Distributed constraint optimization (DCOP or DisCOP) is the distributed analogue to constraint optimization. A DCOP is a problem in which a group of agents must distributedly choose values for a set of variables such that the cost of a set of constraints over the variables is minimized.

Distributed Constraint Satisfaction is a framework for describing a problem in terms of constraints that are known and enforced by distinct participants (agents). The constraints are described on some variables with predefined domains, and have to be assigned to the same values by the different agents.

Problems defined with this framework can be solved by any of the algorithms that are designed for it.

The framework was used under different names in the 1980s. The first known usage with the current name is in 1990.^{[citation needed]}

The main ingredients of a DCOP problem are agents and variables. Importantly, each variable is owned by an agent; this is what makes the problem distributed. Formally, a DCOP is a tuple ${\displaystyle \langle A,V,{\mathfrak {D}},f,\alpha ,\eta \rangle }$, where:

The objective of a DCOP is to have each agent assign values to its associated variables in order to either minimize or maximize ${\displaystyle \eta (f)}$ for a given assignment of the variables.

A value assignment is a pair ${\displaystyle (v_{j},d_{j})}$ where ${\displaystyle d_{j}}$ is an element of the domain ${\displaystyle D_{j}}$.

A partial assignment is a set of value-assignments where each ${\displaystyle v_{j}}$ appears at most once. It is also called a context. This can be thought of as a function mapping variables in the DCOP to their current values:$${\displaystyle t:V\to (D\in {\mathfrak {D}})\cup \{\emptyset \}.}$$ Note that a context is essentially a partial solution and need not contain values for every variable in the problem; therefore, ${\displaystyle t(v_{i})\mapsto \emptyset }$ implies that the agent ${\displaystyle \alpha (v_{i})}$ has not yet assigned a value to variable ${\displaystyle v_{i}}$. Given this representation, the "domain" (that is, the set of input values) of the function f can be thought of as the set of all possible contexts for the DCOP. Therefore, in the remainder of this article we may use the notion of a context (i.e., the ${\displaystyle t}$ function) as an input to the ${\displaystyle f}$ function.