# Multiobjective optimization

Provides an overview of multiobjective optimization.

Optimization problems with multiple linear objective functions can be specified in CPLEX. To solve them, CPLEX offers a mixture of blended and lexicographic (or hierarchical) optimization.

A **blended objective** consists of simply the linear combination of several objectives with
given weights.

A **lexicographic objective** supposes that an order has been given among the various
objective functions. This order allows you to define a lexicographic order among solutions: a
solution is lexicographically smaller than another one if, in the first objective where they differ
(following the order), it is smaller. An optimal solution is then one that is lexicographically
minimal (or maximal depending on the optimization sense).

CPLEX can combine both blended and lexicographic objectives in the same optimization problem.

For a list of examples using multiobjective optimization, see Examples for multiobjective optimization.

The other topics in this section describe in more detail how to work with multiple objectives in CPLEX.