Aggregation of Objective (Criteria) Functions

Let’s have a multi criteria programming problem:


x = (xj)n                   vector of model variables

zk(x)                         k-th criteria function

ck = (ckj)n                        matrix of cost coefficients of k-th criteria function

A = (aij)m.n                     matrix of coefficients of constraints

(bi)m                      RHS vector


All criteria functions can be aggregated into a single one by the following way



Z(x)             aggregated criteria function

vk                 k-th criteria function weight