Plan-Coordination Mechanisms and the Price of Autonomy

Abstract

Abstract. Task-based planning problems for multi-agent systems require multiple agents to find a joint plan for a constrained set of tasks. Typically, each agent receives a subset of tasks to complete. Due to task interdependencies, such task allocations induce interdependencies between agents as well. These interdependencies will prevent the agents from making a plan for their subset of tasks independently from each other, since the combination of such autonomously constructed plans will most probably result in conflicting plans. Therefore, a plan-coordination mechanism is needed to guarantee a conflict-free globally feasible plan. In this paper, we first present a brief overview of the main results achieved on plan coordination for autonomous planning agents, distinguishing between problems associated with deciding whether a coordination mechanism is necessary, designing an arbitrary coordination mechanism, and designing an optimal (minimal) coordination mechanism. After finding out that designing an optimal coordination mechanism is difficult, we concentrate on an algorithm that is able to find a (non-trivial) coordination mechanism that is not always minimal. We then discuss some subclasses of plan-coordination instances where this algorithm performs very badly, but also some class of instances where a nearly optimal coordination mechanism is returned. Hereafter, we discuss the price of autonomy as a measure to determine the loss of (global) performance of a system due to the use of a coordination mechanism, and we offer a case study on multi-modal transportation where a coordination mechanism can be designed that offers minimal restrictions and guarantee nearly optimal performance. We will also place the use of these coordination mechanisms in a more general perspective, claiming that they can be used to reuse existing (single) agent software in a complex multi-agent environment. Finally, we briefly discuss some recent extensions of our coordination framework dealing with temporal planning aspects.

Plan decoupling of agents with qualitatively constrained tasks

“…There, a multi-modal transportation task needs to be executed by transportation agents where a number of precedence constraints hold on the subtasks. Besides optimal coordination sets, it turns out that the quality of the resulting joint plans are comparable to the ones that are a result of centralised planning while taking much less time [17]. It can be shown that there exists no polynomial algorithm for either a cooperative or a selfish multi-agent system solving this multi-modal transportation task with an approximation ratio < 10 9 unless some generally accepted conjecture in complexity theory is violated [17].…”

“…The plan-decoupling problem for moderatelycoupled agents has been studied thoroughly in previous work [2,17,18].…”

“…In previous work [2,16,17,18], PDP for moderately-coupled agents, as well as some of its variants, has been studied quite extensively. It was shown that this problem is Σ p 2 -complete in general [18].…”

“…There exists a simple polynomial-time approximation algorithm that succeeds in finding a sufficient-but not necessarily minimum-coordination set for moderately-coupled agents [17]. This algorithm uses the fact that the time points are partially ordered by a precedence relation, which is necessarily acyclic.…”

“…After at most depth(T ) ≤ |T | iterations, all time points have been accepted exactly once as prerequisite-free. For each agent A i , we now have a set of disjoint subsets T It can easily be shown that, although not creating a minimum coordination set, the resulting set Γ is sufficient for plan decoupling [17]. A description of this depth-partitioning algorithm, delivering the coordination sets Γ i , is given in Algorithm 1.…”