et al. serves as a strong basis for comparison, but their approach is iterative in nature and works to change an initially infeasible schedule into a schedule that violates fewer constraints. We directly consider currently feasible schedules and attempt to insert a new task in a way that least increases schedule duration. We organize our work as follows. In Section II, we formulate the problem of incrementally adding a new task to a schedule as a mixed-