Multi objective optimization

Multi-objective or multi-criteria optimization takes place when more than one objective function is characterized in the optimization problem. In general, these objectives are conflicting, requiring to find a compromise between the possible solutions.

Compromise function approach

A first approach would be combining the different objective functions in a weighted sum:

The choice of the weights w_i determine the importance of each objective function f_i and determines the optimal solution. The constant C is introduced to shift the compromise function, but does not affect the optimal solution.

Hierarchical approach

A second option is choosing one of the objective functions as the main one and rewrite the rest as constrains. Limits can be introduced in those constraints to ensure that the obtained values lie on a certain range.

Pareto optimization