Anytime Heuristic and Monte Carlo Methods for Large-Scale Simultaneous Coalition Structure Generation and Assignment

Optimal simultaneous coalition structure generation and assignment is computationally hard. The state-of-the-art can only compute solutions to problems with severely limited input sizes, and no effective approximation algorithms that are guaranteed to yield high-quality solutions are expected to exist. Real-world optimization problems, however, are often characterized by large-scale inputs and the need for generating feasible solutions of high quality in limited time. In light of this, and to make it possible to generate better feasible solutions for difficult large-scale problems efficiently, we present and benchmark several different anytime algorithms that use general-purpose heuristics and Monte Carlo techniques to guide search. We evaluate our methods using synthetic problem sets of varying distribution and complexity. Our results show that the presented algorithms are superior to previous methods at quickly generating near-optimal solutions for small-scale problems, and greatly superior for efficiently finding high-quality solutions for large-scale problems. For example, for problems with a thousand agents and values generated with a uniform distribution, our best approach generates solutions 99.5% of the expected optimal within seconds. For these problems, the state-of-the-art solvers fail to find any feasible solutions at all.