Resource constrained DCOP solver using virtual variables and conventional pseudo-tree

The Distributed Constraint Optimization Problem (DCOP) is a fundamental formalism for multi-agent cooperation. With DCOPs, the agent states and the relationships between agents are formalized into a constraint optimization problem, which is then solved using distributed cooperative optimization algorithms. In the original DCOP framework, a set of objective functions is employed to represent the relationships between agents. However, constraints for resources that are consumed by teams of agents are not well supported. Resource constraints are necessary to handle practical problems including distributed task scheduling with limited resource availability. A dedicated framework called Resource Constrained DCOP (RCDCOP) has been recently proposed. RCDCOP models objective functions and resource constraints separately. A resource constraint is an n-ary constraint that represents the limit on the number of resources of a given type available to agents. Previous research addressing RCDCOPs employs the Adopt algorithm, which is an efficient solver for DCOPs. An important graph structure for Adopt is the pseudo-tree for constraint networks. A pseudo-tree implies a partial ordering of variables. In this variable ordering, n-ary constrained variables are placed on a single path of the tree. Therefore, resource constraints that have large arity augment the depth of the pseudo-tree. This also reduces the parallelism, and therefore the efficiency of Adopt. In this paper we propose another version of the Adopt algorithm for RCDCOP using a pseudo-tree that is generated ignoring resource constraints. The key ideas of our work are as follows: (i) The pseudo-tree is generated ignoring resource constraints. (ii) Virtual variables are introduced, representing the usage of resources. These virtual variables are used to share resources among subtrees. (iii) The addition of virtual variables increases the search space. To reduce this problem, the search is pruned using the bounds defined by the resource constraints. These ideas are used to extend Adopt. The proposed method reduces the previous limitations in the construction of RCDCOP pseudo-trees. The efficiency of our technique depends on the class of problems being considered, and we describe the obtained experimental results.