Coordinating Self-interested Planning Agents

Abstract

We consider planning problems where a number of non-cooperative agents have to work on a joint problem. Such problems consist in completing a set of interdependent, hierarchically ordered tasks. Each agent is assigned a subset of tasks to perform for which it has to construct a plan. Since the agents are non-cooperative, they insist on planning independently and do not want to revise their individual plans when the joint plan has to be assembled from the individual plans. We present a general formal framework to study some computational aspects of this non-cooperative coordination problem and we establish some complexity results to identify some of the factors that contribute to the complexity of this problem. Finally, we illustrate our approach with an application to coordination in multi-modal logistic planning.

Coordination by design and the price of autonomy

“…Agent A 2 can process tasks t 3 in the interval [4,7] while starting t 4 in [2,2]. Similarly, agent A 3 can process task t 5 in the interval [8,10] with task t 6 starting in the interval [7,7] and task t 7 in [9,9]. Notice here that any schedule produced by the agents such that these intervals are honored will always lead to a global makespan of 11.…”

“…Such protocols require simple forms of problem-specific information exchange before the agents can start planning, and they guarantee that if the agents adhere to the protocol, then the individual plans can easily be assembled into a joint plan for the overall task. Examples of such coordination by design strategies are the Temporal Decoupling Method by Hunsberger [27,28] and the pre-planning coordination method discussed in [10]. In these methods, additional constraints are imposed on a set of tasks given to a collection of agents to ensure that they can plan autonomously, while still ensuring that the plan of every agent will satisfy the original set of constraints.…”

“…In these methods, additional constraints are imposed on a set of tasks given to a collection of agents to ensure that they can plan autonomously, while still ensuring that the plan of every agent will satisfy the original set of constraints. Especially in [10], the main focus is on the complexity issues associated with finding a minimal set of additional constraints to implement such a coordination by design approach. Finally, viewing coordination by design from a broader perspective, two other relevant lines of research on coordination by design should be mentioned.…”

Framework and Complexity Results for Coordinating Non-cooperative Planning Agents

“…In [14], it was shown that every fixed task instance can be transformed into a coordinated one by adding a minimum number of intra-agent constraints ∆ = n i=1 ∆ i such that the resulting instance ({T i } n i=1 , ≺ ∪ ∆), is a coordinated instance. In Figure 2, the reader might check that ∆ = {t 7 ≺ t 2 , t 6 ≺ t 3 , t 5 ≺ t 4 } is such a set of additional constraints that turns the fixed task instance into a coordinated one.…”

“…We study three variants of the plan-coordination problem and some factors that influence their complexity. Some results have been published in [14]; the results about the complexity of coordination when the number of agents is kept fixed are new.…”