Coalition formation with spatial and temporal constraints

The coordination of emergency responders and robots to undertake a number of tasks in disaster scenarios is a grand challenge for multi-agent systems. Central to this endeavour is the problem of forming the best teams (coalitions) of responders to perform the various tasks in the area where the disaster has struck. Moreover, these teams may have to form, disband, and reform in different areas of the disaster region. This is because in most cases there will be more tasks than agents. Hence, agents need to schedule themselves to attempt each task in turn. Second, the tasks themselves can be very complex: requiring the agents to work on them for different lengths of time and having deadlines by when they need to be completed. The problem is complicated still further when different coalitions perform tasks with different levels of efficiency. Given all these facets, we define this as The Coalition Formation with Spatial and Temporal constraints problem (CFSTP). We show that this problem is NP-hard—in particular, it contains the wellknown complex combinatorial problem of Team Orienteering as a special case. Based on this, we design a Mixed Integer Program to optimally solve small-scale instances of the CFSTP and develop new anytime heuristics that can, on average, complete 97% of the tasks for large problems (20 agents and 300 tasks). In so doing, our solutions represent the first results for CFSTP.