Exact Approaches to the Multi-agent Collective Construction Problem

Abstract

The multi-agent collective construction problem tasks agents to construct any given three-dimensional structure on a grid by repositioning blocks. Agents are required to also use the blocks to build ramps in order to access the higher levels necessary to construct the building, and then remove the ramps upon completion of the building. This paper presents a mixed integer linear programming model and a constraint programming model of the problem, either of which can exactly optimize the problem, as previous efforts have only considered heuristic approaches. The two models are evaluated on several small instances with a large number of agents. The plans clearly show the swarm behavior of the agents. The mixed integer linear programming model is able to find optimal solutions faster than the constraint programming model and even some existing incomplete methods due to its highly-exploitable network flow substructures.