Divide and Conquer in Multi-Agent Planning

In this paper, we suggest an approach to multiagent planning that contains heuristic elements. Our method makes use of subgoals, and derived sub-plans, to construct a global plan. Agents solve their individual sub-plans, which are then merged into a global plan. The suggested approach may reduce overall planning time and derives a plan that approximates the optimal global plan that would have been derived by a central planner, given those original subgoals. We consider two different scenarios. The first involves a group of agents with a common goal. The second considers how agents can interleave planning and execution when planning towards a common, though dynamic, goal. ecomposition Reducing Complexity The complexity of a planning process is measured by the time (and space) consumed. Let b be the branching factor of the planning problem (the average number of new states that can be generated from a given state by applying a single operator), and let cb denote the depth of the problem (the optimal path from the initial state to the goal state). The time complexity of the planning problem is then G(bd) (Korf 1987). In a multi-agent environment, where each agent can carry out each of the possible operators (possibly with differing costs), the complexity may be even worse. A centralized planner should consider assigning each operator to each one of the n agents. Thus, finding an optimal plan becomes O(n x b)d. However, if the global goal can be decomposed into n subgoals ((gr, . . . , gn)) the time complexity may be reduced significantly. Let bi and di denote respectively the branching factor and depth of the optimal plan that achieves gi . Then, as shown by Korf in (Korf 1987), if the subgoals are independent or serializable,’ the central multi-agent planning time complexity can be reduced to Ci((n x bi)di), where bi M i and di M $. ‘A set of subg oals is said to be independent if the plans that achieve them do not interact. If the subgoals are seriulizable then there exists an ordering among them such that achieving any subgoal in the series does not violate any of its preceding subgoals. Jeffrey S. Rosenschein Institute of Computer Science The Hebrew University Jerusalem, Israel jeff@cs.huji.ac.il This phenomenon of reduced complexity due to the division of the search space can be exploited most naturally in a multi-agent environment. The underlying idea is to assign to each agent a subgoal and let that agent construct the plan that achieves it. Since agents plan in parallel, planning time is further reduced to max;(n x bi)di. Moreover, if each agent is to generate its plan according to its own view (assuming that the available operators are common knowledge) then the complexity becomes mw(bi)d’. The global plan can then be constructed out of local plans that are based upon the agents’ local knowledge. Unfortunately, unless the subgoals are independent or serial, the plans that achieve the set of subgoals interfere, and conflicts (or redundant actions) may arise and need to be resolved. In this paper we suggest a heuristic approach to multi-agent planning that exploits this phenomenon of decomposed search space. The essential idea is that the individual sub-plans serve to derive a heuristic function that is used to guide the search for the global plan. This global search is then done in the space of world states which is pruned using the A* algorithm. Our method makes use of pre-existing subgoals. These subgoals are not necessarily independent, nor are they necessarily serial. The separate agents’ sub-plans, each derived separately and in parallel, are ultimately merged into a unified, valid global plan. The suggested approach may reduce overall planning time while deriving the optimal global plan that would have been derived, given those original subgoals. In multi-agent environments this approach also removes the need for a central planner that has global knowledge of the domain and of the agents involved. Our scenario involves a group 4. = (al, . . . , a,} of n agents. These agents are to achieve a global goal G. The global goal, G, has been divided into n subgoals W 1,***9 G,}), and formulated as a subgoal planning problem (i.e., the interrelationship among subgoals has been specified). The agents communicate as they construct a global plan.