Co-Optimizating Multi-Agent Placement with Task Assignment and Scheduling
چکیده
To enable large-scale multi-agent coordination under temporal and spatial constraints, we formulate it as a multi-level optimization problem and develop a multi-abstraction search approach for cooptimizing agent placement with task assignment and scheduling. This approach begins with a highly abstract agent placement problem and the rapid computation of an initial solution, which is then improved upon using a hill climbing algorithm for a less abstract problem; finally, the solution is finetuned within the original problem space. Empirical results demonstrate that this multi-abstraction approach significantly outperforms a conventional hill climbing algorithm and an approximate mixedinteger linear programming approach. Introduction Task assignment and scheduling are central problems for multi-agent systems, as they determine which agent should execute which task and at what time in order to optimize system performance. This multi-agent coordination problem with temporal and spatial constraints can be formulated as a mixed integer linear programming (MILP) [Brucker, 2001] and is NP-Hard [Bertsimas and Weismantel, 2005]. Various approaches have been proposed to address this challenging problem [Hooker, 2009; Korsah et al., 2012; Gombolay et al., 2013]; however, these existing approaches do not scale well for many practical problems, which usually incorporate more than 20 agents and 200 tasks. Fortunately, many large-scale problems commonly possess a nearly-decomposable structure, where agents can be grouped according to their capabilities and tasks can be clustered by their spatial or temporal constraints so that constraints between tasks in different clusters can be aggregated and modeled as high-level constraints between clusters. For example, in a production-line factory as shown in Figure 1, agents (e.g., robots and human workers) are grouped by their specialties and tasks are naturally clustered according to the workplaces at which they are located. For the sake of simplicity, we use workplaces to refer to task clusters. Constraints between tasks in different workplaces are modeled as precedence constraints between workplaces. To exploit such nearly-decomposable structure and enable large-scale multi-agent coordination, this paper abstracts a high-level multi-agent placement problem, which determines how many agents of each type are allocated to each workplace in order to optimize overall system performance. The solution to this problem is used to decompose a large multi-agent system into a group of smaller subsystems, for which the task assignment and scheduling problem has exponentially less complexity and can be solved using existing approaches. However, this multi-agent placement problem is challenging because how agents are placed to workplaces depends on how tasks of each workplace are assigned and scheduled to them. The contribution of this paper is twofold. First, we formulate multi-agent coordination as an integrated, multi-level optimization problem. This problem consists of agent placement (i.e., how agents are allocated to workplaces), task assignment (i.e., how tasks are assigned to the agents at each workplace), and task scheduling (i.e, how an agent performs its tasks). Second, we develop a multi-abstraction search approach (MASA) for co-optimizing multi-agent placement with task assignment and scheduling. MASA consists of three phases. It first begins with a highly abstract agent placement problem and rapidly computes an initial solution. This solution is then improved upon using a hill climbing algorithm by considering how task assignment at each workplace affects agent placement. Finally, MASA fine-tunes the improved agent placement solution by considering the effects from both task assignment and scheduling. Search in abstract problems is much faster, as it considers much fewer variables and constraints. In addition, abstract problems may have smoother search space surfaces with less local optima. Therefore, the first two phases prepare a suitable initial solution for the final phase and allow it to avoid inferior local optima, converge to a better solution and improve the search speed. Experimental results indicate that MASA yields a more than 15% and 25% reduction in makespan compared with an MILP-based approximate approach and a conventional hill climbing algorithm, respectively. MASA also improves the convergence speed by more than 10% on average over the conventional hill climbing. Multi-Level Optimization Problem This section illustrates multi-agent coordination with temporal and spatial constraints in the manufacturing domain and Proceedings of the Twenty-Fifth International Joint Conference on Artificial Intelligence (IJCAI-16)