Distributed Constraint Optimization - Definitions - DCOP

A DCOP can be defined as a tuple, where:

• is a set of agents;
• is a set of variables, ;
• is a set of domains, where each is a finite set containing the values to which its associated variable may be assigned;
• is a function that maps every possible variable assignment to a cost. This function can also be thought of as defining constraints between variables however the variables must not Hermitian;
• is a function mapping variables to their associated agent. implies that it is agent 's responsibility to assign the value of variable . Note that it is not necessarily true that is either an injection or surjection; and
• is an operator that aggregates all of the individual costs for all possible variable assignments. This is usually accomplished through summation: .

The objective of a DCOP is to have each agent assign values to its associated variables in order to either minimize or maximize for a given assignment of the variables.