A general formal framework for multi-agent meeting problems

The multi-agent meeting (MAM) problem asks for a meeting location for multiple heterogeneous agents such that the agents can get together within a given time or budget, possibly using different modes of transportation, subject to some constraints and preferences to visit specific locations on their ways to the meeting location. We mathematically model MAM as a graph problem, prove its intractability, and introduce a novel formal method to solve it and its variations using logic-based AI methods. We experimentally evaluate our approach with artificial benchmarks randomly generated over a grid, and show its real world applicability with instances generated over maps of Istanbul and Hong Kong.